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Evolutionary stability of auction and supply chain contracting: An analysis based on disintermediation in the Indian tea supply chains
European Journal of Operational Research 207 (2010) 531–538
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European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor
Innovative Applications of O.R.
Evolutionary stability of auction and supply chain contracting: An analysis based on disintermediation in the Indian tea supply chains S. Dutta a, S.P. Sarmah b,*, S.K. Goyal c a
Proof and Experimental Establishment, DRDO, Chandipur 756025, India Department of Industrial Engineering and Management, IIT, Kharagpur 721302, India c Department of Decision Sciences and MIS, Concordia University, Montreal, Canada b
a r t i c l e
i n f o
Article history: Received 23 July 2008 Accepted 30 April 2010 Available online 12 May 2010 Keywords: Auction Bargaining Supply chain contract Disintermediation Indian tea industry
a b s t r a c t The purpose of this paper is to show that evolutionary stable market equilibrium is achievable through complete disintermediation of auctioneers if the option of bargaining-based supply chain contracting exists. The paper analyzes the evolutionary dynamics of a market that caters both the scopes of auction-intermediation and supply chain contracting to a set of homogeneous buyers and sellers. The motivation of this work developed from the contradiction between the theoretical framework of Lu and McAfee (1996) that identifies auction to be evolutionary stable over bargaining and the real instance of sustained disintermediation of auctioneers in the world’s largest tea industry in India where supply chain contracting is the other option of trading. 2010 Elsevier B.V. All rights reserved.
1. Introduction and literature review Transactions in markets take place through mechanisms like auction and bargaining. A simple two-stage supply chain forms whenever a mechanism realizes a trade by which a pair of buyer and seller exchanges information, funds and goods with each other. However, most of the contemporary supply chain networks are characterized by business entities intermediating between buyers and sellers. These entities are popularly known as supply chain intermediaries. Wu (2004) categorized them as transactional and informational intermediaries. Transactional intermediaries increase supply chain efficiency at the transactional level, whereas informational intermediaries add value at the tactical and the strategic levels. Presence of non-negative incentive for distorting private information allures buyers and sellers to report disfigured estimates of their actual willingness-to-pay levels and opportunity costs, eventually creating information asymmetry that catalyzes adverse partner selection and inflates the risk of inefficient market matching. Wu (2004) reported that the informational intermediaries mainly provide three functions: (i) implementation of coordination mechanisms to reduce adverse selection, (ii) creation of trusted institutions to trim down the necessity of direct negotiation and (iii) price discovery by synthesizing dispersed information of trading agents’ reservation values. Effectiveness of these functions counts on how aptly the intermediary mechanism imple* Corresponding author. Tel.: +91 3222 283734(O)/283735(R). E-mail address: [email protected] (S.P. Sarmah). 0377-2217/$ - see front matter 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.04.035
ments incentive compatibility (IC) and individual rationality (IR). IC is the constraint mechanism imparted on the revelation principle of a transaction mechanism to ensure trading agents’ truthfulness and IR is the constraint mechanism to ensure trading agents’ utilities not to be lesser than their reservation values; see Mas-Colell et al. (1995). Auctioneers are considered to be informational intermediaries who devise price discovery mechanisms to minimize overall market inefficiency through reduction of uncertainty of adverse matching. A powerful auctioneer performs efficient price discovery by implementing IC and thus ensures the optimum strategies of all buyers and sellers as to disclose actual willingnessto-pay levels and opportunity costs. This leads to the realization of ex post efficient market matching. Dutta and Sarmah (2009) studied impacts of market matching patterns on overall market efficiency and reported that, in spite of all transactions being Paretoefficient and the market matching pattern being ex post efficient the overall surplus of all transaction channels may be less than that of a Pareto efficiently matched market. This implies that there could be forms of transaction mechanisms that might prove to be more efficient than auction. If an auctioneer fails to raise the market efficiency to a level that could be achieved by such a mechanism then IR generates risks of disintermediation of the auctioneer from all supply chains in which she operates. Therefore, auctioneers should improvise suitable need-based coordination mechanisms for improving channel surplus. Gellman (1996) reported that the term disintermediation was first used to describe the trend for small investors to cut loose from traditional intermediaries by means of direct investments in
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financial instruments like money market funds. The term became popular in the literature of supply chain management (SCM) only in the recent years. Hoffman (1995) used the term in SCM to describe cutting out of the middlemen by direct transactions and attributed it as the basis of B2B e-commerce. Pinto (2000a,b) described disintermediation as the elimination of an intermediary from a business process owing to the cost of intermediation exceeding the value added by the intermediary. Rapid emergence of new technologies in today’s highly competitive global business has prompted many companies to analyze costs of all links in their supply chains and to indulge in continual exploration of the opportunities for competitive price cuts through direct transactions with their downstream customers bypassing the conventional intermediaries. Several mainstream companies from different business domains have already bridged direct links with their customers with the aid of information technology (IT). For instance, Amazon.com launched a web-based system for selling its items directly to the customers without any form of intermediation. Gunasekaran and Nagi (2004) provided an exhaustive citation on the applications of IT in the SCM paradigm. Though the common wisdom suggests that direct transaction shrinks costs of original sales-links, it is inappropriate to consider the phenomenon of supply chain disintermediation to be obvious and inevitable. If an agent succeeds to devise a transaction mechanism to make a supply chain more efficient than it is in direct transaction then she finds room in that supply chain as an intermediary. Bailey (1998) justified viability of both intermediation and disintermediation hypotheses under different market conditions. Shunk et al. (2007) augmented this with the idea of reintermediation of disintermediated supply chains. Lu and McAfee (1996) studied a market model of homogeneous buyers and sellers having the option to choose one of the trading mechanisms between auction and bargaining. The model depicted evolutionary stability of auction over bargaining. The depiction contradicts the hypothesis of disintermediation of auctioneers in a market with both auction and supply chain contracts since the basic mechanism of such contracts is postulated to be pairwise bargaining. Contrary to the framework of Lu and McAfee (1996), quite a few markets are found where traders spontaneously bypass auction-intermediation and engage in supply chain contracting. For instance, the Indian tea market has been witnessing a steady decline in the volume of auction trading over the last 20 years because of the traders’ increasing affinity with supply chain contracts. The contradiction between the model of Lu and McAfee (1996) and the phenomenon of disintermediation of auctioneers in the Indian tea supply chains has motivated us for the present work. In this paper, we follow the idea of Lu and McAfee (1996) to analyze a market model of homogeneous buyers and sellers that offers both the options of auction-intermediation and supply chain contracting. The intermediated market of our model is analogous to the auction market of Lu and McAfee (1996). The crux of our model is the incorporation of a supply chain contract-based disintermediated market in place of the bargaining market of Lu and McAfee (1996). Though the core transaction mechanism of the disintermediated market is nothing but pairwise bargaining, its matching technology is entirely different from that of the bargaining market of Lu and McAfee (1996). The setting of the bargaining market of Lu and McAfee (1996) does not completely replicate the complexity of the matching technology of contract-based disintermediated markets since choice of partners is not random in disintermediated markets. While Upton and Fuller (2003) attributed trading agents’ trustworthiness to the success of contract-based supply chains, Stringer (2006) identified the scope of information exchange at the operational level as the key to it. Whom to trust and how much information to share is a vital issue in this setting. Gurnani and Mengze (2006) discussed how this issue plays a deci-
sive role in determining efficiencies of supply chain contracts. Keeping in line with these views we propose an identity-based dynamic matching technology for disintermediated market. Hence we show that two unique evolutionary stable steady-state market equilibria exist – one at complete auction-intermediation and the other at complete disintermediation. Further, we show the existence of a unique locally stable steady-state market equilibrium that realizes both auction-intermediation and disintermediation simultaneously. It is found that the selection of the type of the market equilibrium is controlled by the proposed matching technology of the disintermediated market. To test the plausibility of this matching technology we build a hypothesis based on data from the Indian tea industry. The rest of the article is organized as follows. Section 2 presents the model. Section 3 analyzes aptness of the proposed matching technology. Section 4 provides managerial implications of our findings and Section 5 presents conclusions.
2. The model The overall market setting comprises of two separate markets. One is an intermediated market where buyers and sellers trade through free-of-cost auctioneers and the other one is a disintermediated market.
2.1. The market 2.1.1. Goods A single indivisible good is traded for some quantity of a divisible good, i.e., money.
2.1.2. Time Time is discrete and is indexed by non-negative integers, t = 0, 1, 2, . . .
2.1.3. Economic agents The economic agents are buyers and sellers. Each seller enters the market with one unit of the good and each buyer enters with exactly one unit of money. All sellers are homogeneous since the goods they sell are identical and their valuations of the good are equal. All sellers’ use values are fixed at zero. All buyers are also homogeneous since their consumption values are identical and are set at unity. All buyers and sellers have identical bargaining power. At the beginning of each period new agents enter the market and join the existing agents. At time t, there exist Nt sellers and htNt buyers in the market where, Nt is a very large positive integer and 0 < ht < +1. Each agent trades at most once and after trading she exits from the market. The agent who fails to trade in the current period remains in the market till she trades in a later period. There is no restriction on the exited agents to reenter as new entrants in a later period. New entrants are free to choose between the auction-intermediated and the disintermediated markets, although once entered in a certain type of market they are assumed to be prohibited from switching to the other type of market till their exit. The assumption is helpful for analyzing evolutionary dynamics of market and can be found valid in the situation that allows very few agents to switch from one market to the other. We also assume that all buyers and sellers discount values one period ahead by the common discount factor d, 0 < d < 1, which remains constant over time. Expected utilities of buyers and sellers at time t are U it and V it where, i = I, D indicates the types of markets they are in (I for the intermediated and D for the disintermediated market).
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2.1.4. Matching In the intermediated market the auctioneer performs the role of searching and matching by implementing an auction mechanism. The proportions of buyers and sellers in the intermediated market at time t are 1 xt and 1 yt where 0 6 xt 6 1, 0 6 yt 6 1. At the beginning of each period all buyers of the intermediated market are randomly spread over the sellers of that market in such a fashion that a buyer can match with at most one seller while a seller can be visited by many buyers. Number of buyers visiting each seller in this market is a binomial random variable with parameters htNt(1 xt) and Nt(1 yt). Nt being very large, the distribution is approximated as a Poisson distribution with parameter ht(1 xt)/ (1 yt). Once a seller matches with a buyer, the seller and the buyer trade and leave the market at the end of the period. The unmatched agents remain in the market for taking part in another auction in the next period. The proportions of buyers and sellers in the disintermediated market at time t are xt and yt respectively. Unlike intermediated market trading agents in this market individually search for potential partners to negotiate supply chain contracts through pairwise bargaining. Thus, in any period an agent in this market can match with at most one agent of the opposite type. The matched pair of agents trade in the current period and leave the market after the period ends. If an agent fails to search a partner or experiences a negotiation breakdown then she remains unmatched and waits to get matched in the next period. Each agent’s individual estimation about her probability to match with another agent at a particular time is based on two factors – the matching agents’ identities and the index of the period. For a SB seller S and a buyer B, we use the variables bSB t ; 0 6 bt 6 1 and BS BS at ; 0 6 at 6 1 to represent their respective estimated probabilities for matching with each other at time t. The estimate bSB is t the decision variable chosen by the seller S based on her own preferences for matching and her best belief on buyer B’s preferences for matching. Similarly, the estimate aBS t is the decision variable chosen by the buyer B based on her own preferences and her best belief on seller S’s preferences for matching. An individual agent’s belief set is not only controlled by the industry-wide common knowledge about trading agents’ preferences but also by her best belief generated from the private knowledge acquired over time. SB The difference in the estimates of aBS t and bt is attributed to the fact that the best beliefs of the agents B and S may not be identical. SB Rather the estimates aBS t and bt are endogenous decision variables of individual agents and are not set by any external mechanism. The conception of the identity-based dynamic market matching conforms to the following information system. 2.1.5. Information Each agent recognizes identities of the other agents in the disintermediated market and holds information of the indices of time. Each agent possesses past experiences of trading if any and also some information about the matches formed by the other agents.
