Information and competition in Cournot’s model: “evidence from the laboratory” Pablo Fajfar1 2 E-mail: [email protected] August 2005

Abstract: The evolutive configuration of Cournot’s model laid out by Vega-Redondo (1997) leads, in scenarios where there is greater knowledge about opponents’ strategies, to firms’ purely imitative behavior converging globally towards a Walrasian equilibrium rather than to a NashCournot one. Experimental studies carried out by Huck, S.; Normann, H., and Oechssler, J. (1998), & (1999) validate this hypothesis on the basis that firms are not able to adjust their output in all periods. Although it is true that at theoretical level the inclusion of inertia is necessary, it is also true that, in experimental terms, it is innocuous in order to guarantee the convergence to the Nash-Cournot Equilibrium (Huck, S.; Normann, H., & Oechssler, J. 2002). For this reason, this paper shows that, when firms can adjust output levels in every period, increased knowledge about the opponents becomes irrelevant in terms of the market’s competitive performance.

Jel – classifying numbers: L13, C92, C72, D83

1

Centro de Investigación en Métodos Cuantitativos Aplicados a la Economía y la Gestión, Facultad de Ciencias Económicas de la Universidad de Buenos Aires – Argentina, http://www.econ.uba.ar/www/institutos/cma/ 2 Facultad de Ciencias Empresariales, Universidad Abierta Interamericana – Argentina.

I. Introduction The effects of greater knowledge about opponents’ strategies are the object of recurring discussion in the context of issues related to the industrial organization of oligopolistic markets. This debate intensifies when the productive units compete by quantities within scenarios of symmetrical costs and technologies.1 When applied to theoretical models of competition a la Cournot and with symmetrical NashCournot equilibriums, the formal consequence of increased information is that the firms’ aggregated level of output approaches to the Walrasian equilibrium rather than to the perfect subgame Nash-Cournot equilibrium. Based on behavioral patterns such as the one of following the most successful firm, Vega-Redondo (1997) demonstrated that a “purely imitative” dynamics globally converges to the Walrasian equilibrium.2 3 One can spontaneously understand the reason for such conclusion by supposing the existence of a simple market in which inverse demand and individual production cost are known by the firms. In each period, all producing units must decide the quantity to produce by observing the market price and quantity that prevailed in the previous period.4 To the extent that the information regarding the individual quantities produced by the opponents is known - that is, to the extent that it “is disaggregated” – the firm that adopts the mechanism of following the most successful firm will tend to produce a similar quantity than the one of the latter. If the price was higher than the (symmetrical) marginal cost, and if it is assumed that there are no fixed costs, then the firm with the greatest profit will have been the one of the largest output. It should be noted, then, that whoever imitates the best performer would end up necessarily increasing his production and sequentially decreasing the market price. Assuming that the behavioral pattern previously described has a relevant relative weight in the firms that make up the market, the performance of the latter will tend to approach to the Walrasian equilibrium. The experimental evidence of Huck, S.; Normann, H., and Oechssler, J. (1998), & (1999) are consequent with Vega Redondo’s model. Both works analyzed the aggregate and individual quantities produced by a group of four firms in the laboratory. In every case, the inverse demand and the (symmetrical) marginal costs were known by and amongst the firms that made up the market. Moreover, the number of periods in the game was of common knowledge. At every stage of the game, each firm had a probability of 2/3 of being able to adjust its output on the basis of the information gathered from the previous period.5 This information varied according to two groups.6 One of them (the one with less information) only knew the aggregated quantities produced by the opponents, as well as the market price. The other group (the one with the greatest amount of information) had specific knowledge of the individual quantities produced by each one of the opponents, as well as of the market price. The results obtained in terms of “aggregated quantities” (1998) turned out to be closer to the Walrasian equilibrium in those groups with the greatest amount of information. As for the study of individual quantities (1999), the results showed that the adjusting dynamics of

1

The first references on the subject were Stigler (1964); Fouraker & Siegel (1963) Vega- Redondo takes an “evolutive” approach to game theory. In such approach, agents observe relative payments rather than absolute ones (classic approach to game theory). To the extent that agents observe relative payments, evolutive stability is explained by the fact that no player receives less profit than the rest. 3 This paper will not discuss the formal structure of Vega-Redondo’s model, but the experimental evidence to it. 4 On a formal ground, Vega-Redondo supposes the existence of probability “p” – common to every firm – of not being able to adjust the output in each period. 5 The inclusion of the probability of output adjustment responds, once again, to Vega-Redondo. 6 This dichotomy refers to the work of 1998. 2

