- Email: [email protected]
Knowledge is power
European
Journal
of Political
Economy
5 (1989) 161-176.
KNOWLEDGE Informational
IS POWER
Precommitment Gregory
University
North-Holland
in the Capitalist
Firm
K. DOW*
ofAlberta, Edmonton, AB T6G 2H4. Canada
Workers often derive valuable information from their production activities, and may capture a portion of the firm’s quasi-rent by threatening to withhold this information. A non-cooperative bargaining model of this situation yields the Shapley value when organizational roles are randomly assigned. If the ex post bargaining outcome cannot be undone by extracting ex ante payments from new employees, an employer will precommit the firm to a hierarchical structure where information flows up to the employer, who then chooses the firm’s production plan and serves as residual income claimant. Because superiors do not internalize the impact of informational precommitments on their subordinates, this structure may be Pareto inefficient.
1. Introduction Any production activity generates information as well as physical output, because workers learn about the state of the world as they engage in purposive effort [Arrow (1974, p. 42)]. Such information typically has three features: (a) it is a valuable resource for managerial decision-making; (b) it comes in the form of private signals; and (c) it is impossible to compel signal revelation through binding contracts. These conditions create a bargaining problem, because workers can threaten to withhold information unless their employers meet side payment demands. Consider the predicament of an entrepreneur who plans to invest in a specialized physical plant with a low salvage value. The workers hired to operate this plant may be able to capture some quasi-rent by threatening to suppress the knowledge acquired in the course of production activities.’ Unless the entrepreneur can extract ex ante payments from job applicants which completely offset this ex post leakage of quasi-rent, the entrepreneur will fail to appropriate the full social return from the investment. *I would like to thank Murat Sertel, Charles Blackorby, and two anonymous referees for helpful comments on an earlier draft. All opinions are those of the author. ‘Ex post opportunism of this sort figures prominently in the literature of transaction cost economics [Klein, Crawford, and Alchian (1978), and Williamson (1979)]. 017&2680/89/$3.50
cc’) 1989, Elsevier Science Publishers
B.V. (North-Holland)
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Difficulties in arranging for such ex ante compensation make it attractive for an entrepreneur to create an information system that limits ex post worker bargaining power.’ Such precommitment incentives can explain various observed features of capitalist firms, including the assignment of residual income and managerial prerogatives to capital suppliers rather than workers; the use of hierarchical information channels; the bias toward ‘deskilling’ of workers identified by Braverman (1974) and Noble (1977); and the efforts of capitalists to guarantee themselves an essential role in the production process [Marglin (1974)]. The same contractual difficulties that motivate precommitment strategies in the capitalist firm can also undermine the viability of labor-managed firms with marketable membership rights [Sertel (1982), and Dow (1986)]. I examine these issues in the context of a non-cooperative bargaining model [Rubinstein (1982), Gul (1986), Sutton (1986), and Binmore and Dasgupta (1987)]. Such models have already been used to study several related organizational phenomena, including the emergence of self-enforcing authority structures [Dow (1988a)] and the use of credible tiring threats to discipline workers [Skillman (1987)]. In the sealed envelope game constructed here, information is passed sequentially from one player to another in exchange for utility side payments. At the close of bargaining, the employer chooses a production plan in light of all available information and collects the resulting quasi-rent. Since I have recently treated private information as a bargaining resource using cooperative game methods [Dow (1988b)], it is appropriate to sketch out the distinctive features of the non-cooperative approach. One advantage of the latter is that the Pareto efficiency of the bargaining outcome ~ specifically, the result that all information is revealed ~ can be derived as an implication of the equilibrium strategies, and need not be imposed axiomatically. Another benefit is that an extensive-form model illuminates the strategic implications of organizational decision-making procedures, including conventions governing the sequence of play. Finally, the equilibrium payoffs differ in the two models: the cooperative game analysis of Dow (1988b) employed Harsanyi’s (1963) extension of the Nash bargaining solution, but 1 shall show that with random assignment of organizational roles, the Shapley value is the unique equilibrium payoff vector for the sealed envelope game.3 Section 2 establishes the existence of a unique perfect equilibrium for the ‘Williamson (1985, pp. 32-35) makes the related point that when contractual safeguards against ex post opportunism are unavailable, the parties to a transaction will invest in assets which are less relation-specific. ‘In Dow (1988b), the organization is a partnership where each player has a fixed nominal claim on the firm’s quasi-rent, In the sealed envelope game, the owner of the firm has a nominal claim on all quasi-rent, but side payments can be extracted from the owner by subordinates through commitments to take-it-or-leave-it demands.
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163
sealed envelope game. Section 3 shows that this equilibrium generates the Shapley value when each sequence of play occurs with equal probability. In section 4, I introduce a precommitment stage where the firm’s owner can unilaterally commit the firm to a particular information system by investing in a corresponding physical plant. When ex post bargaining outcomes cannot be undone through ex ante transfers and the returns to information are diminishing, the owner will impose a fixed hierarchical pattern of information flow where the owner’s payoff is the expected quasi-rent achievable if all subordinates suppress their private information. Section 5 shows that this precommitment behavior is consistent with several stylized facts about the organization of capitalist firms. 2. The sealed envelope game The list of players is N = { 1 . . . n}. Players 1. i- 1 are called the subordinutes of player i, and players i + 1 n are called i’s superiors. Player n is the owner of the firm. The owner chooses the tirm’s production plan and collects any resulting quasi-rent. Each player i E N receives a signal yip Yi prior to n’s selection of the production plan. I define the value V(S) of each non-empty coalition SG N to be the owner’s expected quasi-rent (computed before any signals are revealed) in the situation where the owner will observe only the signals yi of ieS before choosing the production plan. Except where noted, I use the normalization 1/(4)=0 and V(N)= 1. I’(S) is thus the maximum ex ante bribe that the owner would be willing to pay the members of S for truthful revelation of their signals, given the unavailability of signals from the members of N -S.4 This function is monotonic in the sense that V(S) 5 V(T) whenever SC T [Marschak and Miyasawa (1968)]. I assume that utility is transferable among the players in N. In this section I consider an extensive-form bargaining game called the seuled envelope game, where: (a) Nature sends each i E N a sealed envelope containing the signal yi E Yi. (b) Player 1 states a demand vi~[O, l] as the price of the envelope containing yi. (c) At each of the subsequent stages i = 2.. n - 1, player i chooses d, E {A, R}. If d,=A, then i accepts the demand vi-1 and purchases all envelopes held by i- 1 at this price. If di= R, then i- l’s demand is rejected and the envelopes held by i- 1 are destroyed. Player i then states a demand vi E [0, l] for his or her envelope(s). (d) Let SC N be the set of envelopes held by the last player n after n has chosen d,. Player n opens these envelopes and chooses an optimal 41f n$S. then V(S) is computed on the assumption signal in choosing the firm’s production plan.
that
the owner
ignores
his or her own
G.K. Dow, Knowledge is power
164
production plan payoff is V(S).
in light of the signals
yi for id S. The owner’s
expected
The envelope device restricts attention to the ex ante features of the information system. In this model, subordinates have bargaining power because they control access to information, not because they know the content of this information. Because truthful reports are no more costly to subordinates than false ones, there is no motive for dissembling in the model. However, subordinates cannot be compelled to disclose their information by means of binding contracts. Thus they may refuse to acquire the relevant information, or may opt not to pass it along to their superiors. This capacity to suppress valuable information parallels the potential threat of specialized factor suppliers to withhold physical inputs.5 If the envelope concept were to be dropped, so that player i’s move could be conditioned on i’s private information, then i’s superiors would attempt to infer the content of the signals available to i from the demand ui. Also, since signals might be correlated across players, each player i would try to infer from his or her private information the maximum price that player i+ 1 might be prepared to pay for this information. Analysis of a sequential equilibrium for a model of this sort would thus require a detailed description of player beliefs and their evolution during the course of the game, a task well beyond the scope of the present paper. The players participate in the bargaining procedure in a fixed order, determined by their location in the vertical chain of command. This is a natural assumption for organizations where the formal channels of information flow are hierarchical. In such organizations, each player controls access to his or her own information as well as any additional information that may be acquired from that player’s subordinates. Section 4 endogenizes the order of play and shows that the owner will precommit the firm to a fixed bargaining sequence of this type. The take-it-or-leave-it bargaining process at each stage is analytically convenient but inessential. By having subordinates make all-or-nothing demands, I bias the payoff distribution in favor of the lower echelons within the organization. A more complex bargaining procedure might enable superiors to capture a greater share of the available quasi-rent, but should leave the broad outlines of the analysis intact.‘j The assumption that each player moves only once in the process can be justified informally in terms of ‘For references to the literature on bargaining among suppliers of physical inputs, see Dow, (1985, 1988b). ‘So long as the bargains struck at each stage result in the transfer of the subordinate’s information to the superior, the total expected quasi-rent of the firm will be unaffected by the details of the bargaining process. It is crucial to the analysis in sections 4 and 5, however, that superiors do nor fully internalize the value of the information available to their subordinates i.e., subordinates must capture some part of the overall quasi-rent k’(N) through their control over private information. Most plausible bargaining schemes will have this property.