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the trading agents as surplus over their individual reservation values. Buyers’ consumption values and sellers’ use values being set at 1 and 0 respectively one can express the relation between reservation values and gain from trade of one unit good as, dU Itþ1 þ dV Itþ1 þ GIt ¼ 1 0. i.e.:
GIt ¼ 1 dU Itþ1 dV Itþ1 :
ð1Þ
Expected utility of a buyer in this market depends on two mutually exclusive possibilities: first the buyer may find no other buyer in the market in which her optimal strategy would be to bid at the seller’s reservation value and secure a payoff equal to 1 dV Itþ1 and second there may be at least another competing buyer in the market in which all buyers would contest to win the opportunity to trade. The contest can be identified as a Bertrand game that discloses actual information of the buyers’ willingness-to-pay levels and ensures a payoff of dU Itþ1 for all buyers. The number of buyers participating in an auction follows Poisson distribution with parameter ht(1 xt)/(1 yt), i.e.:
PðK ¼ kÞ ¼ eht ð1xt Þ=ð1yt Þ ðht ð1 xt Þ=ð1 yt ÞÞk =k! for; k ¼ 0; 1; 2; . .. ð2Þ Hence the probability of occurrence of the first case in which a buyer does not find any other buyer is P(K = 0) i.e., eht ð1xt Þ=ð1yt Þ . Similarly the probability of occurrence of the second case in which a buyer finds at least another buyer is 1 P(K = 0), i.e., 1 eht ð1xt Þ=ð1yt Þ . So expected utility of a buyer in the intermediated market at time t is as follows:
U It ¼ eht ð1xt Þ=ð1yt Þ 1 dV Itþ1 þ 1 eht ð1xt Þ=ð1yt Þ dU Itþ1 ¼ eht ð1xt Þ=ð1yt Þ GIt þ dU Itþ1 :
ð3Þ
Expected utility of a seller depends on three mutually exclusive possibilities: first there may be no buyer with probability P(K = 0) i.e., eht ð1xt Þ=ð1yt Þ , second there may be only one buyer with probability P(K = 1) i.e., eht ð1xt Þ=ð1yt Þ ðht ð1 xt Þ=ð1 yt ÞÞ and third there may be more than one buyer with probability 1 P(K = 0) P(K = 1), i.e., 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ. The first and the second cases ensure the seller a payoff equal to her reservation value dV Itþ1 and the third case is characterized by the Bertrand game contest of the buyers ensuring the seller a payoff of 1 dU Itþ1 . So expected utility of a seller in this market at time t is as follows:
V It ¼ eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞdV Itþ1
þ 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ 1 dU Itþ1 ¼ 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ GIt þ dV Itþ1 : ð4Þ
2.3. The disintermediated market 2.2. The auction-intermediated market In the auction-intermediated market, the buyers bid according to their individual willingness-to-pay levels for buying good from a seller in presence of an auctioneer who ensures opportunity of trading to the highest bidder provided the reservation value of the seller is secured. Reservation value can be considered as the point at which a trading agent remains indifferent between trading and not trading and thus it can be identified as the current value of trading in the next period which at time t is identical to the agent’s expected utility of trading at time t + 1 discounted by the factor d. Hence dV Itþ1 and dU Itþ1 are the respective reservation values of the sellers and the buyers in the intermediated market at time t. If a trade yields a non-negative gain GIt then it would be split between
The concepts of reservation value and gain in the disintermediated market are analogous to that in the intermediated market. So the reservation values of buyers and sellers in this market are dU Dtþ1 and dV Dtþ1 and the gain from trade of one unit good is as follows:
GDt ¼ 1 dU Dtþ1 dV Dtþ1 :
ð5Þ
Trades in this market are regulated by supply chain contracts, the core negotiation mechanism of which is an assortment of channel coordination and pairwise bargaining. Nash (1950) described the players of the bargaining problem as two individuals who have the opportunity to collaborate for mutual benefits in more than one way. The framework of Nash bargaining solution complies with the mechanism of supply chain contracting and can be used to
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estimate the negotiable unit price Pt . As per the Nash’s rationale, the optimum gain occurs as the product of negotiators’ payoffs over their reservation values are maximized. For a negotiable unit price Pt, the respective payoffs for seller and buyer over their reservation values are Pt dV Dtþ1 and 1 P t dU Dtþ1 . Thus, Pt is the solution of arg max Pt dV Dtþ1 1 Pt dU Dtþ1 , i.e.: Pt
Pt ¼ 1=2 dU Dtþ1 dV Dtþ1 =2 ¼ GDt =2 þ dV Dtþ1
I
U I ¼ ehð1xÞ=ð1yÞG =ð1 dÞ; I
¼ 1 GDt =2 dU Dtþ1 :
ð6Þ
It can be checked that the maximum value of P t is 1 when, dU Dtþ1 ¼ 0; dV Dtþ1 ¼ 1 and the minimum value of Pt is 0 when, dU Dtþ1 ¼ 1; dV Dtþ1 ¼ 0. Pairwise bargaining allows an agent to negotiate with only one agent of the opposite type in each period. Consider the interaction between the seller S and the buyer B (we will see afterwards that analysis of interaction of a particular pair of agents does not disturb the generality of the market equilibria). Expected utility of the buyer B in this interaction is based on two mutually exclusive possibilities: first the buyer may expect to match with the seller S with probability aBS t and secure a payoff of 1 P t and second the buyer may expect a negotiation breakdown with probability 1 aBS and secure her reservation value dU Dtþ1 . So expected utility t of the buyer B in the disintermediated market at time t is as follows:
D BS BS U Dt ¼ aBS GDt =2 þ dU Dtþ1 : t 1 P t þ 1 at dU tþ1 ¼ at
ð7Þ
Similarly the seller S faces two mutually exclusive possibilities: first she may expect to match with the buyer B with probability bSB t and acquire a payoff of Pt and second she may expect the negotia tion to break down with probability 1 bSB securing her a payoff t equal to her reservation value dV Dtþ1 . So expected utility of the seller S in the disintermediated market at time t is as follows:
V Dt
¼
bSB t Pt
þ 1
bSB t
dV Dtþ1
ket fails to come out of the equilibrium ever since it is attained. Similar arguments hold good for the equilibrium at complete disintermediation. Apart from (x, y) = (0, 0) and (x, y) = (1, 1), any other steady-state market equilibrium can be represented as (xt, yt) = (x, y) " (t = 0, 1, 2, 3, . . . ) where, U it ¼ U i ; V it ¼ V i and subsequently, Git ¼ Gi 8i 2 fI; Dg. This situation simplifies Eqs. (3), (4), (7) and, (8) to the followings:
¼
bSB t
GDt =2 þ dV Dtþ1 :
ð8Þ
hð1xÞ=ð1yÞ
V ¼ 1e
ð1 þ hð1 xÞ=ð1 yÞÞ GI =ð1 dÞ;
ð9Þ ð10Þ
U D ¼ aBS GD =2ð1 dÞ;
ð11Þ
V D ¼ bSB GD =2ð1 dÞ:
ð12Þ
The necessary condition for existence of any such equilibrium requires expected utilities of the new entrants to be equal in both intermediated and disintermediated markets, i.e., UI = UD, VI = VD and hence GI = GD. Using Eqs. (9)–(12) along with GI = GD, the condition reduces to the followings for 0 < x < 1 and 0 < y < 1:
ehð1xÞ=ð1yÞ ¼ aBS =2;
ð13Þ
and
1 ehð1xÞ=ð1yÞ ð1 þ hð1 xÞ=ð1 yÞÞ ¼ bSB =2:
ð14Þ
Now we propose the possibility of existence of a third type steadystate market equilibrium. Proposition 2. {(x, y)j0 < x < 1,0 < y < 1} represents the third type steady-state market equilibrium, independent of agents’ identities, lying on the segment of a concave curve f(a, b) = a a ln (a/ 2) + b 2 = 0 enclosed in the unit square bounded by the lines a = 0, a = 1, b = 0 and b = 1 (henceforth this square will be referred as ab unit square), where a and b represent the respective estimated matching probabilities of buyers and sellers. The third type steady-state market equilibrium {(x, y)j0 < x < 1, 0 < y < 1} represents a situation that makes the market neither completely intermediated nor completely disintermediated (see Fig. 1).
2.4. Equilibrium 2.5. Evolutionary stability of equilibrium First consider a situation in which the ratio of buyers to sellers is constant over time, i.e., ht = h " (t = 0, 1, 2, 3, . . . ). This restricts the concept of market evolution to the evolution of distributions of buyers and sellers in the intermediated and the disintermediated markets. Now a steady-state market equilibrium can be specified as the situation that keeps the proportions of buyers and sellers in the intermediated and the disintermediated markets constant over time, i.e., (xt, yt) = (x, y) " (t = 0, 1, 2, 3, . . . ) where, (x, y) 2 {(x, y)j0 6 x 6 1,0 6 y 6 1}. The following proposition illustrates the existence of two such steady-state market equilibria.
As the third type steady-state market equilibrium is independent of agents’ identities, for the analysis of stability of market equilibria we consider all agents to be anonymous without loss of any detail. Therefore, bSB and aBS are replaced by bt and at, t t respectively. The notion of evolutionary stability of market equilibrium represents a situation in which the new entrants expect their utilities in the next period to be equal to that in the current period (i.e., U itþ1 ¼ U it and, V itþ1 ¼ V it 8i 2 fI; DgÞ while the ratio of buyers to sellers remains fixed over time (i.e., ht = h). Hence the Eqs. (3), (4), (7) and (8) reduce to the followings:
Proposition 1. For 0 < h < +1, the complete auction-intermediation, i.e., (x, y) = (0, 0) and the complete disintermediation, i.e., (x, y) = (1, 1) are the two steady-state market equilibria. The proof of this proposition is not presented here since it is identical to the first proposition of Lu and McAfee (1996). Proofs of all other propositions, lemmas and corollaries can be found in the Supplementary material at the EJOR website. Proposition 1 suggests two types of steady-state market equilibria, (x, y) = (0, 0), i.e., complete auction-intermediation and (x, y) = (1, 1), i.e., complete disintermediation. These two steady-state equilibria are self-reinforcing, i.e., after attaining either of them the market fails to come out of that. For example, the equilibrium at complete auction-intermediation compels new entrants to join auction due to absence of partners in the disintermediated market. Thus the mar-
(0,1) β
β =1
(1,1) f (α , β ) = 0
ME α =1
α =0
(0,0)
β =0
ME: The third type steady-state market equilibrium
(1,0) α
Fig. 1. The third type steady-state market equilibrium enclosed inside the ab unit square.
