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A note comparing the capacity setting performance of the Kreps–Scheinkman duopoly model with the Cournot duopoly model in a laboratory setting
International Journal Int. J. Ind. of Industrial Organ. 28Organization (2010) 522–525 28 (2010) 522–525
Contents lists available at ScienceDirect
International Journal of Industrial Organization j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j i o
A note comparing the capacity setting performance of the Kreps–Scheinkman duopoly model with the Cournot duopoly model in a laboratory setting David Goodwin a, Stuart Mestelman b,⁎ a b
Ontario Ministry of Finance, Toronto, Ontario, Canada McMaster University, Hamilton, Ontario, Canada
a r t i c l e
i n f o
Article history: Received 26 August 2009 Received in revised form 5 January 2010 Accepted 6 January 2010 Available online 14 January 2010 JEL classification: C92 D43 L13
a b s t r a c t The paper reports the results of 39 laboratory duopoly markets for which pricing institution and participant experience are treatments. Cournot (C) duopolies (quantity precommitment and a price determined to clear the market) are contrasted with Kreps–Scheinkman (KS) duopolies (quantity precommitment and posted prices). Inexperienced participants in KS markets have much more difficulty selecting capacities consistent with the theoretical predictions than do those in C markets. With experience, the differences disappear. © 2010 Elsevier B.V. All rights reserved.
Keywords: Duopoly Laboratory experiment Quantity precommitment Posted prices Price competition Market-clearing prices Experience
1. Introduction Holt (1995, 377) states that “despite its prominence in the theoretical literature, the Cournot model is deficient for the experimental study of many IO issues because the essential mechanics of price determination are simulated. One open question, taken from Kreps and Scheinkman (1983), is whether quantity precommitment and Bertrand competition yield Cournot outcomes (in the laboratory).” The objective of this note is to compare the capacity setting performance of the Kreps–Scheinkman (KS) model with the Cournot (C) model in a laboratory setting. C firms select a quantity of output they will produce, and price is set to clear the market based on the quantity produced. In the Bertrand (B) model firms offer a price to sell output, and the firm with the lowest price-offer sells all that is demanded at that price. The KS model incorporates the quantity setting of C and the price setting of B in a two-stage advance-production environment. KS firms first make a binding capacity decision, are informed of the capacity of the entire
⁎ Corresponding author. Department of Economics, McMaster University, Hamilton, Ontario, Canada L8S 4M4. Tel.: + 1 905 525 9140x23113; fax: + 1 905 521 8232. E-mail address: [email protected] (S. Mestelman). 0167-7187/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2010.01.001
market, then decide at what price they wish to sell their output.1 Prices are posted and demand is allocated using an efficient rationing mechanism, matching the low-price sellers with the high-valuation buyers until no further units are demanded or no supply remains. Davis (1999) and Muren (2000) have evaluated the performance of the KS model in laboratory environments with homogeneous goods. Davis runs 12 posted-offer triopoly markets, 6 without binding production commitments, and 6 with binding production commitments prior to posting prices, effectively testing the KS model using the B model as a benchmark for comparison. Davis finds that quantity precommitment raises prices and lowers output from the competitive B benchmark, but that the actual outcomes do not correspond to the theoretical prediction of the KS model. Muren runs 16 posted-offer triopoly markets with binding production precommitment, 10 with inexperienced traders and 6 with experienced traders. The results show that inexperienced participants make capacity choices that are 1 The KS model reconciles the desirable features of the C and B models, having the same equilibrium prediction as C, but better depicting oligopoly markets with its twostage, capacity-setting and price-setting environment. In turn, the KS model has been criticized because of the lack of realism in the efficient pricing rule (Davidson and Deneckere, 1986), because of the assumption that products are homogeneous (Yin and Ng, 1996) and because they do not permit short-run capacity expansion (Boccard and Wauthy, 2000).
D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525
much higher than the choices of inexperienced triopolists in Fouraker and Siegel (1963). When participating in a second session with the same parameters as the first, Muren's participants set capacities that are closer to the prediction of the KS and C models, but on average are still above it. Muren does not run sessions using C triopolies. Capacity setting duopolists who post prices are studied by Anderhub et al. (2003) in an environment characterized by product differentiation. Anderhub et al. (2003, 36) find that average capacities “are above the Cournot-Nash equilibrium level and below the monopolistic competition solution.” Their data supports neither the null hypothesis that their duopolists' capacities are no different from the Nash equilibrium nor the null hypothesis that they are no different from the monopolistic competition solution. This result is consistent with the Davis (1999) and Muren (2000) triopoly results that find the KS model leading to capacities greater than the Nash equilibrium prediction. An experiment has not been reported that compares the capacities set by C and KS oligopolists with identical underlying parameters. This note reports the results of 39 duopoly markets. The treatment variables are the pricing institution and trader experience. The results show that inexperienced participants initially choose excessively large capacities in the KS environment relative to outputs chosen in the C environment. Differences tend to disappear over time. There are no differences between experienced participants in comparable KS and C environments.