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is power
165
time pressures: bargaining has an opportunity cost in the form of foregone output, and information can rapidly become obsolete in a turbulent environment. I make no attempt here to model these time costs in a rigorous fashion. Before the equilibrium of the sealed envelope game can be characterized, some additional notation is needed. Player i’s move will be conditioned on the history hi, where (1)
The extended history &-(hi, di) consists of hi along with the decision by i to accept or reject the demand of i - 1. The set M(&) of players whose envelopes are held by player i following the choice of d, is defined recursively by ifdi=A
M(Li)~{ijUM(Li_l)
if di = R,
={i}
where M(6,) z { 11. from j’s immediate announced by their Player i’s payoff net of the payment ui=ci-ci_1,
(2)
Thus if j E M(&) and j < i, it must be true that all players superior through player i have accepted the demands subordinates. ui is the payment (if any) received from i’s superior i+ 1, (if any) made to i’s subordinate i- 1. That is, where
6, E vi
ifdi+r=A;
d,-0,
otherwise.
(3)
A strategy for player iz2 is some function (To: H,+{A, R} x [0, l] mapping from the set of possible histories hi into the set of possible moves (di,vi). A strategy for player 1 is simply a number 0, = u1 E [0,11. For player n, it will be convenient to introduce a dummy player n+ 1 such that d n+1 =A
if V[M(I;,)]
d ll+1--R
otherwise.
2 u,; (4)
In equilibrium player n will always demand V[M(&)], and this demand will always be granted by n + 1. I adopt a tie-breaking assumption needed to ensure the existence of an equilibrium.
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G.K. Dow,
Knowledge is power
A.1. For all iEN, if i is indifferent chosen. I also assume that each player’s which he or she is a member: A.2.
between
information
For all id N and any S containing
di=A
and d,=R,
is valuable
i, V(S) - V[S-
then d,=A
to any coalition
of
{i}] >O.
Proposition 1. The unique perfect equilibrium for the sealed envelope described by the following strategies for each i E N: di+,=A,
is
game is
if
V[(i+l...n)uM(&)]-V(i+l...n)zvi;
di+l=R,
otherwise;
(54
and (5b)
The equilibrium
payoff to each i E N is
ui=V(i...n)-V(i+l...n)>O. Proof. Remark.
(6)
See appendix. For i = n, we set V(i + 1 . . . n)-
V(4)=0
in (5b) and u,= L’(n)>0
in
(6). Remark. Player i’s equilibrium observes the set M(hi_ i) and history hi are redundant.
strategy can be implemented so long as i the demand vi_ ,. All other aspects of the
These results are quite intuitive. According to (5a), i+ 1 information M(&) controlled by the subordinate player i only does not exceed the marginal value of this information to ji+ I . . r~} consisting of i’s superiors. By (5b), player i makes that extracts the full marginal value of the information coalition. In equilibrium all players purchase the information their subordindates, and receive as a net payoff the marginal own signals to their superiors.
purchases the if its price vi the coalition a demand vi M(&) to this controlled by value of their
G.K.
3. Random role assignments
Dow,
Knowledge
is power
167
and the Shapley value
The Shapley value [Shapley (1953)] has often been interpreted as arising through a sequential process of coalition formation, where each player’s payoff is the marginal contribution of that player to the existing coalition. We can obtain a result of this type using Proposition 1. Define a permutation t of the player set N to be an ordered sequence of players (ri . . . z,) such that each ZjE N and Zj# zk for all j # k. Now consider the modified sealed envelope game where the players move in an arbitrary sequence z, but where each player’s informational resources remain unaffected by this change in the order of play. It is clear from (6) that if zj=i, so that player i is the jth mover, i’s payoff will be ui= V(Tj... ~.,)-_(Zj+1...Z,)>O.
(7)
Using (7) we can derive the expected payoff to player i when each permutation z has equal probability. Randomization among player sequences could arise in a partnership where the order of play is determined by the random arrival times of the players’ signals. Randomization could also be interpreted as a Rawlsian ‘veil of ignorance’, reflecting an initial situation where the organizational roles of the players, including the identity of the owner, have not yet been determined. Either case provides a non-cooperative rationale for the Shapley value. Proposition paq@f’to
2. player
[fall
permutations
where s is the cardinality Proof.
Follows
z have equal
probability,
then the expected
i E N is
of’ the set S.
from (7) upon taking
an expectation
over r; see Owen (1982,
p. 197). Remark.
followed
The coefficient (s- l)!(n-s)!/n! is the probability in (zr . T,,) by the members of S- {i}.
that
player
i is
Averaging across all permutations of the player set, player i’s payoff pi is the expected contribution of i’s information to i’s superiors, using as probability weights the likelihood that each possible coalition of superiors follows player i. Gul (1986) has previously derived the Shapley value using a related noncooperative bargaining approach. When two resource owners meet in Gul’s
168
G.K. Dow, Knowledge is power
model, the potential buyer of a resource commits to a price offer. This reverses the convention used in the sealed envelope game, where the potential seller of information commits to a demand. More significantly, in Gul’s model a resource owner who rejects an offer in period t rejoins the pool of potential traders in period t+ 1, while in the sealed envelope game each seller is limited to a single transaction opportunity. Gul’s model can have inefficient equilibria, and a Pareto efficient equilibrium may not exist. When efficient equilibria exist and the characteristic function displays value additivity, the payoff vector approaches the Shapley value as the discount rate approaches zero. By contrast, the sealed envelope model involves a finite horizon without discounting, and Proposition 2 requires only that the function C’be monotonic. The interpretations assigned to the characteristic function also differ. Gul’s characteristic function states the payoff that each coalition can guarantee itself via unilateral production activities. In the sealed envelope game, however, the players are already committed to a common production process. Only one player (the owner, as designated by the relevant permutation r) has a direct claim on the quasi-rent generated by these production activities. Because non-owning players or coalitions cannot produce unilaterally, their payoffs derive entirely from the side payments they can extract from the owner.?
4. The precommitment
game
The properties of the signals received by production workers and front-line supervisors are heavily influenced by the layout of a firm’s physical plant, which is determined in turn by the investment decisions of the owner before production activities begin. The owner may also be able to restrict information flows within the firm by requiring upward transmission of reports along lines of vertical authority, or by punishing subordinates who refuse to ‘work through channels’. Such decisions will be made with an eye to the bargaining environment that will arise once the production plant is in place and information channels have been assigned.* I model this situation by a precommitment game played prior to the sealed envelope game of sections 2 and 3. Let the firm’s information system be represented by a vector of parameters q = (q I . q,) E @, where Cp is a compact set. The notation V( .I q) will be used to indicate the dependence of the characteristic function on the information in ye for each S. I assume that system adopted, where V(S 1y) is continuous ‘In the sealed envelope game, two disjoint coalitions S and T cannot simultaneously guarantee themselves V(S) and V(T) by their own unilateral actions, and hence the function V is typically nol superadditive. “Dow (1985) provides a related analysis of precommitment to a favorable bargaining environment by capital suppliers.
G.K. Dow, Knowledge
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is power
A.2 in section 2 holds for every UE@. The set-up cost C(q) of the system additive in the individual player parameters: c(rl)=
C
all iE N,
with Ci(vi) 20,
ci(Vi)>
9 is
(9)
ieN
where each Ci is continuous. C(q) includes expenditures for the physical plant associated with 9, as well as the cost of worker training.’ Training simultaneously shows workers how to produce output and how to detect the signals generated by the system q.l” The rules of the precommitment game are as follows:
(4 The owner n can unilaterally
choose (q,r) by paying the cost C(q). The sealed envelope game is then played with payoffs given by (7). (b) Alternatively, the owner may choose only (v,,r,) and delegate the choice to player n-l. In this case, the owner pays the of (VI ...~n_l,rl...rn_l) cost C,(v,) only. (4 At each following stage i 5 n - 1, if the entire vector (r], r) has not already been chosen, player i can choose (rr . . . vi, TV.. . zi) by paying the cost F;i;Cj(Vj)Th e sealed envelope game is then played with payoffs given
(4 Alternatively, (Vl...Vi-l>
(4
T1
player i may choose only (qi,si) and delegate . . .zi- 1) to player i- 1. In this case, player
only. If all players iz2 delegate, player 1 has chosen ql.
then the sealed envelope
the choice of i pays Ci(qi)
game is played
after
The relations of superior and subordinate will henceforth be defined by the order of play at the precommitment stage, since the order of play in the sealed envelope game is now endogenous. I characterize the equilibrium outcome of the precommitment game under the following assumptions. A.3 (Diminishing Returns to Injbrmation). Wu all
For every ‘1E @,
(i)I111--I/(SI~)>I/CTu(i)lql-V(TIrl), S,TGN
and
iEN
such that
i$S,i#T,
and
ScT.