S. Dutta et al. / European Journal of Operational Research 207 (2010) 531–538
U It ¼ ehð1xt Þ=ð1yt Þ GIt =ð1 dÞ;
ð15Þ
V It ¼ U Dt ¼ V Dt ¼
ð17Þ
1e
hð1xt Þ=ð1yt Þ
ð1 þ hð1 xt Þ=ð1 yt ÞÞ GIt =ð1 dÞ;
ð16Þ
at GDt =2ð1 dÞ; bt GDt =2ð1 dÞ:
ð18Þ U itþ1
U it
Under the notion of evolutionary stability, i.e., ¼ and V itþ1 ¼ V it 8i 2 fI; Dg, gains from trade of one unit of good in the intermediated and the disintermediated markets are derived in the following using the Eqs. (15)–(18) along with the Eqs. (1) and (5):
GIt ¼ ð1 dÞ= 1 dehð1xt Þ=ð1yt Þ hð1 xt Þ=ð1 yt Þ ;
ð19Þ
GDt ¼ 2ð1 dÞ=ð2ð1 dÞ þ dðat þ bt ÞÞ:
ð20Þ
For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, we define the equilibrium curve for buyers at time t as the locus of the point that represents identical expected utilities of buyers in the auction-intermediated and the disintermediated markets in that period of time, i.e., U It ¼ U Dt . Similarly, for {(xt, yt)j0 < xt < 1, 0 < yt < 1}, we define the equilibrium curve for sellers at time t as the locus of the point that represents identical expected utilities of sellers in the auction-intermediated and the disintermediated markets in that period of time, i.e., V It ¼ V Dt . The following lemma identifies the equilibrium curves for buyers and sellers (see Fig. 2). Lemma 1 (a) For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, the equilibrium curve for buyers is a segment of a straight line enclosed in the ab unit square. The segment makes a positive intercept on the side b = 0 and no intercept on the side a = 0. (b) For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, the equilibrium curve for sellers is a segment of a straight line enclosed in the ab unit square. The segment makes no intercept on the side b = 0 and a positive intercept on the side a = 0. The following lemma depicts the relationship between the third type steady-state market equilibrium and the equilibrium curves for buyers and sellers. Lemma 2. The third type steady-state market equilibrium realizes on the point of intersection of the equilibrium curves for buyers and sellers. β =1
(0,1)
β α =0
(1,1)
SE
SE: The equilibrium curve for sellers BE: The equilibrium curve for buyers
(0,0)
β =0
(1,0 )
α
Fig. 2. The equilibrium curves for buyers and sellers.
(0,1)
(1,1)
β =1 1
2
β
SE α =0 3
Lemma 3 (a) In the regions 2 and 3, expected utility of a buyer is higher in the intermediated market than that in the disintermediated one, i.e., U It > U Dt and, in the regions 4 and 1, expected utility of a buyer is lower in the intermediated market than that in the disintermediated one, i.e., U It < U Dt . (b) In the regions 1 and 2, expected utility of a seller is lower in the intermediated market than that in the disintermediated one, i.e., V It < V Dt and, in the regions 3 and 4, expected utility of a seller is higher in the intermediated market than that in the disintermediated one, i.e., V It > V Dt . According to the standard evolutionary dynamics (Nachbar, 1990), new agents estimate the current matching probabilities and choose the market offering higher utilities because they assume incorrectly that current payoffs will remain throughout all periods. Thus, the proportion of agents increases in the market offering higher utility and decreases in the market offering lower utility. In the region 1, U It < U Dt and V It < V Dt , all new agents choose the disintermediated market resulting in an increase of the proportion of agents in the disintermediated market (xt+1 > xt, yt+1 > yt). In the region 2, U It > U Dt and V It < V Dt , all new buyers choose the intermediated market while all new sellers choose the disintermediated one. This decreases the proportion of buyers and increases the proportion of sellers in the disintermediated market (xt+1 < xt, yt+1 > yt). In the region 3, U It > U Dt and V It > V Dt , all new agents choose the intermediated market resulting in a decrease of the proportion of agents in the disintermediated market (xt+1 < xt, yt+1 < yt). In the region 4, U It < U Dt and V It > V Dt , all new buyers choose the disintermediated market while all new sellers choose the intermediated one. This increases the proportion of buyers and decreases the proportion of sellers in the disintermediated market (xt+1 > xt, yt+1 < yt).
ME
Now we describe the type of stability of the market equilibria in the following.
α =1
BE
β =0
(a) The points in the region 2 follow clockwise dynamic rotational paths heading towards the equilibrium curve for buyers for f(a, b) > 0 and towards the equilibrium curve for sellers for f(a, b) < 0. (b) The points in the region 4 follow anti-clockwise dynamic rotational paths heading towards the equilibrium curve for sellers for f(a, b) > 0 and towards the equilibrium curve for buyers for f(a, b) < 0.
Proposition 3
4
(0,0)
Fig. 3 shows that the equilibrium curves for buyers and sellers intersect each other on the curve representing the third type steady-state market equilibrium inside the ab unit square and thus divide the ab unit square in four distinct regions namely 1, 2, 3 and 4. The following lemma illustrates variations of trading agents’ expected utilities over these regions.
Lemma 4
α =1 BE
535
α
(1,0)
Fig. 3. The third type steady-state market equilibrium on the point of intersection of the equilibrium curves for buyers and sellers.
(a) For f(a, b) < 0, complete auction-intermediation is the unique evolutionary stable steady-state market equilibrium. (b) For f(a, b) > 0, complete disintermediation is the unique evolutionary stable steady-state market equilibrium. (c) For f(a, b) = 0, the market attains a unique locally stable steadystate equilibrium by simultaneous realization of both auctionintermediation and disintermediation.
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Proposition 3 suggests that there are only two unique evolutionary stable steady-state market equilibria, one at complete auction-intermediation for f(a, b) < 0 and the other at complete disintermediation for f(a, b) > 0. The equilibrium at f(a, b) = 0 is a unique locally stable market equilibrium that realizes both auction-intermediation and disintermediation simultaneously. Fig. 3 suggests that the agents’ estimated matching probabilities, a and b, are less for f(a, b) < 0 compared to that for f(a, b) > 0. Therefore, if for some reason the values of agents’ estimated matching probabilities become very high, the evolutionary dynamics of the market lead to complete disintermediation of the auctioneers. The following corollaries provide limiting values of the agents’ estimated matching probabilities for ensuring complete intermediation and complete disintermediation of the auctioneers. Corollary 1. The necessary condition for complete disintermediation of the auctioneers is that the estimated matching probabilities of all the sellers and all the buyers should exceed 0.307 and 0.373, respectively. However this condition is not sufficient. Corollary 2. The necessary and sufficient condition for complete auction-intermediation is that the estimated matching probabilities of all the sellers and all the buyers should be below 0.307 and 0.373, respectively. Our model states that the market matching technology of the disintermediated market plays a decisive role in determining the type of market equilibrium. In the following we discuss the rationale behind the assumption of identity-based dynamic matching technology and the information system of the disintermediated market. 3. Discussion Auction ensures efficient market matching by curbing direct exchange of information between trading agents. On the contrary, disintermediated markets furnish the scope of direct information exchange, albeit such information is prone to distortion in case of incentive incompatible negotiations. Krause et al. (2006) studied the effects of integrative and distributive bargaining stances on the outcomes of negotiations. In spite of the common wisdom that higher degree of integration begets higher volume of channel surplus, agents may refrain from tactical and strategic integration for retaining individual bargaining powers. However, integration at the operational level is quite common. Stringer (2006) reported that information exchange with the customers proves to be vital for the manufacturers to design and modify production processes. Similar advantages can also be found at the buyers’ ends. Absence of intermediaries in supply chain contracts raises question about fairness in division of surplus generated due to integration and thus invokes the notion of trust in SCM. Taylor and Plambeck (2007) portrayed agents’ mutual trust as the conducive factor for generation of relational contracts which are far from legal constraints and base purely on integration. Cohen et al. (2003) and Johnson (2003) identified widespread existence of such integration in the market of semiconductors where the buyers share forecasted demand in advance with their suppliers as soft orders for efficient production planning. Tierney (2005) cited a relevant case of integration from the automobile industry – the Japanese automakers having a history of good relationship with suppliers got a competitive edge over Ford that faced the difficulty to build capacity owing to weak relationships with its hybrid-transmission suppliers. A pair of buyer and seller may not take integrative stance at their very first course of negotiation, but rather conceal information even at the operational level due to lack of mutual trust arising
from asymmetric beliefs on each others’ potentials. Once the negotiation consolidates to a contract, in course of trading, both the agents gather firsthand information to grow private knowledge about each other, thus reducing asymmetry in beliefs and generating mutual trust. This outlines the rationale behind the information system of our model. High level of trust generates a bond of relationship between the pair of agents and motivates them to adopt integrative stance, thus increasing channel surplus through better coordination. Existence of such trust-based bond of supply chain agents is quite common in today’s business and works up to the following hypothesis. 3.1. Hypothesis H1: Formation of a disintermediated supply chain between a buyer and a seller at the current period increases the likelihood of formation of a similar supply chain between the same pair of agents in the subsequent period. Assumptions of the identity-based dynamic matching technology and the information system of the disintermediated market are inherent in the premise of the hypothesis. 3.2. Test of hypothesis 3.2.1. Methodology In order to test the hypothesis H1 we perform a statistical analysis on a set of data of 21 years (1985–2005) extracted from the data bank of Indian tea industry compiled by Ghosh and Singh Deo (2006). The set of data consisting of 11 variables (except ‘Year’) is provided as Table S1 in the Supplementary material at the EJOR website. First four variables, namely E: number of estates, A: area under tea (hector), Y: annual yield (ton/hector) and V: annual production volume (ton) are related to the agricultural aspects while the next five variables, namely VEXP: annual export volume (ton), V IIND : annual trading volume at the Indian auction (ton), DpIIND : annual percentage increase in the Indian auction price, V IUK : annual trading volume in the UK auction (ton) and DpIUK : annual percentage increase in the UK auction price are related to the market economy. Among these nine variables, the two modified variables DpIIND and DpIUK are introduced to avoid variations of currency values over the long span of 21 years. For example: DpIIND for the year 1995 Mu=kg in Indian auction in 1995 Mu=kg in Indian auction in 1994 ; ¼ Mu=kg in Indian auction in 1995 100
where Mu refers to monetary unit. The last two variables KI and KD1 , which are also modified ones, act as significant indicators of disintermediation. KI represents the fraction of annual production auction-intermedi traded through ated supply chains, i.e., KI ¼ V IIND þ V IUK =V, and acts as a measure of intermediation. KD1 represents the one-year lag value of the fraction of annual production traded through disintermediated supply chains, i.e., KD1 ¼ 1 previous year’s KI , and acts as a measure of one-year lag value of the extent of disintermediation. The trend of KI fitted as a quadratic curve over the span of 21 years (1985–2005) is shown in Fig. 4. While fitting the curve the year 1985 is taken as t = 1. The overall descending trend of the curve illustrates sustained disintermediation limiting the fraction of annual volume of auction trading from nearly 80% down to 65% over 21 years. The relatively flat trend near the end of the curve indicates some kind of a market equilibrium, which probably represents the unique locally stable steady-state market equilibrium of our model.