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For both C and KS environments, participants had two minutes to make each decision, enter it on their individual record sheets, and return the sheets to the session monitor. The monitor recorded this information and returned the record sheets to the participants after disseminating the relevant information to all participants. The time limit was never a binding constraint. Calculations were checked by the session monitors each time the participants submitted their record sheets. After participating in their first session, the now experienced participants were asked if they wished to participate in another session several days in the future. Names were taken, people were later assigned to slots in market sessions for experienced participants and then they were notified of the time and place of the session.4 Participants were paid privately at the end of each session. $5.00 was guaranteed as a show-up fee. Earnings ranged between $15 and $37 with a mean of $23.15. Sessions lasted between 1 and 2.5 hours, including the reading of instructions. Our intention was to run 15 C markets and 15 KS markets with inexperienced participants. From these we would recruit participants for 10 C markets and 10 KS markets with experienced agents. After running 14 C markets and 10 KS markets with inexperienced participants and reviewing the adjustment patterns in the two treatments (and reconsidering our budget constraint), we decided to conduct 5 C markets with participants experienced in the C market, 5 KS markets with participants experienced in the C market and 5 KS markets with participants experienced in the KS market. This is discussed further in the Results section.
2. Laboratory environment 3. Benchmark outcomes Forty-eight inexperienced participants were recruited using notices posted on bulletin boards on a university campus and messages posted on the university website. Participants were primarily undergraduate students from various disciplines. Sessions were conducted with pencil and paper; each participant had a calculator. Participants were anonymously paired with others in their session; each pair formed a duopoly. Communication was not allowed. Detailed instructions were read to the participants prior to beginning each session.2 Sessions began with two practice periods during which the pairings remained the same. Pairs were then reassigned, and new pairs remained together for 12 paid periods. Demand and cost information was common knowledge. The demand function was Q = 92 − P; P was the price of output in lab dollars (L$) and Q was the total market demand at the given price. The market demand function was explained in the instructions, and presented to participants in a price–quantity table.3 In C sessions, participants made one decision each period, selecting a quantity to produce in the range of 0 to 92. The cost of each unit was L$20. The output of both duopolists was combined to determine the market output and the associated market-clearing price. Participants calculated their earnings, and moved to the next decision period. In KS sessions, participants made two decisions each period, selecting units of capacity in the range of 0 to 92. The cost of each unit was L$20. After being informed of their group's capacity, participants selected a price between L$0 and L$92. They were then informed of the price selected by their group member, as well as the quantities they each were able to sell. These amounts were based on the demand function, using the efficient rationing mechanism. Participants then calculated their earnings. The specific mechanism was described in detail to the participants in the instructions using several different examples (including equal posted prices) to illustrate how the units sold were related to the demand schedule and the prices posted by the duopolists. 2 Go to http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma1.pdf and http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma2.pdf for C and KS instructions. 3 Available at http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma3.pdf.
Given the underlying demand and cost parameters and the pricing institutions characterizing the duopoly markets, three benchmark capacities or outputs are identified. The first benchmark is the joint profit maximizing output or capacity of 36 units. The second benchmark is the competitive zero-profit outcome of 72 units. The third benchmark is the duopoly Nash equilibrium outcome of 48 units. This third outcome is the theoretical prediction for both the C and KS environments.5 The corresponding price benchmarks are L$56, L$20 and L$44. 4. Results 4.1. Capacity decisions Fig. 1 displays mean per-period capacity or output for the two pricing institutions and two levels of experience. The data for inexperienced participants are in the leftmost 12 periods; the data for experienced participants are in the rightmost 12 periods. Circles represent KS duopolies and triangles represent C duopolies. The data reflect the excess capacity decisions of inexperienced KS duopolists as well as their convergence towards the Nash equilibrium benchmark reported by Muren (2000). Capacities set by inexperienced KS duopolists greatly exceed those set by inexperienced C duopolists across the first 8 periods of their sessions. The difference is significant (exact randomization test, nC = 14, nKS = 10, one-sided, p = 0.000). C duopolists tend to select capacities 4 More individuals than needed volunteered for a second session to fill the slots needed for experienced participants. Some chose to return as alternates, who would only participate if someone else was unable to attend. Individuals who participated as inexperienced agents in KS markets earned less on average than those in C markets. This may have introduced a self-selection bias into the recruitment process for the second session. However, because the average first session payoff to people who volunteered for the second sessions is not significantly different from the average payoff to all participants in KS markets with inexperienced participants we do not believe the recruitment process was biased by first session payoffs. 5 In the discrete implementation of this environment in the laboratory, participants must select integer output values. There are three Nash equilibria. One is a symmetric equilibrium when each player selects an output of 24. The other two result if one selects 23 and the other selects 25. This can happen two ways. The equilibrium price remains 44.