‘I retain the normalization )/(d/r))=O on the assumption that the choice of information system does not influence the expected quasi-rent available to the owner when all signals are suppressed. A corresponding normalization is applied to the owner’s set-up cost C,(n,). There is no need to normalize the set-up costs incurred by ijn1, since the payoffs of these players will appear in section 4 only as quasi-rent increments of the form given by (7) and hence are unaffected by the zero point of V. The normalization V(N)= I used in section 2 is no longer needed and will be dropped, so as to permit comparison among the possibly different productivities V(N 1a) of alternative information systems, “1 assume that the owner cannot train redundant workers in order to bring about competitive information supply at each subordinate level within the firm.
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170
is power
This states that the marginal value of a player’s coalition to which it is contributed expands. A.4 (Immunity of Superior Coalitions).
information
declines
as the
For every iE N,
V(i.. . n ) q) = V( i . . . n 1q’), all
v,~I’E@
such that
(vi.. . qn) =(?I..
. $,).
This states that the quasi-rent obtainable unilaterally by the coalition {i.. . n) depends only upon the parameters (vi.. . q.). Precommitments by subordinate players cannot affect the value of superior coalitions. Henceforth I drop the notation V(i.. . n 1ye)in favor of V(i.. . n 1vi), where yli= (vi.. . q,), to emphasize parameters of i’s that V(i.. . n 1q) does not depend upon the information subordinates. It should be noted that the precommitments of superiors can still influence the value of coalitions involving subordinates. A.5 (Tie Breaking). precommitment
When any player iE N is indifferent and delegation, delegation is chosen.
between
Proposition 3. All possible decisions are delegated. Also, every perfect brium outcome (n*, z*) has the following properties for each i E N. 7: = i nT maximizes
(the sealed envelope game is played in natural order);
full equili(104
the expression
V(i.. . n I vi, $+ 1) - Ci(qi)
over the set
{tli:(YI1...~i~l,tli,tlic+l)EQ)
The equilibrium
forsome
(VI...?~-I)).
(lob)
payoff of player i is
V(i.. .n I VT)- V(i+ 1. . . nl ij~+l)-Ci(n~.
(1Oc)
Proof Each player i who has an opportunity to move in the precommitment game will strictly prefer ri = i to any rj= i with j < i, due to diminishing returns to information (A.3). Given ~7 = j for all jzi, player i will always choose to delegate, since due to (7) and the immunity of superior coalitions (A.4) i’s payoff is independent of the decisions made by i’s subordinates. Delegation also enables i to avoid the cost of choosing the subordinates’ information parameters (A.5 is used in case of indifference). Thus all players delegate and (10a) holds. Since the sealed envelope game will be played in natural order, player i chooses vi to maximize the payoff in (6) net of the precommitment cost Ci(qi), given the previous commitments (vi”+ 1.. . ~3. Results (lob) and (10~) follow from (6) upon noting that V(i+ 1.. n) in (6) is independent of ‘li by A.4. Q.E.D. The preceding
argument
is valid so long as each player’s reservation
utility
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171
constraint is non-binding. The payoffs in (6) are shares in firm quasi-rent, and hence market opportunity costs at the production stage are already accounted for. Thus, we need only check whether (10~) is non-negative in equilibrium. Due to A.2, V(i.. . n (ijr)- V(i+ 1.. . n 1qT+l) >O, so the net payoffs in (10~) are non-negative provided that the precommitment costs C,(qT) 20 are sufficiently small. If (10~) is negative for some i, however, it will be necessary to impose reservation utility constraints explicitly. Whenever (10~) is strictly positive for some i, a queue of job applicants will arise for the position of player i. Free entry of new firms, if permitted, would drive (10~) to zero in the case of player n (the owner); on the other hand, if (10~) is negative for player n the firm will not be established at all. Note that because Proposition 3 requires only non-negativity and additivity of the costs C,(qJ, a zero net payoff to the owner can be consistent with strictly positive equilibrium payoffs to some or all subordinates. Finally, consider the set of feasible deviations from equilibrium by player i that leave the productivity of the firm’s information system and its cost to player i unchanged: ~i(~*)-{9i:V]=(Yli,~*i)E~,I/(NI’I)=I/(NIrl*),
Corollary
to Proposition
3.
For every
iE N, r]F minimizes
~(NI~]i,~+i)-l/(i...nlr?i,ri”+l) Proof.
Immediate
and
over
from (lob) and the definition
the expression
qiE@i(v*).
(11)
of @Jv]*).
In equilibrium, each player i minimizes the incremental value of the information held by the subordinate coalition { 1. i- l}, within the class of information systems having the same cost and productivity characteristics as the equilibrium system.”
5. Precommitment The main follows.
and the capitalist firm
organizational
implications
of section
4 can be summarized
as
(A) Let hierarchical relations within the firm be defined by the superior’s greater ability to precommit the firm to specific patterns of information acquisition and exchange. Then once all precommitments have been made, information will flow up from subordinates to superiors, while side “A deviation from equilibrium by player i might trigger deviations by some or all players in the set of subordinates { 1 i - 1 1, but this induced cascade of deviations has no bearing on i’s payoff due to A.4.
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172
(B)
(C)
(D)
(E)
payments inducing information revelation will flow in the reverse direction. The first mover in the precommitment game will take on the role of owner in the sealed envelope game. This player will choose the firm’s production plan and serve as the firm’s residual income claimant. The owner’s equilibrium payoff in the sealed envelope game (gross of precommitment costs) is the expected quasi-rent obtainable by the owner when all subordinates suppress their information. More generally, player i captures a share of quasi-rent determined by the marginal value of i’s signal to the coalition of i’s superiors {i + 1 . . . n}, in the situation where all of i’s subordinates suppress their information. Each player i internalizes the effect of his or her own precommitment decision on the coalition consisting of i and i’s superiors. However, player i does not internalize the effect of such precommitments on i’s subordinates. These decisions are therefore likely to be Pareto inefficient. Player i’s precommitment minimizes the incremental value of the information controlled by i’s subordinates, holding constant the overall productivity of the firm’s information system and the set-up cost incurred by player i. All else equal, precommitments tend to redistribute quasi-rent from subordinate players to their superiors.