2

the markets/groups with more information significantly approached the mechanism of imitating the most successful firm.7 In a previous study (2004) I have attempted to repeat the H.-N.-O. experiment, finding that for any level of information about the opponents, the aggregated quantities tended to be closer to the Nash-Cournot equilibrium at the final stages of the game, in scenarios with no inertia. Although the “greater amount of information” phenomenon wasn’t exhaustively treated, the results obtained didn’t allow us to assert that the greater amount of information about the opponents had a significant impact on the level of competition.8 In the present work I will try to go deep into my previous study, adding enough experimental evidence to question a priori that the alternative between Cournot and Walras is a result of the amount of information about the opponents. The only difference concerning this issue with Huck, S.; Normann, H. and Oechssler, J. (1998) – (1999) is, again, that firms can adjust their output in every period. According with this fact, it is important to clarify that the same authors can’t find significant differences respect to the inclusion of inertia and the convergence to the Nash-Cournot Equilibrium in a later paper (Huck, S.; Normann, H. y Oechssler, J. 2002)9. Since that, the same treatment must be proved for the rival’s information phenomenon and the market’s competitive performance. In the next section the different views of the theoretical model are presented. Section III sets forth the experiment, which was carried out, as well as the research hypotheses. In section IV I present the experiment results and, finally, in section V, the conclusions.

7

The work also included a study on the aggregate quantities. These were significantly greater in the groups with more information. 8 The only evidence found was that the proximity to the Nash-Cournot equilibrium was smaller in the groups with less information about the opponents for the last observations of the game. 9 The paper mentioned is “Stability of the Cournot process – experimental evidence”, International Journal of Game Theory 31: 123 – 136 (2002).

3

II. The Model Let i be a set of N firms that compete simultaneously for a period of time t = {1, 2,3, 4...T } in a market

where

inverse

demand

is

P ( Qt ) = max [ ( a − bQ t ), 0 ] where Q t =

known

and

is

defined

as

N

∑q i =1

it

. In addition, consider the marginal costs of

production to be symmetrical and known, so that ∀i ∈ N ∧ t ∈ T , C (qit ) = cqit , and consider that there is no temporal discount factor. Based on the foregoing, the only subgame perfect Nash equilibrium is the Cournot equilibrium itself, this is: 1. ∀i ∈ N ∧ t ∈ T qitBR =

(a − c) (a − c) , being the total quantity supplied Qt = N . It should b(1 + N ) b(1 + N )

be noted that this result corresponds to the conjunction of best response (strategic behavior) of each of the firms that make up the market. Suppose, now, a bounded rationality scenario, where firms use only the historical information to define their strategies. From a formal point of view, firms observe the total quantity and price of the previous period and, according to that, generated their own supply. Starting from this assumption, the profit function of the firm j ∈ N / j ≠ i will take the following form:

  N −1   2. Max π q jt ( q( N − j ),t −1 ) = a − bq jt − b ∑ qi ,t −1 − c q jt , deriving as Best Respond Function:   i =1 i≠ j   3.

a−c 1 N −1 q (q( N − j ),t −1 ) = − ∑ qi,t −1 . Clearly, this system does not converge 2b 2 i =1 BR jt

i≠ j

asymptotically towards the Nash Cournot equilibrium like the one stated in 1., given the existence of roots outside the unit circle.10 However, the inclusion of certain inertia in the process of adjustment allows us to create the conditions for their convergence. Be it formally considered that at each stage t = 1, 2,3....T of the game, each firm i ∈ N has a probability θ ∈ (0,1) of not being able to adjust their output.11 That is, the possibility of output adjusting is forbidden by technical or cost related reasons in some periods. Note that this partial output adjustment process allows us to re-state the best response function presented in 3. as:

4.

q (q( N − j ),t −1 ) = θ q j ,t −1 BR jt

  a −c 1 N −1  − ∑ qi ,t −1  , θ ∈ (0,1) , + (1 − θ )  2b  2 i =1   i≠ j

asymptotical solution ∀i, j ∈ N ; qit = q jt =

10 11

being

its

(a − c) . b(1 + N )

Convergence rests guaranteed only for the case of a duopoly. For a complete analysis of this process see Szidarovszky, F., Rassenti, S., & Yen, J. (1994).

4

Consider now the layout of Cournot’s model by Vega-Redondo (1997) presented in the introduction. For that, suppose that firms adopt an attitude of “imitation of the best” in those periods in which they are able to adjust their output.12 The necessary condition for such behavior is that firms can dispose of information about the individual quantities produced by their opponents (in addition to the price).13 In this case, the set of relevant information at t for determining the quantities at t + 1 will be: 5.