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D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525 Table 1 Means and standard deviations of output and capacity decisions by period range and treatment. Institution
Inexperienced duopolists Obs.
1–8 C
KS
14
10
Institution
Periods
48.86 (6.40)
74.75 (13.15)
Experienced duopolists Obs.
9–12 48.41 (7.44)
51.10 (7.27)
C
5
KSC
5
KSKS
5
KS Pooled
10
Periods 1–8
9–12
47.03 (8.53) 45.60 (7.76) 43.98 (8.18) 44.79 (8.45)
43.85 (6.07) 44.35 (7.55) 40.25 (5.57) 42.30 (7.32)
C indicates markets with quantity-setting producers who do not post prices. KS indicates markets with quantity-setting producers who post prices. KSC indicates a KS session with agents experienced in C and KSKS indicates experience is gained in a KS session. The data are the mean output or capacity from each duopoly across periods 1–8 or 9–12 averaged across the duopoly sessions run in a treatment. Fig. 1. Capacity.
very close to the Nash equilibrium benchmark. Over time, capacities in KS duopolies fall and approach output in C duopolies. The average capacities selected by inexperienced KS duopolists across periods 9–12 are not significantly different from mean output set by inexperienced C duopolists (exact randomization test, nC = 14, nKS = 10, one-sided, p = 0.125). A conjecture consistent with these observations is that agents with experience in C markets will converge more rapidly to the predicted capacity in KS markets than will agents who gain experience in KS markets. To evaluate this conjecture with experienced agents, 5 KS duopolies had participants experienced in C markets and 5 had participants experienced in KS markets. It was not possible to reject the null hypothesis that the source of experience does not matter to the capacity choices of the experienced duopolists (exact randomization test, nC = 5, nKS = 5, two-sided, p = 0.730 and p = 0.444 for periods 1–8 and 9–12).6 Accordingly, the data for experienced participants in KS markets are pooled. The capacity and output data for periods 1–8 and 9–12 are summarized in Table 1. When duopolists are experienced in these environments, the differences between KS capacities and C output across periods 1–8 and 9–12 are not significantly different (exact randomization tests, nC = 5, nKS = 10, two-sided, p = 0.637 and p = 0.688). Over time there appears to be a tendency for both C and KS duopolists to reduce outputs and capacities below the Cournot benchmark. The evidence for this result from C duopoly markets in the literature is mixed.7 We noted there were no significant differences between the mean capacities and outputs of the experienced KS and C duopolists; their aggregate mean over periods 9–12 is 42.82 units. Simple tests of the hypotheses that mean capacity and output selected by experienced KS and C duopolists does not differ from the benchmark of 48 units and from the benchmark of 36 units can be rejected in favor of the alternatives that it is less than 48 and more than 36 (t = 2.974 for the former and t = 3.912 for the latter, the critical value at one percent for a one-tailed test with 14 degrees of freedom is 2.624).
each is informed of the other's decision. Following this, each KS producer posts a price at which output will be sold. The price in the C market is always the market clearing price. There may be two different prices in the KS market and capacity may exceed sales for the duopolists. The mean per-period contract price in the KS market is a quantity-weighted mean contract price (total sales revenues received by the duopolists divided by total units sold in the market). Fig. 2 displays mean per-period contract prices for the two pricing institutions and two levels of experience. The data for inexperienced participants are in the leftmost 12 periods; the data for experienced participants are in the rightmost 12 periods. Circles represent KS duopolies and triangles represent C duopolies. Price data are summarized in Table 2. If market clearing prices were posted by the inexperienced KS duopolists, mean contract prices would average less than L$20 over the first eight periods. Mean contract prices across periods 1–8 in inexperienced KS markets were slightly greater than L$30. This resulted in unsold units which could not be sold in subsequent periods. Had market clearing prices prevailed and no product was discarded, producers would have realized average losses of L$206 across periods 1–8. Over the first 8 periods, the inexperienced KS duopolists generated average per period profit of L$201. Producers adjust to potential losses in the face of high market capacity by
4.2. Price decisions In addition to capacity decisions, producers in the KS markets also make price decisions. After each duopolist makes a capacity decision,
6 This conclusion can also be supported by an analysis of the contract price data (exact randomization test, nC = 5, nKS = 5, two-sided, p = 0.563 and p = 0.444 for periods 1-8 and 9-12). See Section 4.2. 7 Holt (1995) notes that “in multiperiod Cournot duopolies, the outcomes fall on both sides of the Cournot prediction...”