These results are consistent with several stylized facts about the organization of production in capitalist firms. For example, the ‘deskilling’ hypothesis advanced by Braverman (1974) and Noble (1977) asserts that capitalist firms attempt to reduce the skill content of production-level jobs by redesigning the production process. This tits nicely with the prediction that players at each stage make precommitment decisions that minimize the value of the information controlled by their subordinates. The model is also consistent with Williamson’s observation that experienced workers are sometimes reluctant to transfer their technical knowledge to less senior trainees: ‘The success of on-the-job training is plainly conditional on the information disclosure attitudes of incumbent employees . . . [IIncumbents are in possession of a valuable resource (knowledge) and can be expected to fully and candidly reveal it only in exchange for value. The danger is that incumbent employees will hoard information to their personal advantage.. .’ (1975, p. 63). In the precommitment information of their constant, increased come at the expense Finally, the results that
game, superiors derive no personal benetit from the subordinates. Moreover, when firm productivity is held access to information by subordinates (trainees) must of their superiors (incumbent employees). provide a formal basis for Marglin’s controversial thesis
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is power
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‘[T]he capitalist division of labor . . . was the result of a search not for a technologically superior organization of work, but for an organization which guaranteed to the entrepreneur an essential role in the production process.. . (1974, p. 62). The precommitment game models the role of the owner much as Marglin suggests. Since the owner’s equilibrium payoff is the quasi-rent obtainable without the use of information controlled by subordinates, the owner’s incentive at the precommitment stage is to devise a production system that concentrates valuable information at the top of the managerial hierarchy. The benefits flowing to subordinates from informational decentralization within the firm will not be internalized by the owner, and will play no role in the owner’s investment decisions. One potential objection to this analytical framework must now be addressed. By auctioning off the right to each subordinate job once (q,r) has been chosen, the owner would obtain some ex ante compensation for the leakages of quasi-rent that will occur in the course of the sealed envelope game. In principle, this procedure might permit the owner to completely undo the ex post bargaining result. Under competitive conditions the winning bids would sum to V(N 1q), giving the owner a net payoff of V(N 1q) - C(u) in the precommitment game. The owner could then choose a Pareto efftcient information system at the precommitment stage and appropriate all returns from this investment by collecting application fees, thus avoiding the problem of compelling signal revelation through binding contracts [Dow (1983, Crawford (1988)]. For various reasons, lump sum payments to a firm by newly hired employees are seldom observed.” Consider, for example, a scenario where workers observe the information system chosen by the owner only after they have been trained for their jobs, and where the owner cannot be penalized if workers discover ex post that the characteristics of this information system have been misrepresented. Dishonest owners could then demand ex ante fees from job applicants by promising a valuable information system, when in fact a worthless system (one giving no ex post bargaining power to workers) had been installed.’ 3 Moral hazard problems of this sort could prove fatal to “Apart from the informational asymmetries discussed in the text, personal wealth constraints along with capital market imperfections stemming from the limited liability of workers could make it impossible for workers to finance the purchase of a present claim on future quasi-rents (I thank Gil Skillman for this point). Another problem is posed by the understandable reluctance of entrepreneurs to make public all pertinent details of their investment ideas [Marglin (1982)]. Perhaps the most important obstacle to the creation of property rights in jobs, however, is the fact that this would undermine the use of tiring threats as a worker discipline device by employers [Shapiro and Stiglitz (1984), Bowles (1985) and Skillman (1987)]. 13The owner cannot expect to obtain compensation for leakages of quasi-rent once training has occurred, because the worker will then be costly to replace, and the same bargaining problem would arise with the replacement worker. Credible disclosure of the true information system through training occurs ‘too late’ from the owner’s point of view.
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an auction market for jobs, and might motivate the establishment of hierarchical capitalist firms along the lines described in section 4. Similar market failures may help to explain the relative rarity of labormanaged firms (LMFs) in Western market economies. It is well known that an LMF with marketable membership rights will have comparative static and efficiency properties identical to those of a capital-managed firm with marketable common stock [Sertel (1982), Dow (1986)]. Marketability of membership rights allows current LMF members to extract ex ante compensation for the quasi-rent that will be appropriated by new workers after their acceptance into the lirm. However, if current members have better information about the future income of the firm than new members, or know more about the internal bargaining position that a new member will ultimately enjoy, membership markets may fail for essentially the same reasons that capitalists cannot sell jobs to workersi The capitalist firm and the LMF share the problem that the current ‘owners’ (whether capitalist investors or incumbent workers) cannot completely forestall the leakage of quasi-rents to incoming workers. Policy measures similar to those that would facilitate the purchase of jobs by employees in capitalist firms might therefore prove useful in the context of the labor-managed firm as well. Measures of this sort, which could include the provision of credit, insurance, or information to prospective job purchasers, appear to warrant further investigation by students of organizational design.
Appendix Proof of Proposition 1. Consider i = n. In this case (5a) reduces to (4), which holds by assumption. If u,> V[M(f;.)] then u,sO, while if d,=R and V(n) >_v,,>O, then u,=u,>O. Such a u,, exists by A.2. Therefore in equilibrium ~CWk,)l g u, and 4 +1--A. In this case U, is strictly increasing in v,, so v,, = V[M(h,)] as stated in (5b). [Note that for i=n, {i+ 1 . n} = {4} and
V(4) = 0.1 We proceed by backward induction. Assume that (5a) and (5b) hold for some i 2 2; we then show that these results hold for i - 1. Consider (5a) first. that (5a) and (5b) hold If di = A, then since di+ 1 = A due to the hypothesis for i, ui=ui-vi-,
=V[{i+l...
n}uM(I;,)]-V(i+l...n)-ui_,
“‘The experience of plywood cooperatives in the U.S. with dishonest promoters who sold worthless shares to prospective worker-owners is instructive [Bellas (1972, pp. 11521)]. A viable market for LMF membership rights would need to protect applicants against such fraud, much as conventional stock markets guard against insider trading schemes.
G.K. Dow, Knowledge
= V[{i... ui = ui =
~} uM(l;i_,)]-I/(i+l
is power
. ..n)-Ui_.,
175
while if d,=R
then
V(i . . . n) - V(i + 1 . . . n).
Using A.l, di=A
if
I’[{i...
di = R
otherwise,
n}uM(h^i_,)]-V(i...n)~vi_,;
verifying (5a) for i - 1. If V[{i...n) u M(~i~,)]-V(i...n)<~i_Ir then u,_r~O since di=R. HOWever, if di_l=R and V(i-l...n)-V(i...n)>uiP,>O, then ui_l=oi_,>O. Such a uiP I exists by A.2. Thus in equilibrium V[(i.. .n} u M(Gi_ 1)] V(i . . . n) 2 vi _ 1. In this case di = A, so that ui_ 1 is strictly increasing in ui- 1 and (5b) must hold for i - 1. This establishes (5a) and (5b). Finally, note that (5a) and (5b) together imply di+ 1 =A for all ie N, and hence M(&)= { 1.. .i} for all iE N. It follows from (3) and (5b) that the equilibrium payoffs are given by (6). Q.E.D.
References Arrow, K., 1974, The limits of organization (Norton, New York). Bellas, C., 1972, Industrial democracy and the worker-owned firm (Praeger, New York). Binmore. K. and P. Dasgupta, eds., 1987, The economics of bargaining (Basil Blackwell, New York). Bowles, S., 1985, The production process in a competitive economy, American Economic Review 75, 1636. Braverman, H., 1974, Labor and monopoly capital (Monthly Review Press, New York). Crawford, V., 1988, Long-term relationships governed by short-term contracts, American Economic Review 78, 485-499. Dow, G., 1985, Internal bargaining and strategic innovation in the theory of the firm, Journal of Economic Behavior and Organization 6, 301-320. Dow, G., 1986, Control rights, competitive markets, and the labor management debate, Journal of Comparative Economics 10, 48861. Dow, G., 1988a, Self-enforcing authority structures, Unpublished manuscript (Department of Economics, University of Alberta, Edmonton, Alb.). Dow, G., 1988b, Information, production decisions and intra-Iirm bargaining, International Economic Review 29, 57779. GUI, F., 1986, Bargaining foundations of Shapley value, Unpublished manuscript (Graduate School of Business, Stanford University, Stanford, CA). Harsanyi, J., 1963, A simplified bargaining model for the n-person cooperative game, International Economic Review 4, 194220. Klein, B., R. Crawford and A. Alchian, 1978, Vertical integration, appropriable rents, and the competitive contracting process, Journal of Law and Economics 21, 297-326. Marglin, S., 1974, What do bosses do? The origin and function of hierarchy in capitalist production, Review of Radical Political Economics 6, 60-l 12. Marglin, S., 1982, Knowledge and power, in: F. Stephen, ed., Firms, organization and labour (St Martin’s Press, New York).
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is power
Marschak, J. and K. Miyasawa, 1968, Economic comparability of information systems, International Economic Review 9, 137-174. Noble, D., 1977, America by design (Oxford University Press, New York). Owen, G., 1982, Game theory (Academic Press, New York). Rubinstein, A., 1982, Perfect equilibrium in a bargaining model, Econometrica 50, 97-109. Sertel, M., 1982, Workers and incentives (North-Holland, New York). Shapley, L., 1953, A value for n-person games, in: H. Kuhn and A.W. Tucker, eds., Contributions to the theory of games 2 (Princeton University Press, Princeton, NJ). Shapiro. C. and J. Stiglitz. 1984. Eauilibrium unemnlovment as a worker discinline device. 1 _ American Economic-Review 74, 433444. Skillman, G., 1987, Bargaining and replacement in the employment relation, Unpublished manuscript (Department of Economics, Brown University, Providence, RI). Sutton, J., 1986, Non-cooperative bargaining theory: An introduction, Review of Economic Studies 53, 7099724. Williamson, O., 1975, Markets and hierarchies (Free Press, New York). Williamson, O., 1979, Transaction-cost economics: The governance of contractual relations, Journal of Law and Economics 22, 233-260. Williamson, O., 1985, The economic institutions of capitalism (Free Press, New York).
Journal
of Political
Economy
5 (1989) 161-176.