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4. Managerial implications
0.8 Accuracy Measures
ΛI
537
Mean Absolute Percentage Error: 3.03597 Mean Absolute Deviation: 0.0182190 Mean Squared Deviation: 0.000529890
0.7
Λ I = 0 .832638 − 0 .032 × t + 0 .000861 × t 2
0.6
0.5 t=0
t=20
t=10
t (years) Fig. 4. The decreasing trend of auction-intermediation in the Indian tea market.
3.2.2. Data analysis and results For testing the hypothesis H1 we analyze the data in two stages. Stage 1: A stepwise regression analysis is conducted over the response variable KI and the predictor variables E; A; Y; V; V EXP ; V IIND ; DpIIND ; V IUK ; DpIUK and KD1 , with a type I error a = 0.001 (see Table S2 in the Supplementary material at the EJOR website). Value of a is instrumental in determining the F-statistic to ensure entry of variables in the regression model. The analysis is based on the data for the years 1986–2004 since the values of the variables E, A, Y are missing for 2005 and the value of KD1 is missing for 1985. The analysis shows that the single variable KD1 accounts for R2adj ¼ 85:16%. Hence the predictor variable KD1 is selected and the other predictor variables are discarded. The link between the response and the predictor variables is investigated in the next stage. Stage 2: In this stage a regression analysis is conducted with the response variable KI and the predictor variable KD1 (see Table S3 in the Supplementary material at the EJOR website). Here we include the data for 2005 since the values of KI and KD1 are available for that year. Regression models of time-series variables are prone to make erroneous inferences in case influential observations and autocorrelated errors are present in the dataset; see Hines et al. (2003). Cook’s distance is a measure to identify influential observations. A value of Cook’s distance higher than unity identifies an observation as influential. In the current analysis Cook’s distance has not exceeded unity for any observation implying absence of influential observations. Durbin–Watson test is a statistical procedure to determine the presence of autocorrelated errors in regression models. If the Durbin–Watson test statistic D is greater than the upper critical value Da,U, i.e., D > Da,U for a type I error a, then the autocorrelateion coefficients of the first order autoregressive model of errors can be hypothesized to be equal to zero. The Durbin–Watson statistic of our model is D = 2.53 and D0.05,U = 1.41 for a sample size of 20. Hence the possibility of autocorrelated errors is overruled. The normal probability plot of the residuals also does not reveal any severe model inadequacy. Hence the following regression equation is acceptable:
KI ¼ 0:933 0:856KD1 :
ð21Þ
Eq. (21) confirms that the degree of intermediation of a year gets adversely affected by its previous year’s degree of disintermediation and hence the more generalized conclusion is that disintermediation in a period intensifies the likelihood of disintermediation in the subsequent period. Hence H1 cannot be rejected, and consequently the practicability of the proposed matching technology and the information system of the disintermediated market model is justified.
The model presented in this paper provides an important insight into the phenomenon of disintermediation of auctioneers. It attributes the increments in traders’ estimated matching probabilities in disintermediated market to the evolution of the stable steady-state equilibrium at complete disintermediation. However this paper does not negate the chances of evolution of the stable steady-state equilibrium at complete auction-intermediation and the existence of locally stable market equilibrium at simultaneous realization of intermediation and disintermediation. The paper rather confirms inevitability of auction-intermediation in case of traders’ estimated matching probabilities going down to a certain threshold. This might encourage auctioneers to adopt strategies for reducing trading agents’ estimated matching probabilities. Such strategies could be put into action by reengineering an existing auction mechanism to an extent that spontaneously outperforms the old mechanism by enhancing efficiency and trustworthiness of the transaction process. The increasing trend of disintermediation in the Indian tea market has prompted the Ministry of Commerce and the Tea Board of India to reengineer the prevailing manual outcry auction process that started in this industry long back in 1861. The six geographically spread main tea auction centers (Guwahati, Siliguri, Kolkata, Coimbatore, Coonoor and Kochi) of the country have been planned to bring to the ambit of a common e-auction platform. The aim of this initiative is to increase efficiency of auction mechanism by standardizing processes across auction centers, reducing transaction time, providing more flexible auction sessions, ensuring transparency, establishing a more robust price discovery mechanism and stopping collusion between bidders. Nevertheless, the new format of e-auction failed to attract a large section of traders to whom it was piloted in December 2008 and notably complaints were raised against its user-friendliness. But the implementation authority did not treat the complaints seriously as they had anticipated the initial hindrance to be obvious since a new transaction process was replacing a century-old process that had been deeply rooted to the trading culture of the market. However, this is not the first initiative to implement e-auction in the Indian tea market. Earlier in 2004 a similar attempt by the Tea Board failed and the expensive electronic-auction software developed by top-class business solution providers had to be shelved. The main cause of failure was reckoned to be in the business process of the software system that was merely an electronic replica of the old outcry process. The Board and the ministry are optimistic about the new software system as the technology behind it has shifted to a more powerful web-based platform than the previous one. The level of optimism is so high that the ministry expects nearly 5–10% of the private sales to be snatched by e-auction. We have to wait for the future to see whether the reengineered auction mechanism will really stop disintermediation in the Indian tea market. However, unlike relational contracts, auctions fail to cater the vital scope of information exchange at the operational level. In this context, the auctioneers may be suggested to device auxiliary mechanisms for information exchange to confront disintermediation. If such mechanisms are not devised, no matter how efficient the auction process may be, the risk of disintermediation will be unavoidable in a market where buyers and sellers get the scope of repeated interactions.
5. Conclusions Lu and McAfee (1996) speculated evolutionary stability of auction over bargaining, although several instances of disintermediation of auctioneers have been recorded worldwide over years. We have illustrated one such case of disintermediation
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from the Indian tea market where the options of auction-intermediation and bargaining-based supply chain contracting coexist. To resolve the conflict between Lu and McAfee (1996) and the phenomenon of disintermediation, we have analyzed a market model of homogeneous buyers and sellers having both the options of auction-intermediation and supply chain contracting and found out the possibility of occurrences of either of the two unique evolutionary stable steady-state market equilibria: one at complete auction-intermediation and the other at complete disintermediation. We have also identified a unique locally stable steady-state market equilibrium that realizes both intermediation and disintermediation simultaneously. It has been shown that evolution process of these market equilibria is controlled by the matching technology of the disintermediated market. The matching technology has been rendered with a suitable information system and a pair of identity-based dynamic decision variables: buyer’s and seller’s estimated matching probabilities. It has been found that if the values of these matching probabilities are very low auction-intermediation becomes evolutionary stable over disintermediation and the reverse for the high values of the matching probabilities. The model has also earmarked the limiting values of these probabilities for ensuring occurrences of auction-intermediation and disintermediation. The practicality of the modeled matching technology of the disintermediated market has been justified with a hypothesis based on the data from the Indian tea market. Trading agents’ estimated matching probabilities could be contemplated to act as the parameters for quantifying the qualitative concept of business relationships. We hope that this idea would provide initial impetus for using the concept of estimated matching probabilities in empirical research on buyer–seller relationships. To overcome the restraint of the assumption of homogeneous buyers and sellers, a game of heterogeneous players could be selected in future study for capturing the asymptotic inequality of market system. The inherent advantage of auction over bargaining in terms of its ability to discriminate among buyers and to choose the highest value buyer could also be incorporated in the environment of random matching. The hypothesis of the practicability of the proposed matching technology in the disintermediated market stands upon a set of data pertaining to the Indian tea market. We emphasize on the need to test the hypothesis in context of other markets since generalizability of results is always of concern in research. We hope that replication and extension of the present work could make valuable contributions to the research in supply chain disintermediation. Finally, the challenge is to answer how the intermediaries might confront disintermediation and retain their positions in supply chains. Overall, the present paper has attempted a small advancement to the understanding of supply chain disintermediation. We hope that other researchers will contribute more to this area.
Acknowledgements The authors thank three anonymous referees for their constructive comments and suggestions. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ejor.2010.04.035. References Bailey, J.P., 1998. Intermediation and Electronic Markets: Aggregation and Pricing in Internet Commerce. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA. Cohen, M.A., Ho, T.H., Ren, Z.J., Terwiesch, C., 2003. Measuring imputed cost in the semiconductor equipment supply chain. Management Science 49 (12), 1653– 1670. Dutta, S., Sarmah, S.P., 2009. An analysis of supply chain coordination in a multiagent market. International Journal of Operational Research 6 (4), 475–499. Gellman, R., 1996. Disintermediation and the internet. Government Information Quarterly 13 (1), 1–8. Ghosh, R., Singh Deo, A., 2006. Tea Statistics 2005. J. Thomas & Company Pvt. Ltd., Kolkata, India. Gunasekaran, A., Nagi, E.W.T., 2004. Information systems in supply chain integration and management. European Journal of Operational Research 159 (2), 269–295. Gurnani, H., Mengze, S., 2006. A bargaining model for a first-time interaction under asymmetric beliefs of supply reliability. Management Science 52 (6), 865–880. Hines, W.W., Montgomery, D.C., Goldsman, D.M., Borror, C.M., 2003. Probability and Statistics in Engineering. John Wiley & Sons (Asia) Pte. Ltd., Singapore 129809. Hoffman, T., 1995. No More Middleman. Computerworld. Johnson, B., 2003. Quantifying and Managing Supply Risk and Flexibility at Agilent Technologies. Teaching Case, Stanford Graduate School of Business, Stanford, CA. Krause, D.R., Terpend, R., Petersen, K.J., 2006. Bargaining stances and outcomes in buyer–seller negotiations: Experimental results. The Journal of Supply Chain Management 42 (3), 4–15. Lu, X., McAfee, R.P., 1996. The evolutionary stability of auctions over bargaining. Games and Economic Behavior 15 (2), 228–254. Mas-Colell, A., Whinston, M.D., Green, J.R., 1995. Microeconomic Theory. Oxford University Press, New York. Nachbar, J., 1990. Evolutionary selection dynamics in games: Convergence and limit properties. International Journal of Game Theory 19, 59–89. Nash Jr., J.F., 1950. The bargaining problem. Econometrica 18 (2), 155–162. Pinto, J., 2000a. Disintermediation-II: The Customer Perspective.. Pinto, J., 2000b. Disintermediation Stirs Up Industrial Automation. . Shunk, D.L., Carter, J.R., Hovis, J., Talwar, A., 2007. Electronics industry drivers of intermediation and disintermediation. International Journal of Physical Distribution and Logistics Management 37 (3), 248–261. Stringer, G., 2006. Conceptual Issues in Cyberspace. University of Exeter, UK. . Taylor, T.A., Plambeck, E.L., 2007. Supply chain relationships and contracts: The impact of repeated interaction on capacity investment and procurement. Management Science 53 (10), 1577–1593. Tierney, C., 2005. Ford Slams Toyota on Hybrids. Detroit News (August 8) A1. Upton, D.M., Fuller, V.A., 2003. The ITC eChoupal Initiative. Harvard Business School Publishing, Boston, MA 02163 . Wu, S.D., 2004. Supply chain intermediation. In: Simchi-Levi, D., Wu, S.D., Max Shen, Z. (Eds.), Handbook of Quantitative Supply Chain Analysis: Modeling in the EBusiness Era. Kluwer Academic Publishers. Chapter 3.