Fig. 2. Contract prices.
D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525 Table 2 Means and standard deviations of contract prices by period range and treatment. Institution
Inexperienced duopolists Obs.
C
KS
14
10
Institution
Periods 9–12
43.14 (6.40)
43.59 (7.44)
30.37 (6.84)
40.62 (5.79)
C
5
KSC
5
KSKS
5
KS Pooled
from periods 9–12 while only 1 of 5 experienced C duopolies achieved this coordination.
Experienced duopolists Obs.
1–8
525
10
5. Conclusions
Periods 1–8
9–12
44.98 (8.53) 45.14 (7.14) 48.32 (8.37) 46.73 (7.83)
48.15 (6.07) 47.84 (7.26) 51.77 (5.53) 49.81 (7.11)
C indicates markets with quantity-setting producers who do not post prices. KS indicates markets with quantity-setting producers who post prices. KSC indicates a KS session with agents experienced in C and KSKS indicates experience is gained in a KS session. The data are the mean contract prices from each duopoly across periods 1–8 or 9–12 averaged across the duopoly sessions run in a treatment.
posting higher than clearing prices.8 In this experiment, the coordination of capacity decisions and price decisions takes about eight periods. By the ninth period, KS and C markets with inexperienced agents are not very different, and across periods 9–12 there is no significant difference between mean contract prices in C and KS markets (exact randomization tests, nC = 14, nKS = 10, one-sided, p = 0.154). The mean contract prices realized by experienced KS producers are generally slightly higher than those resulting from the output decisions of the experienced C producers, but the prices in both C and KS markets tend to rise above the benchmark Cournot price of L$44. There are no statistically significant differences in mean contract prices in C and KS markets across periods 1–8 and 9–12 (exact randomization tests, nC = 5, nKS = 10, two-sided, p = 0.706 and p = 0.656). Suetens and Potters (2007, 71) “argue that there is often significantly more tacit collusion in Bertrand price-choice than in Cournot quantity–choice markets.” This suggests that KS duopolists may display more tacit collusion than C duopolists. In this experiment there is some support for this conclusion. Although the mean price and capacity data for experienced C and KS markets are not significantly different, 5 of 10 experienced KS duopolies were able to coordinate on the joint profit maximizing outcome in each period
8 This is consistent with Proposition 1 in Kreps and Scheinkman (1983, 335) for behavior given excessive capacity.
Holt (1995, 377) notes that “an open question ... is whether quantity precommitment and Bertrand competition yield Cournot outcomes (in the laboratory).” Although laboratory experiments which evaluate the performance of markets with quantity precommitment and price posting have been conducted, none have directly addressed Holt's question by contrasting the KS and C environments with the same cost and demand parameters. The results of this experiment show that with experience, traders in laboratory duopoly markets who have to make quantity commitments will make comparable commitments regardless of whether they also post prices at which to sell their output or they defer the pricing decision to an exogenous clearing mechanism. While the behavior is comparable across pricing institutions, it does not necessarily conform to the specific theoretical quantity and price predictions when the market structure is duopoly. Experienced duopolists in this experiment tend to produce less output and receive higher prices than predicted. References Anderhub, V., Güth, W., Kamecke, U., Nomann, H.-T., 2003. Capacity choices and price competition in experimental markets. Experimental Economics 6, 27–52. Boccard, N., Wauthy, X., 2000. Bertrand competition and Cournot outcomes: further results. Economics Letters 68, 279–285. Davidson, C., Deneckere, R., 1986. Long-run competition in capacity, short-run competition in price, and the Cournot model. Rand Journal of Economics 17, 404–415. Davis, D., 1999. Advance production and Cournot outcomes: an experimental investigation. Journal of Economic Behavior and Organization 40, 59–79. Fouraker, L., Siegel, S., 1963. Bargaining behavior. McGraw-Hill, New York. Holt, C.A., 1995. Industrial organization: a survey of laboratory research. In: Kagel, J.H., Roth, A.E. (Eds.), Handbook of Experimental Economics (Princeton University Press. Princeton, NJ), pp. 349–443. Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics 14, 326–337. Muren, A., 2000. Quantity precommitment in an experimental oligopoly market. Journal of Economic Behavior and Organization 41, 147–157. Suetens, S., Potters, J., 2007. Bertrand colludes more than Cournot. Experimental Economics 10, 71–78. Yin, X., Ng, Y.-K., 1996. Quantity precommitment and Bertrand competition yield Cournot outcomes: a case with product differentiation. Australian Economic Papers 36, 14–22.