KNOWLEDGE Informational
IS POWER
Precommitment Gregory
University
North-Holland
in the Capitalist
Firm
K. DOW*
ofAlberta, Edmonton, AB T6G 2H4. Canada
Workers often derive valuable information from their production activities, and may capture a portion of the firm’s quasi-rent by threatening to withhold this information. A non-cooperative bargaining model of this situation yields the Shapley value when organizational roles are randomly assigned. If the ex post bargaining outcome cannot be undone by extracting ex ante payments from new employees, an employer will precommit the firm to a hierarchical structure where information flows up to the employer, who then chooses the firm’s production plan and serves as residual income claimant. Because superiors do not internalize the impact of informational precommitments on their subordinates, this structure may be Pareto inefficient.
1. Introduction Any production activity generates information as well as physical output, because workers learn about the state of the world as they engage in purposive effort [Arrow (1974, p. 42)]. Such information typically has three features: (a) it is a valuable resource for managerial decision-making; (b) it comes in the form of private signals; and (c) it is impossible to compel signal revelation through binding contracts. These conditions create a bargaining problem, because workers can threaten to withhold information unless their employers meet side payment demands. Consider the predicament of an entrepreneur who plans to invest in a specialized physical plant with a low salvage value. The workers hired to operate this plant may be able to capture some quasi-rent by threatening to suppress the knowledge acquired in the course of production activities.’ Unless the entrepreneur can extract ex ante payments from job applicants which completely offset this ex post leakage of quasi-rent, the entrepreneur will fail to appropriate the full social return from the investment. *I would like to thank Murat Sertel, Charles Blackorby, and two anonymous referees for helpful comments on an earlier draft. All opinions are those of the author. ‘Ex post opportunism of this sort figures prominently in the literature of transaction cost economics [Klein, Crawford, and Alchian (1978), and Williamson (1979)]. 017&2680/89/$3.50
cc’) 1989, Elsevier Science Publishers
B.V. (North-Holland)
162
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Difficulties in arranging for such ex ante compensation make it attractive for an entrepreneur to create an information system that limits ex post worker bargaining power.’ Such precommitment incentives can explain various observed features of capitalist firms, including the assignment of residual income and managerial prerogatives to capital suppliers rather than workers; the use of hierarchical information channels; the bias toward ‘deskilling’ of workers identified by Braverman (1974) and Noble (1977); and the efforts of capitalists to guarantee themselves an essential role in the production process [Marglin (1974)]. The same contractual difficulties that motivate precommitment strategies in the capitalist firm can also undermine the viability of labor-managed firms with marketable membership rights [Sertel (1982), and Dow (1986)]. I examine these issues in the context of a non-cooperative bargaining model [Rubinstein (1982), Gul (1986), Sutton (1986), and Binmore and Dasgupta (1987)]. Such models have already been used to study several related organizational phenomena, including the emergence of self-enforcing authority structures [Dow (1988a)] and the use of credible tiring threats to discipline workers [Skillman (1987)]. In the sealed envelope game constructed here, information is passed sequentially from one player to another in exchange for utility side payments. At the close of bargaining, the employer chooses a production plan in light of all available information and collects the resulting quasi-rent. Since I have recently treated private information as a bargaining resource using cooperative game methods [Dow (1988b)], it is appropriate to sketch out the distinctive features of the non-cooperative approach. One advantage of the latter is that the Pareto efficiency of the bargaining outcome ~ specifically, the result that all information is revealed ~ can be derived as an implication of the equilibrium strategies, and need not be imposed axiomatically. Another benefit is that an extensive-form model illuminates the strategic implications of organizational decision-making procedures, including conventions governing the sequence of play. Finally, the equilibrium payoffs differ in the two models: the cooperative game analysis of Dow (1988b) employed Harsanyi’s (1963) extension of the Nash bargaining solution, but 1 shall show that with random assignment of organizational roles, the Shapley value is the unique equilibrium payoff vector for the sealed envelope game.3 Section 2 establishes the existence of a unique perfect equilibrium for the ‘Williamson (1985, pp. 32-35) makes the related point that when contractual safeguards against ex post opportunism are unavailable, the parties to a transaction will invest in assets which are less relation-specific. ‘In Dow (1988b), the organization is a partnership where each player has a fixed nominal claim on the firm’s quasi-rent, In the sealed envelope game, the owner of the firm has a nominal claim on all quasi-rent, but side payments can be extracted from the owner by subordinates through commitments to take-it-or-leave-it demands.
G.K. Dow, Knowledge
is power
163
sealed envelope game. Section 3 shows that this equilibrium generates the Shapley value when each sequence of play occurs with equal probability. In section 4, I introduce a precommitment stage where the firm’s owner can unilaterally commit the firm to a particular information system by investing in a corresponding physical plant. When ex post bargaining outcomes cannot be undone through ex ante transfers and the returns to information are diminishing, the owner will impose a fixed hierarchical pattern of information flow where the owner’s payoff is the expected quasi-rent achievable if all subordinates suppress their private information. Section 5 shows that this precommitment behavior is consistent with several stylized facts about the organization of capitalist firms. 2. The sealed envelope game The list of players is N = { 1 . . . n}. Players 1. i- 1 are called the subordinutes of player i, and players i + 1 n are called i’s superiors. Player n is the owner of the firm. The owner chooses the tirm’s production plan and collects any resulting quasi-rent. Each player i E N receives a signal yip Yi prior to n’s selection of the production plan. I define the value V(S) of each non-empty coalition SG N to be the owner’s expected quasi-rent (computed before any signals are revealed) in the situation where the owner will observe only the signals yi of ieS before choosing the production plan. Except where noted, I use the normalization 1/(4)=0 and V(N)= 1. I’(S) is thus the maximum ex ante bribe that the owner would be willing to pay the members of S for truthful revelation of their signals, given the unavailability of signals from the members of N -S.4 This function is monotonic in the sense that V(S) 5 V(T) whenever SC T [Marschak and Miyasawa (1968)]. I assume that utility is transferable among the players in N. In this section I consider an extensive-form bargaining game called the seuled envelope game, where: (a) Nature sends each i E N a sealed envelope containing the signal yi E Yi. (b) Player 1 states a demand vi~[O, l] as the price of the envelope containing yi. (c) At each of the subsequent stages i = 2.. n - 1, player i chooses d, E {A, R}. If d,=A, then i accepts the demand vi-1 and purchases all envelopes held by i- 1 at this price. If di= R, then i- l’s demand is rejected and the envelopes held by i- 1 are destroyed. Player i then states a demand vi E [0, l] for his or her envelope(s). (d) Let SC N be the set of envelopes held by the last player n after n has chosen d,. Player n opens these envelopes and chooses an optimal 41f n$S. then V(S) is computed on the assumption signal in choosing the firm’s production plan.
that
the owner
ignores
his or her own
G.K. Dow, Knowledge is power
164
production plan payoff is V(S).
in light of the signals
yi for id S. The owner’s
expected
The envelope device restricts attention to the ex ante features of the information system. In this model, subordinates have bargaining power because they control access to information, not because they know the content of this information. Because truthful reports are no more costly to subordinates than false ones, there is no motive for dissembling in the model. However, subordinates cannot be compelled to disclose their information by means of binding contracts. Thus they may refuse to acquire the relevant information, or may opt not to pass it along to their superiors. This capacity to suppress valuable information parallels the potential threat of specialized factor suppliers to withhold physical inputs.5 If the envelope concept were to be dropped, so that player i’s move could be conditioned on i’s private information, then i’s superiors would attempt to infer the content of the signals available to i from the demand ui. Also, since signals might be correlated across players, each player i would try to infer from his or her private information the maximum price that player i+ 1 might be prepared to pay for this information. Analysis of a sequential equilibrium for a model of this sort would thus require a detailed description of player beliefs and their evolution during the course of the game, a task well beyond the scope of the present paper. The players participate in the bargaining procedure in a fixed order, determined by their location in the vertical chain of command. This is a natural assumption for organizations where the formal channels of information flow are hierarchical. In such organizations, each player controls access to his or her own information as well as any additional information that may be acquired from that player’s subordinates. Section 4 endogenizes the order of play and shows that the owner will precommit the firm to a fixed bargaining sequence of this type. The take-it-or-leave-it bargaining process at each stage is analytically convenient but inessential. By having subordinates make all-or-nothing demands, I bias the payoff distribution in favor of the lower echelons within the organization. A more complex bargaining procedure might enable superiors to capture a greater share of the available quasi-rent, but should leave the broad outlines of the analysis intact.‘j The assumption that each player moves only once in the process can be justified informally in terms of ‘For references to the literature on bargaining among suppliers of physical inputs, see Dow, (1985, 1988b). ‘So long as the bargains struck at each stage result in the transfer of the subordinate’s information to the superior, the total expected quasi-rent of the firm will be unaffected by the details of the bargaining process. It is crucial to the analysis in sections 4 and 5, however, that superiors do nor fully internalize the value of the information available to their subordinates i.e., subordinates must capture some part of the overall quasi-rent k’(N) through their control over private information. Most plausible bargaining schemes will have this property.