Contents lists available at ScienceDirect
European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor
Innovative Applications of O.R.
Evolutionary stability of auction and supply chain contracting: An analysis based on disintermediation in the Indian tea supply chains S. Dutta a, S.P. Sarmah b,*, S.K. Goyal c a
Proof and Experimental Establishment, DRDO, Chandipur 756025, India Department of Industrial Engineering and Management, IIT, Kharagpur 721302, India c Department of Decision Sciences and MIS, Concordia University, Montreal, Canada b
a r t i c l e
i n f o
Article history: Received 23 July 2008 Accepted 30 April 2010 Available online 12 May 2010 Keywords: Auction Bargaining Supply chain contract Disintermediation Indian tea industry
a b s t r a c t The purpose of this paper is to show that evolutionary stable market equilibrium is achievable through complete disintermediation of auctioneers if the option of bargaining-based supply chain contracting exists. The paper analyzes the evolutionary dynamics of a market that caters both the scopes of auction-intermediation and supply chain contracting to a set of homogeneous buyers and sellers. The motivation of this work developed from the contradiction between the theoretical framework of Lu and McAfee (1996) that identifies auction to be evolutionary stable over bargaining and the real instance of sustained disintermediation of auctioneers in the world’s largest tea industry in India where supply chain contracting is the other option of trading. 2010 Elsevier B.V. All rights reserved.
1. Introduction and literature review Transactions in markets take place through mechanisms like auction and bargaining. A simple two-stage supply chain forms whenever a mechanism realizes a trade by which a pair of buyer and seller exchanges information, funds and goods with each other. However, most of the contemporary supply chain networks are characterized by business entities intermediating between buyers and sellers. These entities are popularly known as supply chain intermediaries. Wu (2004) categorized them as transactional and informational intermediaries. Transactional intermediaries increase supply chain efficiency at the transactional level, whereas informational intermediaries add value at the tactical and the strategic levels. Presence of non-negative incentive for distorting private information allures buyers and sellers to report disfigured estimates of their actual willingness-to-pay levels and opportunity costs, eventually creating information asymmetry that catalyzes adverse partner selection and inflates the risk of inefficient market matching. Wu (2004) reported that the informational intermediaries mainly provide three functions: (i) implementation of coordination mechanisms to reduce adverse selection, (ii) creation of trusted institutions to trim down the necessity of direct negotiation and (iii) price discovery by synthesizing dispersed information of trading agents’ reservation values. Effectiveness of these functions counts on how aptly the intermediary mechanism imple* Corresponding author. Tel.: +91 3222 283734(O)/283735(R). E-mail address: [email protected] (S.P. Sarmah). 0377-2217/$ - see front matter 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2010.04.035
ments incentive compatibility (IC) and individual rationality (IR). IC is the constraint mechanism imparted on the revelation principle of a transaction mechanism to ensure trading agents’ truthfulness and IR is the constraint mechanism to ensure trading agents’ utilities not to be lesser than their reservation values; see Mas-Colell et al. (1995). Auctioneers are considered to be informational intermediaries who devise price discovery mechanisms to minimize overall market inefficiency through reduction of uncertainty of adverse matching. A powerful auctioneer performs efficient price discovery by implementing IC and thus ensures the optimum strategies of all buyers and sellers as to disclose actual willingnessto-pay levels and opportunity costs. This leads to the realization of ex post efficient market matching. Dutta and Sarmah (2009) studied impacts of market matching patterns on overall market efficiency and reported that, in spite of all transactions being Paretoefficient and the market matching pattern being ex post efficient the overall surplus of all transaction channels may be less than that of a Pareto efficiently matched market. This implies that there could be forms of transaction mechanisms that might prove to be more efficient than auction. If an auctioneer fails to raise the market efficiency to a level that could be achieved by such a mechanism then IR generates risks of disintermediation of the auctioneer from all supply chains in which she operates. Therefore, auctioneers should improvise suitable need-based coordination mechanisms for improving channel surplus. Gellman (1996) reported that the term disintermediation was first used to describe the trend for small investors to cut loose from traditional intermediaries by means of direct investments in
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financial instruments like money market funds. The term became popular in the literature of supply chain management (SCM) only in the recent years. Hoffman (1995) used the term in SCM to describe cutting out of the middlemen by direct transactions and attributed it as the basis of B2B e-commerce. Pinto (2000a,b) described disintermediation as the elimination of an intermediary from a business process owing to the cost of intermediation exceeding the value added by the intermediary. Rapid emergence of new technologies in today’s highly competitive global business has prompted many companies to analyze costs of all links in their supply chains and to indulge in continual exploration of the opportunities for competitive price cuts through direct transactions with their downstream customers bypassing the conventional intermediaries. Several mainstream companies from different business domains have already bridged direct links with their customers with the aid of information technology (IT). For instance, Amazon.com launched a web-based system for selling its items directly to the customers without any form of intermediation. Gunasekaran and Nagi (2004) provided an exhaustive citation on the applications of IT in the SCM paradigm. Though the common wisdom suggests that direct transaction shrinks costs of original sales-links, it is inappropriate to consider the phenomenon of supply chain disintermediation to be obvious and inevitable. If an agent succeeds to devise a transaction mechanism to make a supply chain more efficient than it is in direct transaction then she finds room in that supply chain as an intermediary. Bailey (1998) justified viability of both intermediation and disintermediation hypotheses under different market conditions. Shunk et al. (2007) augmented this with the idea of reintermediation of disintermediated supply chains. Lu and McAfee (1996) studied a market model of homogeneous buyers and sellers having the option to choose one of the trading mechanisms between auction and bargaining. The model depicted evolutionary stability of auction over bargaining. The depiction contradicts the hypothesis of disintermediation of auctioneers in a market with both auction and supply chain contracts since the basic mechanism of such contracts is postulated to be pairwise bargaining. Contrary to the framework of Lu and McAfee (1996), quite a few markets are found where traders spontaneously bypass auction-intermediation and engage in supply chain contracting. For instance, the Indian tea market has been witnessing a steady decline in the volume of auction trading over the last 20 years because of the traders’ increasing affinity with supply chain contracts. The contradiction between the model of Lu and McAfee (1996) and the phenomenon of disintermediation of auctioneers in the Indian tea supply chains has motivated us for the present work. In this paper, we follow the idea of Lu and McAfee (1996) to analyze a market model of homogeneous buyers and sellers that offers both the options of auction-intermediation and supply chain contracting. The intermediated market of our model is analogous to the auction market of Lu and McAfee (1996). The crux of our model is the incorporation of a supply chain contract-based disintermediated market in place of the bargaining market of Lu and McAfee (1996). Though the core transaction mechanism of the disintermediated market is nothing but pairwise bargaining, its matching technology is entirely different from that of the bargaining market of Lu and McAfee (1996). The setting of the bargaining market of Lu and McAfee (1996) does not completely replicate the complexity of the matching technology of contract-based disintermediated markets since choice of partners is not random in disintermediated markets. While Upton and Fuller (2003) attributed trading agents’ trustworthiness to the success of contract-based supply chains, Stringer (2006) identified the scope of information exchange at the operational level as the key to it. Whom to trust and how much information to share is a vital issue in this setting. Gurnani and Mengze (2006) discussed how this issue plays a deci-
sive role in determining efficiencies of supply chain contracts. Keeping in line with these views we propose an identity-based dynamic matching technology for disintermediated market. Hence we show that two unique evolutionary stable steady-state market equilibria exist – one at complete auction-intermediation and the other at complete disintermediation. Further, we show the existence of a unique locally stable steady-state market equilibrium that realizes both auction-intermediation and disintermediation simultaneously. It is found that the selection of the type of the market equilibrium is controlled by the proposed matching technology of the disintermediated market. To test the plausibility of this matching technology we build a hypothesis based on data from the Indian tea industry. The rest of the article is organized as follows. Section 2 presents the model. Section 3 analyzes aptness of the proposed matching technology. Section 4 provides managerial implications of our findings and Section 5 presents conclusions.
2. The model The overall market setting comprises of two separate markets. One is an intermediated market where buyers and sellers trade through free-of-cost auctioneers and the other one is a disintermediated market.
2.1. The market 2.1.1. Goods A single indivisible good is traded for some quantity of a divisible good, i.e., money.
2.1.2. Time Time is discrete and is indexed by non-negative integers, t = 0, 1, 2, . . .
2.1.3. Economic agents The economic agents are buyers and sellers. Each seller enters the market with one unit of the good and each buyer enters with exactly one unit of money. All sellers are homogeneous since the goods they sell are identical and their valuations of the good are equal. All sellers’ use values are fixed at zero. All buyers are also homogeneous since their consumption values are identical and are set at unity. All buyers and sellers have identical bargaining power. At the beginning of each period new agents enter the market and join the existing agents. At time t, there exist Nt sellers and htNt buyers in the market where, Nt is a very large positive integer and 0 < ht < +1. Each agent trades at most once and after trading she exits from the market. The agent who fails to trade in the current period remains in the market till she trades in a later period. There is no restriction on the exited agents to reenter as new entrants in a later period. New entrants are free to choose between the auction-intermediated and the disintermediated markets, although once entered in a certain type of market they are assumed to be prohibited from switching to the other type of market till their exit. The assumption is helpful for analyzing evolutionary dynamics of market and can be found valid in the situation that allows very few agents to switch from one market to the other. We also assume that all buyers and sellers discount values one period ahead by the common discount factor d, 0 < d < 1, which remains constant over time. Expected utilities of buyers and sellers at time t are U it and V it where, i = I, D indicates the types of markets they are in (I for the intermediated and D for the disintermediated market).