Contents lists available at ScienceDirect
International Journal of Industrial Organization j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j i o
A note comparing the capacity setting performance of the Kreps–Scheinkman duopoly model with the Cournot duopoly model in a laboratory setting David Goodwin a, Stuart Mestelman b,⁎ a b
Ontario Ministry of Finance, Toronto, Ontario, Canada McMaster University, Hamilton, Ontario, Canada
a r t i c l e
i n f o
Article history: Received 26 August 2009 Received in revised form 5 January 2010 Accepted 6 January 2010 Available online 14 January 2010 JEL classification: C92 D43 L13
a b s t r a c t The paper reports the results of 39 laboratory duopoly markets for which pricing institution and participant experience are treatments. Cournot (C) duopolies (quantity precommitment and a price determined to clear the market) are contrasted with Kreps–Scheinkman (KS) duopolies (quantity precommitment and posted prices). Inexperienced participants in KS markets have much more difficulty selecting capacities consistent with the theoretical predictions than do those in C markets. With experience, the differences disappear. © 2010 Elsevier B.V. All rights reserved.
Keywords: Duopoly Laboratory experiment Quantity precommitment Posted prices Price competition Market-clearing prices Experience
1. Introduction Holt (1995, 377) states that “despite its prominence in the theoretical literature, the Cournot model is deficient for the experimental study of many IO issues because the essential mechanics of price determination are simulated. One open question, taken from Kreps and Scheinkman (1983), is whether quantity precommitment and Bertrand competition yield Cournot outcomes (in the laboratory).” The objective of this note is to compare the capacity setting performance of the Kreps–Scheinkman (KS) model with the Cournot (C) model in a laboratory setting. C firms select a quantity of output they will produce, and price is set to clear the market based on the quantity produced. In the Bertrand (B) model firms offer a price to sell output, and the firm with the lowest price-offer sells all that is demanded at that price. The KS model incorporates the quantity setting of C and the price setting of B in a two-stage advance-production environment. KS firms first make a binding capacity decision, are informed of the capacity of the entire
⁎ Corresponding author. Department of Economics, McMaster University, Hamilton, Ontario, Canada L8S 4M4. Tel.: + 1 905 525 9140x23113; fax: + 1 905 521 8232. E-mail address: [email protected] (S. Mestelman). 0167-7187/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2010.01.001
market, then decide at what price they wish to sell their output.1 Prices are posted and demand is allocated using an efficient rationing mechanism, matching the low-price sellers with the high-valuation buyers until no further units are demanded or no supply remains. Davis (1999) and Muren (2000) have evaluated the performance of the KS model in laboratory environments with homogeneous goods. Davis runs 12 posted-offer triopoly markets, 6 without binding production commitments, and 6 with binding production commitments prior to posting prices, effectively testing the KS model using the B model as a benchmark for comparison. Davis finds that quantity precommitment raises prices and lowers output from the competitive B benchmark, but that the actual outcomes do not correspond to the theoretical prediction of the KS model. Muren runs 16 posted-offer triopoly markets with binding production precommitment, 10 with inexperienced traders and 6 with experienced traders. The results show that inexperienced participants make capacity choices that are 1 The KS model reconciles the desirable features of the C and B models, having the same equilibrium prediction as C, but better depicting oligopoly markets with its twostage, capacity-setting and price-setting environment. In turn, the KS model has been criticized because of the lack of realism in the efficient pricing rule (Davidson and Deneckere, 1986), because of the assumption that products are homogeneous (Yin and Ng, 1996) and because they do not permit short-run capacity expansion (Boccard and Wauthy, 2000).
D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525
much higher than the choices of inexperienced triopolists in Fouraker and Siegel (1963). When participating in a second session with the same parameters as the first, Muren's participants set capacities that are closer to the prediction of the KS and C models, but on average are still above it. Muren does not run sessions using C triopolies. Capacity setting duopolists who post prices are studied by Anderhub et al. (2003) in an environment characterized by product differentiation. Anderhub et al. (2003, 36) find that average capacities “are above the Cournot-Nash equilibrium level and below the monopolistic competition solution.” Their data supports neither the null hypothesis that their duopolists' capacities are no different from the Nash equilibrium nor the null hypothesis that they are no different from the monopolistic competition solution. This result is consistent with the Davis (1999) and Muren (2000) triopoly results that find the KS model leading to capacities greater than the Nash equilibrium prediction. An experiment has not been reported that compares the capacities set by C and KS oligopolists with identical underlying parameters. This note reports the results of 39 duopoly markets. The treatment variables are the pricing institution and trader experience. The results show that inexperienced participants initially choose excessively large capacities in the KS environment relative to outputs chosen in the C environment. Differences tend to disappear over time. There are no differences between experienced participants in comparable KS and C environments.