G.K. Dow, Knowledge
is power
165
time pressures: bargaining has an opportunity cost in the form of foregone output, and information can rapidly become obsolete in a turbulent environment. I make no attempt here to model these time costs in a rigorous fashion. Before the equilibrium of the sealed envelope game can be characterized, some additional notation is needed. Player i’s move will be conditioned on the history hi, where (1)
The extended history &-(hi, di) consists of hi along with the decision by i to accept or reject the demand of i - 1. The set M(&) of players whose envelopes are held by player i following the choice of d, is defined recursively by ifdi=A
M(Li)~{ijUM(Li_l)
if di = R,
={i}
where M(6,) z { 11. from j’s immediate announced by their Player i’s payoff net of the payment ui=ci-ci_1,
(2)
Thus if j E M(&) and j < i, it must be true that all players superior through player i have accepted the demands subordinates. ui is the payment (if any) received from i’s superior i+ 1, (if any) made to i’s subordinate i- 1. That is, where
6, E vi
ifdi+r=A;
d,-0,
otherwise.
(3)
A strategy for player iz2 is some function (To: H,+{A, R} x [0, l] mapping from the set of possible histories hi into the set of possible moves (di,vi). A strategy for player 1 is simply a number 0, = u1 E [0,11. For player n, it will be convenient to introduce a dummy player n+ 1 such that d n+1 =A
if V[M(I;,)]
d ll+1--R
otherwise.
2 u,; (4)
In equilibrium player n will always demand V[M(&)], and this demand will always be granted by n + 1. I adopt a tie-breaking assumption needed to ensure the existence of an equilibrium.
166
G.K. Dow,
Knowledge is power
A.1. For all iEN, if i is indifferent chosen. I also assume that each player’s which he or she is a member: A.2.
between
information
For all id N and any S containing
di=A
and d,=R,
is valuable
i, V(S) - V[S-
then d,=A
to any coalition
of
{i}] >O.
Proposition 1. The unique perfect equilibrium for the sealed envelope described by the following strategies for each i E N: di+,=A,
is
game is
if
V[(i+l...n)uM(&)]-V(i+l...n)zvi;
di+l=R,
otherwise;
(54
and (5b)
The equilibrium
payoff to each i E N is
ui=V(i...n)-V(i+l...n)>O. Proof. Remark.
(6)
See appendix. For i = n, we set V(i + 1 . . . n)-
V(4)=0
in (5b) and u,= L’(n)>0
in
(6). Remark. Player i’s equilibrium observes the set M(hi_ i) and history hi are redundant.
strategy can be implemented so long as i the demand vi_ ,. All other aspects of the
These results are quite intuitive. According to (5a), i+ 1 information M(&) controlled by the subordinate player i only does not exceed the marginal value of this information to ji+ I . . r~} consisting of i’s superiors. By (5b), player i makes that extracts the full marginal value of the information coalition. In equilibrium all players purchase the information their subordindates, and receive as a net payoff the marginal own signals to their superiors.
purchases the if its price vi the coalition a demand vi M(&) to this controlled by value of their
G.K.
3. Random role assignments
Dow,
Knowledge
is power
167
and the Shapley value
The Shapley value [Shapley (1953)] has often been interpreted as arising through a sequential process of coalition formation, where each player’s payoff is the marginal contribution of that player to the existing coalition. We can obtain a result of this type using Proposition 1. Define a permutation t of the player set N to be an ordered sequence of players (ri . . . z,) such that each ZjE N and Zj# zk for all j # k. Now consider the modified sealed envelope game where the players move in an arbitrary sequence z, but where each player’s informational resources remain unaffected by this change in the order of play. It is clear from (6) that if zj=i, so that player i is the jth mover, i’s payoff will be ui= V(Tj... ~.,)-_(Zj+1...Z,)>O.
(7)
Using (7) we can derive the expected payoff to player i when each permutation z has equal probability. Randomization among player sequences could arise in a partnership where the order of play is determined by the random arrival times of the players’ signals. Randomization could also be interpreted as a Rawlsian ‘veil of ignorance’, reflecting an initial situation where the organizational roles of the players, including the identity of the owner, have not yet been determined. Either case provides a non-cooperative rationale for the Shapley value. Proposition paq@f’to
2. player
[fall
permutations
where s is the cardinality Proof.
Follows
z have equal
probability,
then the expected
i E N is
of’ the set S.
from (7) upon taking
an expectation
over r; see Owen (1982,
p. 197). Remark.
followed
The coefficient (s- l)!(n-s)!/n! is the probability in (zr . T,,) by the members of S- {i}.
that
player
i is
Averaging across all permutations of the player set, player i’s payoff pi is the expected contribution of i’s information to i’s superiors, using as probability weights the likelihood that each possible coalition of superiors follows player i. Gul (1986) has previously derived the Shapley value using a related noncooperative bargaining approach. When two resource owners meet in Gul’s
168
G.K. Dow, Knowledge is power
model, the potential buyer of a resource commits to a price offer. This reverses the convention used in the sealed envelope game, where the potential seller of information commits to a demand. More significantly, in Gul’s model a resource owner who rejects an offer in period t rejoins the pool of potential traders in period t+ 1, while in the sealed envelope game each seller is limited to a single transaction opportunity. Gul’s model can have inefficient equilibria, and a Pareto efficient equilibrium may not exist. When efficient equilibria exist and the characteristic function displays value additivity, the payoff vector approaches the Shapley value as the discount rate approaches zero. By contrast, the sealed envelope model involves a finite horizon without discounting, and Proposition 2 requires only that the function C’be monotonic. The interpretations assigned to the characteristic function also differ. Gul’s characteristic function states the payoff that each coalition can guarantee itself via unilateral production activities. In the sealed envelope game, however, the players are already committed to a common production process. Only one player (the owner, as designated by the relevant permutation r) has a direct claim on the quasi-rent generated by these production activities. Because non-owning players or coalitions cannot produce unilaterally, their payoffs derive entirely from the side payments they can extract from the owner.?
4. The precommitment
game
The properties of the signals received by production workers and front-line supervisors are heavily influenced by the layout of a firm’s physical plant, which is determined in turn by the investment decisions of the owner before production activities begin. The owner may also be able to restrict information flows within the firm by requiring upward transmission of reports along lines of vertical authority, or by punishing subordinates who refuse to ‘work through channels’. Such decisions will be made with an eye to the bargaining environment that will arise once the production plant is in place and information channels have been assigned.* I model this situation by a precommitment game played prior to the sealed envelope game of sections 2 and 3. Let the firm’s information system be represented by a vector of parameters q = (q I . q,) E @, where Cp is a compact set. The notation V( .I q) will be used to indicate the dependence of the characteristic function on the information in ye for each S. I assume that system adopted, where V(S 1y) is continuous ‘In the sealed envelope game, two disjoint coalitions S and T cannot simultaneously guarantee themselves V(S) and V(T) by their own unilateral actions, and hence the function V is typically nol superadditive. “Dow (1985) provides a related analysis of precommitment to a favorable bargaining environment by capital suppliers.
G.K. Dow, Knowledge
169
is power
A.2 in section 2 holds for every UE@. The set-up cost C(q) of the system additive in the individual player parameters: c(rl)=
C
all iE N,
with Ci(vi) 20,
ci(Vi)>
9 is
(9)
ieN
where each Ci is continuous. C(q) includes expenditures for the physical plant associated with 9, as well as the cost of worker training.’ Training simultaneously shows workers how to produce output and how to detect the signals generated by the system q.l” The rules of the precommitment game are as follows:
(4 The owner n can unilaterally
choose (q,r) by paying the cost C(q). The sealed envelope game is then played with payoffs given by (7). (b) Alternatively, the owner may choose only (v,,r,) and delegate the choice to player n-l. In this case, the owner pays the of (VI ...~n_l,rl...rn_l) cost C,(v,) only. (4 At each following stage i 5 n - 1, if the entire vector (r], r) has not already been chosen, player i can choose (rr . . . vi, TV.. . zi) by paying the cost F;i;Cj(Vj)Th e sealed envelope game is then played with payoffs given
(4 Alternatively, (Vl...Vi-l>
(4
T1
player i may choose only (qi,si) and delegate . . .zi- 1) to player i- 1. In this case, player
only. If all players iz2 delegate, player 1 has chosen ql.
then the sealed envelope
the choice of i pays Ci(qi)
game is played
after
The relations of superior and subordinate will henceforth be defined by the order of play at the precommitment stage, since the order of play in the sealed envelope game is now endogenous. I characterize the equilibrium outcome of the precommitment game under the following assumptions. A.3 (Diminishing Returns to Injbrmation). Wu all
For every ‘1E @,
(i)I111--I/(SI~)>I/CTu(i)lql-V(TIrl), S,TGN
and
iEN
such that
i$S,i#T,
and
ScT.