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2.1.4. Matching In the intermediated market the auctioneer performs the role of searching and matching by implementing an auction mechanism. The proportions of buyers and sellers in the intermediated market at time t are 1 xt and 1 yt where 0 6 xt 6 1, 0 6 yt 6 1. At the beginning of each period all buyers of the intermediated market are randomly spread over the sellers of that market in such a fashion that a buyer can match with at most one seller while a seller can be visited by many buyers. Number of buyers visiting each seller in this market is a binomial random variable with parameters htNt(1 xt) and Nt(1 yt). Nt being very large, the distribution is approximated as a Poisson distribution with parameter ht(1 xt)/ (1 yt). Once a seller matches with a buyer, the seller and the buyer trade and leave the market at the end of the period. The unmatched agents remain in the market for taking part in another auction in the next period. The proportions of buyers and sellers in the disintermediated market at time t are xt and yt respectively. Unlike intermediated market trading agents in this market individually search for potential partners to negotiate supply chain contracts through pairwise bargaining. Thus, in any period an agent in this market can match with at most one agent of the opposite type. The matched pair of agents trade in the current period and leave the market after the period ends. If an agent fails to search a partner or experiences a negotiation breakdown then she remains unmatched and waits to get matched in the next period. Each agent’s individual estimation about her probability to match with another agent at a particular time is based on two factors – the matching agents’ identities and the index of the period. For a SB seller S and a buyer B, we use the variables bSB t ; 0 6 bt 6 1 and BS BS at ; 0 6 at 6 1 to represent their respective estimated probabilities for matching with each other at time t. The estimate bSB is t the decision variable chosen by the seller S based on her own preferences for matching and her best belief on buyer B’s preferences for matching. Similarly, the estimate aBS t is the decision variable chosen by the buyer B based on her own preferences and her best belief on seller S’s preferences for matching. An individual agent’s belief set is not only controlled by the industry-wide common knowledge about trading agents’ preferences but also by her best belief generated from the private knowledge acquired over time. SB The difference in the estimates of aBS t and bt is attributed to the fact that the best beliefs of the agents B and S may not be identical. SB Rather the estimates aBS t and bt are endogenous decision variables of individual agents and are not set by any external mechanism. The conception of the identity-based dynamic market matching conforms to the following information system. 2.1.5. Information Each agent recognizes identities of the other agents in the disintermediated market and holds information of the indices of time. Each agent possesses past experiences of trading if any and also some information about the matches formed by the other agents.
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the trading agents as surplus over their individual reservation values. Buyers’ consumption values and sellers’ use values being set at 1 and 0 respectively one can express the relation between reservation values and gain from trade of one unit good as, dU Itþ1 þ dV Itþ1 þ GIt ¼ 1 0. i.e.:
GIt ¼ 1 dU Itþ1 dV Itþ1 :
ð1Þ
Expected utility of a buyer in this market depends on two mutually exclusive possibilities: first the buyer may find no other buyer in the market in which her optimal strategy would be to bid at the seller’s reservation value and secure a payoff equal to 1 dV Itþ1 and second there may be at least another competing buyer in the market in which all buyers would contest to win the opportunity to trade. The contest can be identified as a Bertrand game that discloses actual information of the buyers’ willingness-to-pay levels and ensures a payoff of dU Itþ1 for all buyers. The number of buyers participating in an auction follows Poisson distribution with parameter ht(1 xt)/(1 yt), i.e.:
PðK ¼ kÞ ¼ eht ð1xt Þ=ð1yt Þ ðht ð1 xt Þ=ð1 yt ÞÞk =k! for; k ¼ 0; 1; 2; . .. ð2Þ Hence the probability of occurrence of the first case in which a buyer does not find any other buyer is P(K = 0) i.e., eht ð1xt Þ=ð1yt Þ . Similarly the probability of occurrence of the second case in which a buyer finds at least another buyer is 1 P(K = 0), i.e., 1 eht ð1xt Þ=ð1yt Þ . So expected utility of a buyer in the intermediated market at time t is as follows:
U It ¼ eht ð1xt Þ=ð1yt Þ 1 dV Itþ1 þ 1 eht ð1xt Þ=ð1yt Þ dU Itþ1 ¼ eht ð1xt Þ=ð1yt Þ GIt þ dU Itþ1 :
ð3Þ
Expected utility of a seller depends on three mutually exclusive possibilities: first there may be no buyer with probability P(K = 0) i.e., eht ð1xt Þ=ð1yt Þ , second there may be only one buyer with probability P(K = 1) i.e., eht ð1xt Þ=ð1yt Þ ðht ð1 xt Þ=ð1 yt ÞÞ and third there may be more than one buyer with probability 1 P(K = 0) P(K = 1), i.e., 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ. The first and the second cases ensure the seller a payoff equal to her reservation value dV Itþ1 and the third case is characterized by the Bertrand game contest of the buyers ensuring the seller a payoff of 1 dU Itþ1 . So expected utility of a seller in this market at time t is as follows:
V It ¼ eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞdV Itþ1
þ 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ 1 dU Itþ1 ¼ 1 eht ð1xt Þ=ð1yt Þ ð1 þ ht ð1 xt Þ=ð1 yt ÞÞ GIt þ dV Itþ1 : ð4Þ
2.3. The disintermediated market 2.2. The auction-intermediated market In the auction-intermediated market, the buyers bid according to their individual willingness-to-pay levels for buying good from a seller in presence of an auctioneer who ensures opportunity of trading to the highest bidder provided the reservation value of the seller is secured. Reservation value can be considered as the point at which a trading agent remains indifferent between trading and not trading and thus it can be identified as the current value of trading in the next period which at time t is identical to the agent’s expected utility of trading at time t + 1 discounted by the factor d. Hence dV Itþ1 and dU Itþ1 are the respective reservation values of the sellers and the buyers in the intermediated market at time t. If a trade yields a non-negative gain GIt then it would be split between
The concepts of reservation value and gain in the disintermediated market are analogous to that in the intermediated market. So the reservation values of buyers and sellers in this market are dU Dtþ1 and dV Dtþ1 and the gain from trade of one unit good is as follows:
GDt ¼ 1 dU Dtþ1 dV Dtþ1 :
ð5Þ
Trades in this market are regulated by supply chain contracts, the core negotiation mechanism of which is an assortment of channel coordination and pairwise bargaining. Nash (1950) described the players of the bargaining problem as two individuals who have the opportunity to collaborate for mutual benefits in more than one way. The framework of Nash bargaining solution complies with the mechanism of supply chain contracting and can be used to
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estimate the negotiable unit price Pt . As per the Nash’s rationale, the optimum gain occurs as the product of negotiators’ payoffs over their reservation values are maximized. For a negotiable unit price Pt, the respective payoffs for seller and buyer over their reservation values are Pt dV Dtþ1 and 1 P t dU Dtþ1 . Thus, Pt is the solution of arg max Pt dV Dtþ1 1 Pt dU Dtþ1 , i.e.: Pt
Pt ¼ 1=2 dU Dtþ1 dV Dtþ1 =2 ¼ GDt =2 þ dV Dtþ1
I
U I ¼ ehð1xÞ=ð1yÞG =ð1 dÞ; I
¼ 1 GDt =2 dU Dtþ1 :
ð6Þ
It can be checked that the maximum value of P t is 1 when, dU Dtþ1 ¼ 0; dV Dtþ1 ¼ 1 and the minimum value of Pt is 0 when, dU Dtþ1 ¼ 1; dV Dtþ1 ¼ 0. Pairwise bargaining allows an agent to negotiate with only one agent of the opposite type in each period. Consider the interaction between the seller S and the buyer B (we will see afterwards that analysis of interaction of a particular pair of agents does not disturb the generality of the market equilibria). Expected utility of the buyer B in this interaction is based on two mutually exclusive possibilities: first the buyer may expect to match with the seller S with probability aBS t and secure a payoff of 1 P t and second the buyer may expect a negotiation breakdown with probability 1 aBS and secure her reservation value dU Dtþ1 . So expected utility t of the buyer B in the disintermediated market at time t is as follows:
D BS BS U Dt ¼ aBS GDt =2 þ dU Dtþ1 : t 1 P t þ 1 at dU tþ1 ¼ at
ð7Þ
Similarly the seller S faces two mutually exclusive possibilities: first she may expect to match with the buyer B with probability bSB t and acquire a payoff of Pt and second she may expect the negotia tion to break down with probability 1 bSB securing her a payoff t equal to her reservation value dV Dtþ1 . So expected utility of the seller S in the disintermediated market at time t is as follows:
V Dt
¼
bSB t Pt
þ 1
bSB t
dV Dtþ1
ket fails to come out of the equilibrium ever since it is attained. Similar arguments hold good for the equilibrium at complete disintermediation. Apart from (x, y) = (0, 0) and (x, y) = (1, 1), any other steady-state market equilibrium can be represented as (xt, yt) = (x, y) " (t = 0, 1, 2, 3, . . . ) where, U it ¼ U i ; V it ¼ V i and subsequently, Git ¼ Gi 8i 2 fI; Dg. This situation simplifies Eqs. (3), (4), (7) and, (8) to the followings:
¼
bSB t
GDt =2 þ dV Dtþ1 :
ð8Þ
hð1xÞ=ð1yÞ
V ¼ 1e
ð1 þ hð1 xÞ=ð1 yÞÞ GI =ð1 dÞ;
ð9Þ ð10Þ
U D ¼ aBS GD =2ð1 dÞ;
ð11Þ
V D ¼ bSB GD =2ð1 dÞ:
ð12Þ
The necessary condition for existence of any such equilibrium requires expected utilities of the new entrants to be equal in both intermediated and disintermediated markets, i.e., UI = UD, VI = VD and hence GI = GD. Using Eqs. (9)–(12) along with GI = GD, the condition reduces to the followings for 0 < x < 1 and 0 < y < 1:
ehð1xÞ=ð1yÞ ¼ aBS =2;
ð13Þ
and
1 ehð1xÞ=ð1yÞ ð1 þ hð1 xÞ=ð1 yÞÞ ¼ bSB =2:
ð14Þ
Now we propose the possibility of existence of a third type steadystate market equilibrium. Proposition 2. {(x, y)j0 < x < 1,0 < y < 1} represents the third type steady-state market equilibrium, independent of agents’ identities, lying on the segment of a concave curve f(a, b) = a a ln (a/ 2) + b 2 = 0 enclosed in the unit square bounded by the lines a = 0, a = 1, b = 0 and b = 1 (henceforth this square will be referred as ab unit square), where a and b represent the respective estimated matching probabilities of buyers and sellers. The third type steady-state market equilibrium {(x, y)j0 < x < 1, 0 < y < 1} represents a situation that makes the market neither completely intermediated nor completely disintermediated (see Fig. 1).
2.4. Equilibrium 2.5. Evolutionary stability of equilibrium First consider a situation in which the ratio of buyers to sellers is constant over time, i.e., ht = h " (t = 0, 1, 2, 3, . . . ). This restricts the concept of market evolution to the evolution of distributions of buyers and sellers in the intermediated and the disintermediated markets. Now a steady-state market equilibrium can be specified as the situation that keeps the proportions of buyers and sellers in the intermediated and the disintermediated markets constant over time, i.e., (xt, yt) = (x, y) " (t = 0, 1, 2, 3, . . . ) where, (x, y) 2 {(x, y)j0 6 x 6 1,0 6 y 6 1}. The following proposition illustrates the existence of two such steady-state market equilibria.