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For both C and KS environments, participants had two minutes to make each decision, enter it on their individual record sheets, and return the sheets to the session monitor. The monitor recorded this information and returned the record sheets to the participants after disseminating the relevant information to all participants. The time limit was never a binding constraint. Calculations were checked by the session monitors each time the participants submitted their record sheets. After participating in their first session, the now experienced participants were asked if they wished to participate in another session several days in the future. Names were taken, people were later assigned to slots in market sessions for experienced participants and then they were notified of the time and place of the session.4 Participants were paid privately at the end of each session. $5.00 was guaranteed as a show-up fee. Earnings ranged between $15 and $37 with a mean of $23.15. Sessions lasted between 1 and 2.5 hours, including the reading of instructions. Our intention was to run 15 C markets and 15 KS markets with inexperienced participants. From these we would recruit participants for 10 C markets and 10 KS markets with experienced agents. After running 14 C markets and 10 KS markets with inexperienced participants and reviewing the adjustment patterns in the two treatments (and reconsidering our budget constraint), we decided to conduct 5 C markets with participants experienced in the C market, 5 KS markets with participants experienced in the C market and 5 KS markets with participants experienced in the KS market. This is discussed further in the Results section.
2. Laboratory environment 3. Benchmark outcomes Forty-eight inexperienced participants were recruited using notices posted on bulletin boards on a university campus and messages posted on the university website. Participants were primarily undergraduate students from various disciplines. Sessions were conducted with pencil and paper; each participant had a calculator. Participants were anonymously paired with others in their session; each pair formed a duopoly. Communication was not allowed. Detailed instructions were read to the participants prior to beginning each session.2 Sessions began with two practice periods during which the pairings remained the same. Pairs were then reassigned, and new pairs remained together for 12 paid periods. Demand and cost information was common knowledge. The demand function was Q = 92 − P; P was the price of output in lab dollars (L$) and Q was the total market demand at the given price. The market demand function was explained in the instructions, and presented to participants in a price–quantity table.3 In C sessions, participants made one decision each period, selecting a quantity to produce in the range of 0 to 92. The cost of each unit was L$20. The output of both duopolists was combined to determine the market output and the associated market-clearing price. Participants calculated their earnings, and moved to the next decision period. In KS sessions, participants made two decisions each period, selecting units of capacity in the range of 0 to 92. The cost of each unit was L$20. After being informed of their group's capacity, participants selected a price between L$0 and L$92. They were then informed of the price selected by their group member, as well as the quantities they each were able to sell. These amounts were based on the demand function, using the efficient rationing mechanism. Participants then calculated their earnings. The specific mechanism was described in detail to the participants in the instructions using several different examples (including equal posted prices) to illustrate how the units sold were related to the demand schedule and the prices posted by the duopolists. 2 Go to http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma1.pdf and http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma2.pdf for C and KS instructions. 3 Available at http://socserv2.socsci.mcmaster.ca/~econ/mceel/papers/gma3.pdf.
Given the underlying demand and cost parameters and the pricing institutions characterizing the duopoly markets, three benchmark capacities or outputs are identified. The first benchmark is the joint profit maximizing output or capacity of 36 units. The second benchmark is the competitive zero-profit outcome of 72 units. The third benchmark is the duopoly Nash equilibrium outcome of 48 units. This third outcome is the theoretical prediction for both the C and KS environments.5 The corresponding price benchmarks are L$56, L$20 and L$44. 4. Results 4.1. Capacity decisions Fig. 1 displays mean per-period capacity or output for the two pricing institutions and two levels of experience. The data for inexperienced participants are in the leftmost 12 periods; the data for experienced participants are in the rightmost 12 periods. Circles represent KS duopolies and triangles represent C duopolies. The data reflect the excess capacity decisions of inexperienced KS duopolists as well as their convergence towards the Nash equilibrium benchmark reported by Muren (2000). Capacities set by inexperienced KS duopolists greatly exceed those set by inexperienced C duopolists across the first 8 periods of their sessions. The difference is significant (exact randomization test, nC = 14, nKS = 10, one-sided, p = 0.000). C duopolists tend to select capacities 4 More individuals than needed volunteered for a second session to fill the slots needed for experienced participants. Some chose to return as alternates, who would only participate if someone else was unable to attend. Individuals who participated as inexperienced agents in KS markets earned less on average than those in C markets. This may have introduced a self-selection bias into the recruitment process for the second session. However, because the average first session payoff to people who volunteered for the second sessions is not significantly different from the average payoff to all participants in KS markets with inexperienced participants we do not believe the recruitment process was biased by first session payoffs. 5 In the discrete implementation of this environment in the laboratory, participants must select integer output values. There are three Nash equilibria. One is a symmetric equilibrium when each player selects an output of 24. The other two result if one selects 23 and the other selects 25. This can happen two ways. The equilibrium price remains 44.