‘I retain the normalization )/(d/r))=O on the assumption that the choice of information system does not influence the expected quasi-rent available to the owner when all signals are suppressed. A corresponding normalization is applied to the owner’s set-up cost C,(n,). There is no need to normalize the set-up costs incurred by ijn1, since the payoffs of these players will appear in section 4 only as quasi-rent increments of the form given by (7) and hence are unaffected by the zero point of V. The normalization V(N)= I used in section 2 is no longer needed and will be dropped, so as to permit comparison among the possibly different productivities V(N 1a) of alternative information systems, “1 assume that the owner cannot train redundant workers in order to bring about competitive information supply at each subordinate level within the firm.
G.K. Dow, Knowledge
170
is power
This states that the marginal value of a player’s coalition to which it is contributed expands. A.4 (Immunity of Superior Coalitions).
information
declines
as the
For every iE N,
V(i.. . n ) q) = V( i . . . n 1q’), all
v,~I’E@
such that
(vi.. . qn) =(?I..
. $,).
This states that the quasi-rent obtainable unilaterally by the coalition {i.. . n) depends only upon the parameters (vi.. . q.). Precommitments by subordinate players cannot affect the value of superior coalitions. Henceforth I drop the notation V(i.. . n 1ye)in favor of V(i.. . n 1vi), where yli= (vi.. . q,), to emphasize parameters of i’s that V(i.. . n 1q) does not depend upon the information subordinates. It should be noted that the precommitments of superiors can still influence the value of coalitions involving subordinates. A.5 (Tie Breaking). precommitment
When any player iE N is indifferent and delegation, delegation is chosen.
between
Proposition 3. All possible decisions are delegated. Also, every perfect brium outcome (n*, z*) has the following properties for each i E N. 7: = i nT maximizes
(the sealed envelope game is played in natural order);
full equili(104
the expression
V(i.. . n I vi, $+ 1) - Ci(qi)
over the set
{tli:(YI1...~i~l,tli,tlic+l)EQ)
The equilibrium
forsome
(VI...?~-I)).
(lob)
payoff of player i is
V(i.. .n I VT)- V(i+ 1. . . nl ij~+l)-Ci(n~.
(1Oc)
Proof Each player i who has an opportunity to move in the precommitment game will strictly prefer ri = i to any rj= i with j < i, due to diminishing returns to information (A.3). Given ~7 = j for all jzi, player i will always choose to delegate, since due to (7) and the immunity of superior coalitions (A.4) i’s payoff is independent of the decisions made by i’s subordinates. Delegation also enables i to avoid the cost of choosing the subordinates’ information parameters (A.5 is used in case of indifference). Thus all players delegate and (10a) holds. Since the sealed envelope game will be played in natural order, player i chooses vi to maximize the payoff in (6) net of the precommitment cost Ci(qi), given the previous commitments (vi”+ 1.. . ~3. Results (lob) and (10~) follow from (6) upon noting that V(i+ 1.. n) in (6) is independent of ‘li by A.4. Q.E.D. The preceding
argument
is valid so long as each player’s reservation
utility
G.K.Dow, Knowledge is power
171
constraint is non-binding. The payoffs in (6) are shares in firm quasi-rent, and hence market opportunity costs at the production stage are already accounted for. Thus, we need only check whether (10~) is non-negative in equilibrium. Due to A.2, V(i.. . n (ijr)- V(i+ 1.. . n 1qT+l) >O, so the net payoffs in (10~) are non-negative provided that the precommitment costs C,(qT) 20 are sufficiently small. If (10~) is negative for some i, however, it will be necessary to impose reservation utility constraints explicitly. Whenever (10~) is strictly positive for some i, a queue of job applicants will arise for the position of player i. Free entry of new firms, if permitted, would drive (10~) to zero in the case of player n (the owner); on the other hand, if (10~) is negative for player n the firm will not be established at all. Note that because Proposition 3 requires only non-negativity and additivity of the costs C,(qJ, a zero net payoff to the owner can be consistent with strictly positive equilibrium payoffs to some or all subordinates. Finally, consider the set of feasible deviations from equilibrium by player i that leave the productivity of the firm’s information system and its cost to player i unchanged: ~i(~*)-{9i:V]=(Yli,~*i)E~,I/(NI’I)=I/(NIrl*),
Corollary
to Proposition
3.
For every
iE N, r]F minimizes
~(NI~]i,~+i)-l/(i...nlr?i,ri”+l) Proof.
Immediate
and
over
from (lob) and the definition
the expression
qiE@i(v*).
(11)
of @Jv]*).
In equilibrium, each player i minimizes the incremental value of the information held by the subordinate coalition { 1. i- l}, within the class of information systems having the same cost and productivity characteristics as the equilibrium system.”
5. Precommitment The main follows.
and the capitalist firm
organizational
implications
of section
4 can be summarized
as
(A) Let hierarchical relations within the firm be defined by the superior’s greater ability to precommit the firm to specific patterns of information acquisition and exchange. Then once all precommitments have been made, information will flow up from subordinates to superiors, while side “A deviation from equilibrium by player i might trigger deviations by some or all players in the set of subordinates { 1 i - 1 1, but this induced cascade of deviations has no bearing on i’s payoff due to A.4.
G.K. Dow, Knowledge is power
172
(B)
(C)
(D)
(E)
payments inducing information revelation will flow in the reverse direction. The first mover in the precommitment game will take on the role of owner in the sealed envelope game. This player will choose the firm’s production plan and serve as the firm’s residual income claimant. The owner’s equilibrium payoff in the sealed envelope game (gross of precommitment costs) is the expected quasi-rent obtainable by the owner when all subordinates suppress their information. More generally, player i captures a share of quasi-rent determined by the marginal value of i’s signal to the coalition of i’s superiors {i + 1 . . . n}, in the situation where all of i’s subordinates suppress their information. Each player i internalizes the effect of his or her own precommitment decision on the coalition consisting of i and i’s superiors. However, player i does not internalize the effect of such precommitments on i’s subordinates. These decisions are therefore likely to be Pareto inefficient. Player i’s precommitment minimizes the incremental value of the information controlled by i’s subordinates, holding constant the overall productivity of the firm’s information system and the set-up cost incurred by player i. All else equal, precommitments tend to redistribute quasi-rent from subordinate players to their superiors.