As the third type steady-state market equilibrium is independent of agents’ identities, for the analysis of stability of market equilibria we consider all agents to be anonymous without loss of any detail. Therefore, bSB and aBS are replaced by bt and at, t t respectively. The notion of evolutionary stability of market equilibrium represents a situation in which the new entrants expect their utilities in the next period to be equal to that in the current period (i.e., U itþ1 ¼ U it and, V itþ1 ¼ V it 8i 2 fI; DgÞ while the ratio of buyers to sellers remains fixed over time (i.e., ht = h). Hence the Eqs. (3), (4), (7) and (8) reduce to the followings:
Proposition 1. For 0 < h < +1, the complete auction-intermediation, i.e., (x, y) = (0, 0) and the complete disintermediation, i.e., (x, y) = (1, 1) are the two steady-state market equilibria. The proof of this proposition is not presented here since it is identical to the first proposition of Lu and McAfee (1996). Proofs of all other propositions, lemmas and corollaries can be found in the Supplementary material at the EJOR website. Proposition 1 suggests two types of steady-state market equilibria, (x, y) = (0, 0), i.e., complete auction-intermediation and (x, y) = (1, 1), i.e., complete disintermediation. These two steady-state equilibria are self-reinforcing, i.e., after attaining either of them the market fails to come out of that. For example, the equilibrium at complete auction-intermediation compels new entrants to join auction due to absence of partners in the disintermediated market. Thus the mar-
(0,1) β
β =1
(1,1) f (α , β ) = 0
ME α =1
α =0
(0,0)
β =0
ME: The third type steady-state market equilibrium
(1,0) α
Fig. 1. The third type steady-state market equilibrium enclosed inside the ab unit square.
S. Dutta et al. / European Journal of Operational Research 207 (2010) 531–538
U It ¼ ehð1xt Þ=ð1yt Þ GIt =ð1 dÞ;
ð15Þ
V It ¼ U Dt ¼ V Dt ¼
ð17Þ
1e
hð1xt Þ=ð1yt Þ
ð1 þ hð1 xt Þ=ð1 yt ÞÞ GIt =ð1 dÞ;
ð16Þ
at GDt =2ð1 dÞ; bt GDt =2ð1 dÞ:
ð18Þ U itþ1
U it
Under the notion of evolutionary stability, i.e., ¼ and V itþ1 ¼ V it 8i 2 fI; Dg, gains from trade of one unit of good in the intermediated and the disintermediated markets are derived in the following using the Eqs. (15)–(18) along with the Eqs. (1) and (5):
GIt ¼ ð1 dÞ= 1 dehð1xt Þ=ð1yt Þ hð1 xt Þ=ð1 yt Þ ;
ð19Þ
GDt ¼ 2ð1 dÞ=ð2ð1 dÞ þ dðat þ bt ÞÞ:
ð20Þ
For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, we define the equilibrium curve for buyers at time t as the locus of the point that represents identical expected utilities of buyers in the auction-intermediated and the disintermediated markets in that period of time, i.e., U It ¼ U Dt . Similarly, for {(xt, yt)j0 < xt < 1, 0 < yt < 1}, we define the equilibrium curve for sellers at time t as the locus of the point that represents identical expected utilities of sellers in the auction-intermediated and the disintermediated markets in that period of time, i.e., V It ¼ V Dt . The following lemma identifies the equilibrium curves for buyers and sellers (see Fig. 2). Lemma 1 (a) For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, the equilibrium curve for buyers is a segment of a straight line enclosed in the ab unit square. The segment makes a positive intercept on the side b = 0 and no intercept on the side a = 0. (b) For {(xt, yt)j0 < xt < 1, 0 < yt < 1}, the equilibrium curve for sellers is a segment of a straight line enclosed in the ab unit square. The segment makes no intercept on the side b = 0 and a positive intercept on the side a = 0. The following lemma depicts the relationship between the third type steady-state market equilibrium and the equilibrium curves for buyers and sellers. Lemma 2. The third type steady-state market equilibrium realizes on the point of intersection of the equilibrium curves for buyers and sellers. β =1
(0,1)
β α =0
(1,1)
SE
SE: The equilibrium curve for sellers BE: The equilibrium curve for buyers
(0,0)
β =0
(1,0 )
α
Fig. 2. The equilibrium curves for buyers and sellers.
(0,1)
(1,1)
β =1 1
2
β
SE α =0 3
Lemma 3 (a) In the regions 2 and 3, expected utility of a buyer is higher in the intermediated market than that in the disintermediated one, i.e., U It > U Dt and, in the regions 4 and 1, expected utility of a buyer is lower in the intermediated market than that in the disintermediated one, i.e., U It < U Dt . (b) In the regions 1 and 2, expected utility of a seller is lower in the intermediated market than that in the disintermediated one, i.e., V It < V Dt and, in the regions 3 and 4, expected utility of a seller is higher in the intermediated market than that in the disintermediated one, i.e., V It > V Dt . According to the standard evolutionary dynamics (Nachbar, 1990), new agents estimate the current matching probabilities and choose the market offering higher utilities because they assume incorrectly that current payoffs will remain throughout all periods. Thus, the proportion of agents increases in the market offering higher utility and decreases in the market offering lower utility. In the region 1, U It < U Dt and V It < V Dt , all new agents choose the disintermediated market resulting in an increase of the proportion of agents in the disintermediated market (xt+1 > xt, yt+1 > yt). In the region 2, U It > U Dt and V It < V Dt , all new buyers choose the intermediated market while all new sellers choose the disintermediated one. This decreases the proportion of buyers and increases the proportion of sellers in the disintermediated market (xt+1 < xt, yt+1 > yt). In the region 3, U It > U Dt and V It > V Dt , all new agents choose the intermediated market resulting in a decrease of the proportion of agents in the disintermediated market (xt+1 < xt, yt+1 < yt). In the region 4, U It < U Dt and V It > V Dt , all new buyers choose the disintermediated market while all new sellers choose the intermediated one. This increases the proportion of buyers and decreases the proportion of sellers in the disintermediated market (xt+1 > xt, yt+1 < yt).
ME
Now we describe the type of stability of the market equilibria in the following.
α =1
BE
β =0
(a) The points in the region 2 follow clockwise dynamic rotational paths heading towards the equilibrium curve for buyers for f(a, b) > 0 and towards the equilibrium curve for sellers for f(a, b) < 0. (b) The points in the region 4 follow anti-clockwise dynamic rotational paths heading towards the equilibrium curve for sellers for f(a, b) > 0 and towards the equilibrium curve for buyers for f(a, b) < 0.
Proposition 3
4
(0,0)
Fig. 3 shows that the equilibrium curves for buyers and sellers intersect each other on the curve representing the third type steady-state market equilibrium inside the ab unit square and thus divide the ab unit square in four distinct regions namely 1, 2, 3 and 4. The following lemma illustrates variations of trading agents’ expected utilities over these regions.
Lemma 4
α =1 BE
535
α
(1,0)
Fig. 3. The third type steady-state market equilibrium on the point of intersection of the equilibrium curves for buyers and sellers.
(a) For f(a, b) < 0, complete auction-intermediation is the unique evolutionary stable steady-state market equilibrium. (b) For f(a, b) > 0, complete disintermediation is the unique evolutionary stable steady-state market equilibrium. (c) For f(a, b) = 0, the market attains a unique locally stable steadystate equilibrium by simultaneous realization of both auctionintermediation and disintermediation.
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Proposition 3 suggests that there are only two unique evolutionary stable steady-state market equilibria, one at complete auction-intermediation for f(a, b) < 0 and the other at complete disintermediation for f(a, b) > 0. The equilibrium at f(a, b) = 0 is a unique locally stable market equilibrium that realizes both auction-intermediation and disintermediation simultaneously. Fig. 3 suggests that the agents’ estimated matching probabilities, a and b, are less for f(a, b) < 0 compared to that for f(a, b) > 0. Therefore, if for some reason the values of agents’ estimated matching probabilities become very high, the evolutionary dynamics of the market lead to complete disintermediation of the auctioneers. The following corollaries provide limiting values of the agents’ estimated matching probabilities for ensuring complete intermediation and complete disintermediation of the auctioneers. Corollary 1. The necessary condition for complete disintermediation of the auctioneers is that the estimated matching probabilities of all the sellers and all the buyers should exceed 0.307 and 0.373, respectively. However this condition is not sufficient. Corollary 2. The necessary and sufficient condition for complete auction-intermediation is that the estimated matching probabilities of all the sellers and all the buyers should be below 0.307 and 0.373, respectively. Our model states that the market matching technology of the disintermediated market plays a decisive role in determining the type of market equilibrium. In the following we discuss the rationale behind the assumption of identity-based dynamic matching technology and the information system of the disintermediated market. 3. Discussion Auction ensures efficient market matching by curbing direct exchange of information between trading agents. On the contrary, disintermediated markets furnish the scope of direct information exchange, albeit such information is prone to distortion in case of incentive incompatible negotiations. Krause et al. (2006) studied the effects of integrative and distributive bargaining stances on the outcomes of negotiations. In spite of the common wisdom that higher degree of integration begets higher volume of channel surplus, agents may refrain from tactical and strategic integration for retaining individual bargaining powers. However, integration at the operational level is quite common. Stringer (2006) reported that information exchange with the customers proves to be vital for the manufacturers to design and modify production processes. Similar advantages can also be found at the buyers’ ends. Absence of intermediaries in supply chain contracts raises question about fairness in division of surplus generated due to integration and thus invokes the notion of trust in SCM. Taylor and Plambeck (2007) portrayed agents’ mutual trust as the conducive factor for generation of relational contracts which are far from legal constraints and base purely on integration. Cohen et al. (2003) and Johnson (2003) identified widespread existence of such integration in the market of semiconductors where the buyers share forecasted demand in advance with their suppliers as soft orders for efficient production planning. Tierney (2005) cited a relevant case of integration from the automobile industry – the Japanese automakers having a history of good relationship with suppliers got a competitive edge over Ford that faced the difficulty to build capacity owing to weak relationships with its hybrid-transmission suppliers. A pair of buyer and seller may not take integrative stance at their very first course of negotiation, but rather conceal information even at the operational level due to lack of mutual trust arising
from asymmetric beliefs on each others’ potentials. Once the negotiation consolidates to a contract, in course of trading, both the agents gather firsthand information to grow private knowledge about each other, thus reducing asymmetry in beliefs and generating mutual trust. This outlines the rationale behind the information system of our model. High level of trust generates a bond of relationship between the pair of agents and motivates them to adopt integrative stance, thus increasing channel surplus through better coordination. Existence of such trust-based bond of supply chain agents is quite common in today’s business and works up to the following hypothesis. 3.1. Hypothesis H1: Formation of a disintermediated supply chain between a buyer and a seller at the current period increases the likelihood of formation of a similar supply chain between the same pair of agents in the subsequent period. Assumptions of the identity-based dynamic matching technology and the information system of the disintermediated market are inherent in the premise of the hypothesis. 3.2. Test of hypothesis 3.2.1. Methodology In order to test the hypothesis H1 we perform a statistical analysis on a set of data of 21 years (1985–2005) extracted from the data bank of Indian tea industry compiled by Ghosh and Singh Deo (2006). The set of data consisting of 11 variables (except ‘Year’) is provided as Table S1 in the Supplementary material at the EJOR website. First four variables, namely E: number of estates, A: area under tea (hector), Y: annual yield (ton/hector) and V: annual production volume (ton) are related to the agricultural aspects while the next five variables, namely VEXP: annual export volume (ton), V IIND : annual trading volume at the Indian auction (ton), DpIIND : annual percentage increase in the Indian auction price, V IUK : annual trading volume in the UK auction (ton) and DpIUK : annual percentage increase in the UK auction price are related to the market economy. Among these nine variables, the two modified variables DpIIND and DpIUK are introduced to avoid variations of currency values over the long span of 21 years. For example: DpIIND for the year 1995 Mu=kg in Indian auction in 1995 Mu=kg in Indian auction in 1994 ; ¼ Mu=kg in Indian auction in 1995 100
where Mu refers to monetary unit. The last two variables KI and KD1 , which are also modified ones, act as significant indicators of disintermediation. KI represents the fraction of annual production auction-intermedi traded through ated supply chains, i.e., KI ¼ V IIND þ V IUK =V, and acts as a measure of intermediation. KD1 represents the one-year lag value of the fraction of annual production traded through disintermediated supply chains, i.e., KD1 ¼ 1 previous year’s KI , and acts as a measure of one-year lag value of the extent of disintermediation. The trend of KI fitted as a quadratic curve over the span of 21 years (1985–2005) is shown in Fig. 4. While fitting the curve the year 1985 is taken as t = 1. The overall descending trend of the curve illustrates sustained disintermediation limiting the fraction of annual volume of auction trading from nearly 80% down to 65% over 21 years. The relatively flat trend near the end of the curve indicates some kind of a market equilibrium, which probably represents the unique locally stable steady-state market equilibrium of our model.