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D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525 Table 1 Means and standard deviations of output and capacity decisions by period range and treatment. Institution
Inexperienced duopolists Obs.
1–8 C
KS
14
10
Institution
Periods
48.86 (6.40)
74.75 (13.15)
Experienced duopolists Obs.
9–12 48.41 (7.44)
51.10 (7.27)
C
5
KSC
5
KSKS
5
KS Pooled
10
Periods 1–8
9–12
47.03 (8.53) 45.60 (7.76) 43.98 (8.18) 44.79 (8.45)
43.85 (6.07) 44.35 (7.55) 40.25 (5.57) 42.30 (7.32)
C indicates markets with quantity-setting producers who do not post prices. KS indicates markets with quantity-setting producers who post prices. KSC indicates a KS session with agents experienced in C and KSKS indicates experience is gained in a KS session. The data are the mean output or capacity from each duopoly across periods 1–8 or 9–12 averaged across the duopoly sessions run in a treatment. Fig. 1. Capacity.
very close to the Nash equilibrium benchmark. Over time, capacities in KS duopolies fall and approach output in C duopolies. The average capacities selected by inexperienced KS duopolists across periods 9–12 are not significantly different from mean output set by inexperienced C duopolists (exact randomization test, nC = 14, nKS = 10, one-sided, p = 0.125). A conjecture consistent with these observations is that agents with experience in C markets will converge more rapidly to the predicted capacity in KS markets than will agents who gain experience in KS markets. To evaluate this conjecture with experienced agents, 5 KS duopolies had participants experienced in C markets and 5 had participants experienced in KS markets. It was not possible to reject the null hypothesis that the source of experience does not matter to the capacity choices of the experienced duopolists (exact randomization test, nC = 5, nKS = 5, two-sided, p = 0.730 and p = 0.444 for periods 1–8 and 9–12).6 Accordingly, the data for experienced participants in KS markets are pooled. The capacity and output data for periods 1–8 and 9–12 are summarized in Table 1. When duopolists are experienced in these environments, the differences between KS capacities and C output across periods 1–8 and 9–12 are not significantly different (exact randomization tests, nC = 5, nKS = 10, two-sided, p = 0.637 and p = 0.688). Over time there appears to be a tendency for both C and KS duopolists to reduce outputs and capacities below the Cournot benchmark. The evidence for this result from C duopoly markets in the literature is mixed.7 We noted there were no significant differences between the mean capacities and outputs of the experienced KS and C duopolists; their aggregate mean over periods 9–12 is 42.82 units. Simple tests of the hypotheses that mean capacity and output selected by experienced KS and C duopolists does not differ from the benchmark of 48 units and from the benchmark of 36 units can be rejected in favor of the alternatives that it is less than 48 and more than 36 (t = 2.974 for the former and t = 3.912 for the latter, the critical value at one percent for a one-tailed test with 14 degrees of freedom is 2.624).
each is informed of the other's decision. Following this, each KS producer posts a price at which output will be sold. The price in the C market is always the market clearing price. There may be two different prices in the KS market and capacity may exceed sales for the duopolists. The mean per-period contract price in the KS market is a quantity-weighted mean contract price (total sales revenues received by the duopolists divided by total units sold in the market). Fig. 2 displays mean per-period contract prices for the two pricing institutions and two levels of experience. The data for inexperienced participants are in the leftmost 12 periods; the data for experienced participants are in the rightmost 12 periods. Circles represent KS duopolies and triangles represent C duopolies. Price data are summarized in Table 2. If market clearing prices were posted by the inexperienced KS duopolists, mean contract prices would average less than L$20 over the first eight periods. Mean contract prices across periods 1–8 in inexperienced KS markets were slightly greater than L$30. This resulted in unsold units which could not be sold in subsequent periods. Had market clearing prices prevailed and no product was discarded, producers would have realized average losses of L$206 across periods 1–8. Over the first 8 periods, the inexperienced KS duopolists generated average per period profit of L$201. Producers adjust to potential losses in the face of high market capacity by
4.2. Price decisions In addition to capacity decisions, producers in the KS markets also make price decisions. After each duopolist makes a capacity decision,
6 This conclusion can also be supported by an analysis of the contract price data (exact randomization test, nC = 5, nKS = 5, two-sided, p = 0.563 and p = 0.444 for periods 1-8 and 9-12). See Section 4.2. 7 Holt (1995) notes that “in multiperiod Cournot duopolies, the outcomes fall on both sides of the Cournot prediction...”