These results are consistent with several stylized facts about the organization of production in capitalist firms. For example, the ‘deskilling’ hypothesis advanced by Braverman (1974) and Noble (1977) asserts that capitalist firms attempt to reduce the skill content of production-level jobs by redesigning the production process. This tits nicely with the prediction that players at each stage make precommitment decisions that minimize the value of the information controlled by their subordinates. The model is also consistent with Williamson’s observation that experienced workers are sometimes reluctant to transfer their technical knowledge to less senior trainees: ‘The success of on-the-job training is plainly conditional on the information disclosure attitudes of incumbent employees . . . [IIncumbents are in possession of a valuable resource (knowledge) and can be expected to fully and candidly reveal it only in exchange for value. The danger is that incumbent employees will hoard information to their personal advantage.. .’ (1975, p. 63). In the precommitment information of their constant, increased come at the expense Finally, the results that
game, superiors derive no personal benetit from the subordinates. Moreover, when firm productivity is held access to information by subordinates (trainees) must of their superiors (incumbent employees). provide a formal basis for Marglin’s controversial thesis
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is power
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‘[T]he capitalist division of labor . . . was the result of a search not for a technologically superior organization of work, but for an organization which guaranteed to the entrepreneur an essential role in the production process.. . (1974, p. 62). The precommitment game models the role of the owner much as Marglin suggests. Since the owner’s equilibrium payoff is the quasi-rent obtainable without the use of information controlled by subordinates, the owner’s incentive at the precommitment stage is to devise a production system that concentrates valuable information at the top of the managerial hierarchy. The benefits flowing to subordinates from informational decentralization within the firm will not be internalized by the owner, and will play no role in the owner’s investment decisions. One potential objection to this analytical framework must now be addressed. By auctioning off the right to each subordinate job once (q,r) has been chosen, the owner would obtain some ex ante compensation for the leakages of quasi-rent that will occur in the course of the sealed envelope game. In principle, this procedure might permit the owner to completely undo the ex post bargaining result. Under competitive conditions the winning bids would sum to V(N 1q), giving the owner a net payoff of V(N 1q) - C(u) in the precommitment game. The owner could then choose a Pareto efftcient information system at the precommitment stage and appropriate all returns from this investment by collecting application fees, thus avoiding the problem of compelling signal revelation through binding contracts [Dow (1983, Crawford (1988)]. For various reasons, lump sum payments to a firm by newly hired employees are seldom observed.” Consider, for example, a scenario where workers observe the information system chosen by the owner only after they have been trained for their jobs, and where the owner cannot be penalized if workers discover ex post that the characteristics of this information system have been misrepresented. Dishonest owners could then demand ex ante fees from job applicants by promising a valuable information system, when in fact a worthless system (one giving no ex post bargaining power to workers) had been installed.’ 3 Moral hazard problems of this sort could prove fatal to “Apart from the informational asymmetries discussed in the text, personal wealth constraints along with capital market imperfections stemming from the limited liability of workers could make it impossible for workers to finance the purchase of a present claim on future quasi-rents (I thank Gil Skillman for this point). Another problem is posed by the understandable reluctance of entrepreneurs to make public all pertinent details of their investment ideas [Marglin (1982)]. Perhaps the most important obstacle to the creation of property rights in jobs, however, is the fact that this would undermine the use of tiring threats as a worker discipline device by employers [Shapiro and Stiglitz (1984), Bowles (1985) and Skillman (1987)]. 13The owner cannot expect to obtain compensation for leakages of quasi-rent once training has occurred, because the worker will then be costly to replace, and the same bargaining problem would arise with the replacement worker. Credible disclosure of the true information system through training occurs ‘too late’ from the owner’s point of view.
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an auction market for jobs, and might motivate the establishment of hierarchical capitalist firms along the lines described in section 4. Similar market failures may help to explain the relative rarity of labormanaged firms (LMFs) in Western market economies. It is well known that an LMF with marketable membership rights will have comparative static and efficiency properties identical to those of a capital-managed firm with marketable common stock [Sertel (1982), Dow (1986)]. Marketability of membership rights allows current LMF members to extract ex ante compensation for the quasi-rent that will be appropriated by new workers after their acceptance into the lirm. However, if current members have better information about the future income of the firm than new members, or know more about the internal bargaining position that a new member will ultimately enjoy, membership markets may fail for essentially the same reasons that capitalists cannot sell jobs to workersi The capitalist firm and the LMF share the problem that the current ‘owners’ (whether capitalist investors or incumbent workers) cannot completely forestall the leakage of quasi-rents to incoming workers. Policy measures similar to those that would facilitate the purchase of jobs by employees in capitalist firms might therefore prove useful in the context of the labor-managed firm as well. Measures of this sort, which could include the provision of credit, insurance, or information to prospective job purchasers, appear to warrant further investigation by students of organizational design.
Appendix Proof of Proposition 1. Consider i = n. In this case (5a) reduces to (4), which holds by assumption. If u,> V[M(f;.)] then u,sO, while if d,=R and V(n) >_v,,>O, then u,=u,>O. Such a u,, exists by A.2. Therefore in equilibrium ~CWk,)l g u, and 4 +1--A. In this case U, is strictly increasing in v,, so v,, = V[M(h,)] as stated in (5b). [Note that for i=n, {i+ 1 . n} = {4} and
V(4) = 0.1 We proceed by backward induction. Assume that (5a) and (5b) hold for some i 2 2; we then show that these results hold for i - 1. Consider (5a) first. that (5a) and (5b) hold If di = A, then since di+ 1 = A due to the hypothesis for i, ui=ui-vi-,
=V[{i+l...
n}uM(I;,)]-V(i+l...n)-ui_,
“‘The experience of plywood cooperatives in the U.S. with dishonest promoters who sold worthless shares to prospective worker-owners is instructive [Bellas (1972, pp. 11521)]. A viable market for LMF membership rights would need to protect applicants against such fraud, much as conventional stock markets guard against insider trading schemes.
G.K. Dow, Knowledge
= V[{i... ui = ui =
~} uM(l;i_,)]-I/(i+l
is power
. ..n)-Ui_.,
175
while if d,=R
then
V(i . . . n) - V(i + 1 . . . n).
Using A.l, di=A
if
I’[{i...
di = R
otherwise,
n}uM(h^i_,)]-V(i...n)~vi_,;
verifying (5a) for i - 1. If V[{i...n) u M(~i~,)]-V(i...n)<~i_Ir then u,_r~O since di=R. HOWever, if di_l=R and V(i-l...n)-V(i...n)>uiP,>O, then ui_l=oi_,>O. Such a uiP I exists by A.2. Thus in equilibrium V[(i.. .n} u M(Gi_ 1)] V(i . . . n) 2 vi _ 1. In this case di = A, so that ui_ 1 is strictly increasing in ui- 1 and (5b) must hold for i - 1. This establishes (5a) and (5b). Finally, note that (5a) and (5b) together imply di+ 1 =A for all ie N, and hence M(&)= { 1.. .i} for all iE N. It follows from (3) and (5b) that the equilibrium payoffs are given by (6). Q.E.D.
References Arrow, K., 1974, The limits of organization (Norton, New York). Bellas, C., 1972, Industrial democracy and the worker-owned firm (Praeger, New York). Binmore. K. and P. Dasgupta, eds., 1987, The economics of bargaining (Basil Blackwell, New York). Bowles, S., 1985, The production process in a competitive economy, American Economic Review 75, 1636. Braverman, H., 1974, Labor and monopoly capital (Monthly Review Press, New York). Crawford, V., 1988, Long-term relationships governed by short-term contracts, American Economic Review 78, 485-499. Dow, G., 1985, Internal bargaining and strategic innovation in the theory of the firm, Journal of Economic Behavior and Organization 6, 301-320. Dow, G., 1986, Control rights, competitive markets, and the labor management debate, Journal of Comparative Economics 10, 48861. Dow, G., 1988a, Self-enforcing authority structures, Unpublished manuscript (Department of Economics, University of Alberta, Edmonton, Alb.). Dow, G., 1988b, Information, production decisions and intra-Iirm bargaining, International Economic Review 29, 57779. GUI, F., 1986, Bargaining foundations of Shapley value, Unpublished manuscript (Graduate School of Business, Stanford University, Stanford, CA). Harsanyi, J., 1963, A simplified bargaining model for the n-person cooperative game, International Economic Review 4, 194220. Klein, B., R. Crawford and A. Alchian, 1978, Vertical integration, appropriable rents, and the competitive contracting process, Journal of Law and Economics 21, 297-326. Marglin, S., 1974, What do bosses do? The origin and function of hierarchy in capitalist production, Review of Radical Political Economics 6, 60-l 12. Marglin, S., 1982, Knowledge and power, in: F. Stephen, ed., Firms, organization and labour (St Martin’s Press, New York).
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Marschak, J. and K. Miyasawa, 1968, Economic comparability of information systems, International Economic Review 9, 137-174. Noble, D., 1977, America by design (Oxford University Press, New York). Owen, G., 1982, Game theory (Academic Press, New York). Rubinstein, A., 1982, Perfect equilibrium in a bargaining model, Econometrica 50, 97-109. Sertel, M., 1982, Workers and incentives (North-Holland, New York). Shapley, L., 1953, A value for n-person games, in: H. Kuhn and A.W. Tucker, eds., Contributions to the theory of games 2 (Princeton University Press, Princeton, NJ). Shapiro. C. and J. Stiglitz. 1984. Eauilibrium unemnlovment as a worker discinline device. 1 _ American Economic-Review 74, 433444. Skillman, G., 1987, Bargaining and replacement in the employment relation, Unpublished manuscript (Department of Economics, Brown University, Providence, RI). Sutton, J., 1986, Non-cooperative bargaining theory: An introduction, Review of Economic Studies 53, 7099724. Williamson, O., 1975, Markets and hierarchies (Free Press, New York). Williamson, O., 1979, Transaction-cost economics: The governance of contractual relations, Journal of Law and Economics 22, 233-260. Williamson, O., 1985, The economic institutions of capitalism (Free Press, New York).