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4. Managerial implications
0.8 Accuracy Measures
ΛI
537
Mean Absolute Percentage Error: 3.03597 Mean Absolute Deviation: 0.0182190 Mean Squared Deviation: 0.000529890
0.7
Λ I = 0 .832638 − 0 .032 × t + 0 .000861 × t 2
0.6
0.5 t=0
t=20
t=10
t (years) Fig. 4. The decreasing trend of auction-intermediation in the Indian tea market.
3.2.2. Data analysis and results For testing the hypothesis H1 we analyze the data in two stages. Stage 1: A stepwise regression analysis is conducted over the response variable KI and the predictor variables E; A; Y; V; V EXP ; V IIND ; DpIIND ; V IUK ; DpIUK and KD1 , with a type I error a = 0.001 (see Table S2 in the Supplementary material at the EJOR website). Value of a is instrumental in determining the F-statistic to ensure entry of variables in the regression model. The analysis is based on the data for the years 1986–2004 since the values of the variables E, A, Y are missing for 2005 and the value of KD1 is missing for 1985. The analysis shows that the single variable KD1 accounts for R2adj ¼ 85:16%. Hence the predictor variable KD1 is selected and the other predictor variables are discarded. The link between the response and the predictor variables is investigated in the next stage. Stage 2: In this stage a regression analysis is conducted with the response variable KI and the predictor variable KD1 (see Table S3 in the Supplementary material at the EJOR website). Here we include the data for 2005 since the values of KI and KD1 are available for that year. Regression models of time-series variables are prone to make erroneous inferences in case influential observations and autocorrelated errors are present in the dataset; see Hines et al. (2003). Cook’s distance is a measure to identify influential observations. A value of Cook’s distance higher than unity identifies an observation as influential. In the current analysis Cook’s distance has not exceeded unity for any observation implying absence of influential observations. Durbin–Watson test is a statistical procedure to determine the presence of autocorrelated errors in regression models. If the Durbin–Watson test statistic D is greater than the upper critical value Da,U, i.e., D > Da,U for a type I error a, then the autocorrelateion coefficients of the first order autoregressive model of errors can be hypothesized to be equal to zero. The Durbin–Watson statistic of our model is D = 2.53 and D0.05,U = 1.41 for a sample size of 20. Hence the possibility of autocorrelated errors is overruled. The normal probability plot of the residuals also does not reveal any severe model inadequacy. Hence the following regression equation is acceptable:
KI ¼ 0:933 0:856KD1 :
ð21Þ
Eq. (21) confirms that the degree of intermediation of a year gets adversely affected by its previous year’s degree of disintermediation and hence the more generalized conclusion is that disintermediation in a period intensifies the likelihood of disintermediation in the subsequent period. Hence H1 cannot be rejected, and consequently the practicability of the proposed matching technology and the information system of the disintermediated market model is justified.
The model presented in this paper provides an important insight into the phenomenon of disintermediation of auctioneers. It attributes the increments in traders’ estimated matching probabilities in disintermediated market to the evolution of the stable steady-state equilibrium at complete disintermediation. However this paper does not negate the chances of evolution of the stable steady-state equilibrium at complete auction-intermediation and the existence of locally stable market equilibrium at simultaneous realization of intermediation and disintermediation. The paper rather confirms inevitability of auction-intermediation in case of traders’ estimated matching probabilities going down to a certain threshold. This might encourage auctioneers to adopt strategies for reducing trading agents’ estimated matching probabilities. Such strategies could be put into action by reengineering an existing auction mechanism to an extent that spontaneously outperforms the old mechanism by enhancing efficiency and trustworthiness of the transaction process. The increasing trend of disintermediation in the Indian tea market has prompted the Ministry of Commerce and the Tea Board of India to reengineer the prevailing manual outcry auction process that started in this industry long back in 1861. The six geographically spread main tea auction centers (Guwahati, Siliguri, Kolkata, Coimbatore, Coonoor and Kochi) of the country have been planned to bring to the ambit of a common e-auction platform. The aim of this initiative is to increase efficiency of auction mechanism by standardizing processes across auction centers, reducing transaction time, providing more flexible auction sessions, ensuring transparency, establishing a more robust price discovery mechanism and stopping collusion between bidders. Nevertheless, the new format of e-auction failed to attract a large section of traders to whom it was piloted in December 2008 and notably complaints were raised against its user-friendliness. But the implementation authority did not treat the complaints seriously as they had anticipated the initial hindrance to be obvious since a new transaction process was replacing a century-old process that had been deeply rooted to the trading culture of the market. However, this is not the first initiative to implement e-auction in the Indian tea market. Earlier in 2004 a similar attempt by the Tea Board failed and the expensive electronic-auction software developed by top-class business solution providers had to be shelved. The main cause of failure was reckoned to be in the business process of the software system that was merely an electronic replica of the old outcry process. The Board and the ministry are optimistic about the new software system as the technology behind it has shifted to a more powerful web-based platform than the previous one. The level of optimism is so high that the ministry expects nearly 5–10% of the private sales to be snatched by e-auction. We have to wait for the future to see whether the reengineered auction mechanism will really stop disintermediation in the Indian tea market. However, unlike relational contracts, auctions fail to cater the vital scope of information exchange at the operational level. In this context, the auctioneers may be suggested to device auxiliary mechanisms for information exchange to confront disintermediation. If such mechanisms are not devised, no matter how efficient the auction process may be, the risk of disintermediation will be unavoidable in a market where buyers and sellers get the scope of repeated interactions.
5. Conclusions Lu and McAfee (1996) speculated evolutionary stability of auction over bargaining, although several instances of disintermediation of auctioneers have been recorded worldwide over years. We have illustrated one such case of disintermediation
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from the Indian tea market where the options of auction-intermediation and bargaining-based supply chain contracting coexist. To resolve the conflict between Lu and McAfee (1996) and the phenomenon of disintermediation, we have analyzed a market model of homogeneous buyers and sellers having both the options of auction-intermediation and supply chain contracting and found out the possibility of occurrences of either of the two unique evolutionary stable steady-state market equilibria: one at complete auction-intermediation and the other at complete disintermediation. We have also identified a unique locally stable steady-state market equilibrium that realizes both intermediation and disintermediation simultaneously. It has been shown that evolution process of these market equilibria is controlled by the matching technology of the disintermediated market. The matching technology has been rendered with a suitable information system and a pair of identity-based dynamic decision variables: buyer’s and seller’s estimated matching probabilities. It has been found that if the values of these matching probabilities are very low auction-intermediation becomes evolutionary stable over disintermediation and the reverse for the high values of the matching probabilities. The model has also earmarked the limiting values of these probabilities for ensuring occurrences of auction-intermediation and disintermediation. The practicality of the modeled matching technology of the disintermediated market has been justified with a hypothesis based on the data from the Indian tea market. Trading agents’ estimated matching probabilities could be contemplated to act as the parameters for quantifying the qualitative concept of business relationships. We hope that this idea would provide initial impetus for using the concept of estimated matching probabilities in empirical research on buyer–seller relationships. To overcome the restraint of the assumption of homogeneous buyers and sellers, a game of heterogeneous players could be selected in future study for capturing the asymptotic inequality of market system. The inherent advantage of auction over bargaining in terms of its ability to discriminate among buyers and to choose the highest value buyer could also be incorporated in the environment of random matching. The hypothesis of the practicability of the proposed matching technology in the disintermediated market stands upon a set of data pertaining to the Indian tea market. We emphasize on the need to test the hypothesis in context of other markets since generalizability of results is always of concern in research. We hope that replication and extension of the present work could make valuable contributions to the research in supply chain disintermediation. Finally, the challenge is to answer how the intermediaries might confront disintermediation and retain their positions in supply chains. Overall, the present paper has attempted a small advancement to the understanding of supply chain disintermediation. We hope that other researchers will contribute more to this area.
Acknowledgements The authors thank three anonymous referees for their constructive comments and suggestions. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ejor.2010.04.035. References Bailey, J.P., 1998. Intermediation and Electronic Markets: Aggregation and Pricing in Internet Commerce. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA. Cohen, M.A., Ho, T.H., Ren, Z.J., Terwiesch, C., 2003. Measuring imputed cost in the semiconductor equipment supply chain. Management Science 49 (12), 1653– 1670. Dutta, S., Sarmah, S.P., 2009. An analysis of supply chain coordination in a multiagent market. International Journal of Operational Research 6 (4), 475–499. Gellman, R., 1996. Disintermediation and the internet. Government Information Quarterly 13 (1), 1–8. Ghosh, R., Singh Deo, A., 2006. Tea Statistics 2005. J. Thomas & Company Pvt. Ltd., Kolkata, India. Gunasekaran, A., Nagi, E.W.T., 2004. Information systems in supply chain integration and management. European Journal of Operational Research 159 (2), 269–295. Gurnani, H., Mengze, S., 2006. A bargaining model for a first-time interaction under asymmetric beliefs of supply reliability. Management Science 52 (6), 865–880. Hines, W.W., Montgomery, D.C., Goldsman, D.M., Borror, C.M., 2003. Probability and Statistics in Engineering. John Wiley & Sons (Asia) Pte. Ltd., Singapore 129809. Hoffman, T., 1995. No More Middleman. Computerworld. Johnson, B., 2003. Quantifying and Managing Supply Risk and Flexibility at Agilent Technologies. Teaching Case, Stanford Graduate School of Business, Stanford, CA. Krause, D.R., Terpend, R., Petersen, K.J., 2006. Bargaining stances and outcomes in buyer–seller negotiations: Experimental results. The Journal of Supply Chain Management 42 (3), 4–15. Lu, X., McAfee, R.P., 1996. The evolutionary stability of auctions over bargaining. Games and Economic Behavior 15 (2), 228–254. Mas-Colell, A., Whinston, M.D., Green, J.R., 1995. Microeconomic Theory. Oxford University Press, New York. Nachbar, J., 1990. Evolutionary selection dynamics in games: Convergence and limit properties. International Journal of Game Theory 19, 59–89. Nash Jr., J.F., 1950. The bargaining problem. Econometrica 18 (2), 155–162. Pinto, J., 2000a. Disintermediation-II: The Customer Perspective.