St = {qit / i ∈{1, 2....N} ∧ π qit ≥ π qi′t ∀i′ = 1, 2,3...N } where π qi ' t = π q ( q ( N − i ′ ),t ) i ′ ,t

Note that firm’s j attitude represented in 4 will now be: 6. q jt = qi ,t −1 where qi ,t −1 ∈ St −1 .14 Intuitively, this result is easily understood: to the extent in which t − 1 price has been greater than the marginal cost, the firm with the greatest profit will have been the one with the greatest output. Given that the behavioral pattern of firms is the one of following the company with the greatest profit, the quantities produced will tend sequentially to increase.15 The experiments carried out by Huck, S.; Normann, H., and Oechssler, J. (1998) - (1999) tried to test equations 4 and 6 on the basis of greater amounts of information about the opponents. Based on a context where the probability of revising the quantities was of 2/3, the results obtained in terms of aggregate output quantities was significantly greater when information regarding the individual quantities produced by the opponents was available by the agents. On the other hand, concerning the individual adjustment’s dynamics, equation 6, had a greater explanatory power than equation 4 in groups with information about the quantities produced by the opponents.16

12

Consider, in addition, that deviation from this behavior tends to zero as the stages of the game increase. In other words, the probability of mutation or making mistakes tends to be negligible as the game develops. 13 Note that for the fulfillment of 4. only information regarding the aggregate quantity and the price is required. 14 Note that, while the result obtained in 4. respond to a strategic behavior in agents with bounded rationality, the one of imitation of the best doesn’t. That is, it is not derived from the best-response function. 15 When the price is smaller than the marginal cost, the firm with the greatest profit (smaller loss) will be the one that produced the smaller quantity. In this case, quantities would tend to decrease systematically until once again the price exceeds the marginal cost. After that, the dynamics of the game will approach once more the marginal cost. 16 It has to be mentioned that, in a later paper (2002) - referenced in the introduction -; authors had found no significant differences in an experimental level between equations 3 and 4. So, the incorporation of inertia results innocuous to guarantee the convergence or the approximation to the Nash-Cournot Equilibrium.

5

III. The experiment; its parameters, and the hypotheses of behavior. The experiment was carried out with students from Microeconomics I and Mathematics for Economists courses from the Facultad de Ciencias Económicas de la Universidad de Buenos Aires (School of Economics, University of Buenos Aires) – Argentina, using the OLIGOP software created by the Economic Science Laboratory of Arizona University.17 The participants had an average age of 22, being all of them students in their first professional year of the Economics program. All in all, the experiment was carried out in a group of 112 volunteers divided in 16 groups, each one consisting of seven randomly selected members. It should be noted that most of them ignored the existence of Cournot’s model, and those who knew it, had only read about it in very broad ways in an introductory course. Each participant was presented the choice of playing in the OLIGOP simulation program, knowing that he/she was going to receive a monetary amount based on a scale of 1 Argentine peso for every 1000 monetary units obtained in the game. The 16 groups distributed in pairs played during 8 Saturdays between June and September of 2004 in the computer lab. The 14 participants of each pair were instructed together as to the game and which commands they were to use. In every case, the use of intensive mathematical formalisms was avoided during the instruction process. None of the participants was told exactly how long the game was going to last; but they were told that the maximal duration would not exceed 35 stages.18 Moreover, it was pressed upon them that any type of communication amongst them during the course of the game would be banned. Once the rules of the game and the commands used were understood, a simple test of understanding was carried out in each of the 8 sessions. Of the 14 participants involved in each session, 7 of them started playing while the other 7 waited their turns outside the lab. Following the assumptions of Cournot’s generalized model, the seven participantscompetitors that made up each market (each group) knew the demand function they were facing, as well as their own costs function and the one of their opponents. The information that was available to each competitor in relation to the quantities sold by their opponents was the following: In “show groups”, each participant knew the individual quantities sold by their opponents in the previous period, while in the “no show groups” they only knew the aggregated quantities.19 Out of the 16 groups studied, half took the “show” category and the other half the “no show” category. 20 Each stage of the game ended when all the participants determined their output.21 After that, the next stage began, in which each participant knew their own profits made in the previous play the price and quantities (the latter depending on the group category in question; that is “show” or “no show”). The OLIGOP software includes a personal calculator for each participant that suggests him or her, the optimum quantities to be sold given the participant’s subjective conjecture about the opponents’ output in stage t. The inverse demand function that all the groups faced was: 17

The software animates Cournot’s model for a group of up to 7 participants. Each one of them plays simultaneously competing for quantities during a limited number of times. The duration of the game as well as the parameters used in the simulation is discretional for the researcher. 18 Note that the terminal condition was finite but uncertain for the agents. 19 “Show” groups had more information concerning their opponents’ strategies available to them. 20 In each of the 8 sessions 14 participants entered the lab, of which 7 would be in the “show” category and 7 in the “no show”. This division was only known to the researcher; that is, participants found out once the game had started. 21 The time limit to decide the quantities was of 60 seconds per stage. In case the participant-firm did not change his o her quantities during this time, the program automatically considered the quantity produced (sold) in the previous period.