Fig. 2. Contract prices.
D. Goodwin, S. Mestelman / Int. J. Ind. Organ. 28 (2010) 522–525 Table 2 Means and standard deviations of contract prices by period range and treatment. Institution
Inexperienced duopolists Obs.
C
KS
14
10
Institution
Periods 9–12
43.14 (6.40)
43.59 (7.44)
30.37 (6.84)
40.62 (5.79)
C
5
KSC
5
KSKS
5
KS Pooled
from periods 9–12 while only 1 of 5 experienced C duopolies achieved this coordination.
Experienced duopolists Obs.
1–8
525
10
5. Conclusions
Periods 1–8
9–12
44.98 (8.53) 45.14 (7.14) 48.32 (8.37) 46.73 (7.83)
48.15 (6.07) 47.84 (7.26) 51.77 (5.53) 49.81 (7.11)
C indicates markets with quantity-setting producers who do not post prices. KS indicates markets with quantity-setting producers who post prices. KSC indicates a KS session with agents experienced in C and KSKS indicates experience is gained in a KS session. The data are the mean contract prices from each duopoly across periods 1–8 or 9–12 averaged across the duopoly sessions run in a treatment.
posting higher than clearing prices.8 In this experiment, the coordination of capacity decisions and price decisions takes about eight periods. By the ninth period, KS and C markets with inexperienced agents are not very different, and across periods 9–12 there is no significant difference between mean contract prices in C and KS markets (exact randomization tests, nC = 14, nKS = 10, one-sided, p = 0.154). The mean contract prices realized by experienced KS producers are generally slightly higher than those resulting from the output decisions of the experienced C producers, but the prices in both C and KS markets tend to rise above the benchmark Cournot price of L$44. There are no statistically significant differences in mean contract prices in C and KS markets across periods 1–8 and 9–12 (exact randomization tests, nC = 5, nKS = 10, two-sided, p = 0.706 and p = 0.656). Suetens and Potters (2007, 71) “argue that there is often significantly more tacit collusion in Bertrand price-choice than in Cournot quantity–choice markets.” This suggests that KS duopolists may display more tacit collusion than C duopolists. In this experiment there is some support for this conclusion. Although the mean price and capacity data for experienced C and KS markets are not significantly different, 5 of 10 experienced KS duopolies were able to coordinate on the joint profit maximizing outcome in each period
8 This is consistent with Proposition 1 in Kreps and Scheinkman (1983, 335) for behavior given excessive capacity.
Holt (1995, 377) notes that “an open question ... is whether quantity precommitment and Bertrand competition yield Cournot outcomes (in the laboratory).” Although laboratory experiments which evaluate the performance of markets with quantity precommitment and price posting have been conducted, none have directly addressed Holt's question by contrasting the KS and C environments with the same cost and demand parameters. The results of this experiment show that with experience, traders in laboratory duopoly markets who have to make quantity commitments will make comparable commitments regardless of whether they also post prices at which to sell their output or they defer the pricing decision to an exogenous clearing mechanism. While the behavior is comparable across pricing institutions, it does not necessarily conform to the specific theoretical quantity and price predictions when the market structure is duopoly. Experienced duopolists in this experiment tend to produce less output and receive higher prices than predicted. References Anderhub, V., Güth, W., Kamecke, U., Nomann, H.-T., 2003. Capacity choices and price competition in experimental markets. Experimental Economics 6, 27–52. Boccard, N., Wauthy, X., 2000. Bertrand competition and Cournot outcomes: further results. Economics Letters 68, 279–285. Davidson, C., Deneckere, R., 1986. Long-run competition in capacity, short-run competition in price, and the Cournot model. Rand Journal of Economics 17, 404–415. Davis, D., 1999. Advance production and Cournot outcomes: an experimental investigation. Journal of Economic Behavior and Organization 40, 59–79. Fouraker, L., Siegel, S., 1963. Bargaining behavior. McGraw-Hill, New York. Holt, C.A., 1995. Industrial organization: a survey of laboratory research. In: Kagel, J.H., Roth, A.E. (Eds.), Handbook of Experimental Economics (Princeton University Press. Princeton, NJ), pp. 349–443. Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell Journal of Economics 14, 326–337. Muren, A., 2000. Quantity precommitment in an experimental oligopoly market. Journal of Economic Behavior and Organization 41, 147–157. Suetens, S., Potters, J., 2007. Bertrand colludes more than Cournot. Experimental Economics 10, 71–78. Yin, X., Ng, Y.-K., 1996. Quantity precommitment and Bertrand competition yield Cournot outcomes: a case with product differentiation. Australian Economic Papers 36, 14–22.