6

7

7.

P(Qt ) = max [100 − Qt , 0] ; being Qt = ∑ qit the total quantity sold by the group of seven i =1

firms that made up each group (market). The cost structure was: C (qit ) = 32qit for the “show groups” and C (qit ) = 30qit for the “no show groups” respectively. The differentiation of marginal costs was fundamentally due to the fact that the people leaving the lab often exchanged words with those entering to the room.22 The duration of the game was of 32 periods for the eight groups in the “show” category, and of 30 for the “no show” category. It is worth informing that in some groups of both categories the duration of the game was changed with respect to the pre-arranged one. The reason for this lied in the above paragraph23 According to the parameters that were inputted in the program, the Nash-Cournot subgame perfect equilibriums are: 7

8.

Qt = ∑ qit = 59.5 ∧ qit = 8.5 , for groups in the “show” category; and

9. Qt =

i =1 7

∑q i =1

it

= 61.25 ∧ qit = 8.75 , for those in the “no show”. The individual profits each

participant would receive (given the decided scale) compatible with SPE were 7.2/100 Argentine pesos for ”show” and 7.6/100 for “no show”.24 In all cases participants started off with no monetary endowment; and those who ended up with a negative balance after the end of the game wouldn’t have to pay anything. In accordance with the results obtained by Huck, S.; Normann, H., and Oechssler, J. (1998) (1999), the hypotheses considered will be the following: groups "show"

 Qt observed  H1 : mean  Nash −Cournot   Qt  1  for : t ∈[1, T ] ∧ t ∈  T ,T  . 3  max π t −1 i ,t −1

H 2 : q jt = prox  q

 Qt obseved  > mean  Nash −Cournot   Qt 

groups "no show"

,

  1 6   " groups show " ∧ q jt = prox 35 − ∑ qi ,t −1    2 i =1 i≠ j  

1  "groups no show " for : j ≠ i; t ∈ [1, T ] ∧ t ∈  T , T  3  H 2′ : The information regarding the mean quantity produced by the opponents (of common knowledge to both groups) would prove irrelevant. 22

Once again, recall that two groups took part in each Saturday session. Formally, in three groups from the “show” category and in three from the “no show”, the number of stages differs from 32 and 30 periods respectively. 24 These profits refer to the SPE at each stage. 23

7

The first hypothesis holds that the ratio between the observed aggregate quantities and those predicted by the Nash-Cournot equilibrium must be, in average, higher in those groups with greater amounts of information about the opponents.25 The second one states that the dynamic adjustment of individual quantities must approach to the imitation of the best in the groups with greater amounts of information, and must approach to the BRF (myopic but with no inertia) in the groups with smaller amounts of information. Related to this, an ad hoc hypothesis is added that states that information of the mean quantity produced by the opponents should prove irrelevant to the adjustment process.26

25

This hypothesis is presented both for the total of periods played as for the two last thirds of the game. 26 The periods studied are the same as those of hypothesis 1.

8

IV. Experiment Results Table 1 below shows the ratios between observed aggregated quantities and aggregated quantities predicted by the Nash-Cournot equilibrium for different lapses of the game. (Table 1.1 included in the appendix contains detailed information for each market). Table 1:

Groups1) and Periods studied:

1) 2)

2) Qtobserved Statistical: Nash −Cournot ; Mann – Whitney Z stat & Qt (P-value) Mean (Deviation)

Show; t ∈ [1, T ]

1.11 (0.25)

No Show; t ∈ [1, T ]

1.28 (0.6)

1  Show; t ∈  T , T  3 

1.10 (0.18)

1  No Show; t ∈  T , T  3 

1.13 (0.32)

 1  Show; t ∈ 1, T   3 

1.14 (0.35)

 1  No Show; t ∈ 1, T   3 

1.58 (0.87)

1 2  Show; t ∈  T , T  3 3 

1.08 (0.18)

1 2  No Show; t ∈  T , T  3 3 

1.17 (0.36)

2  Show; t ∈  T , T  3 

1.11 (0.18)

2  No Show; t ∈  T , T  3 

1.08 (0.26)

-1.009 * (0.3128)

-1.091* (0.2754)

2.86 ** (0.0038)

0.726 * (0.468)

-2.242 ** (0.024)

Each group includes the 8 markets in the experiment. The null hypothesis contrasted through this ”non parametrical” test is that the mean value

Qtobserved of Nash −Cournot is the same for both groups. Qt (*) Under 5% significance cannot be rejected the hypothesis of equal means. (**) Under 5% significance cannot be accepted the hypothesis of equal means

9

 Qt observed  Note that in contrast to the first proposed hypothesis, the rate  Nash −Cournot  is not  Qt  1  significantly different in t ∈ [1, T ] ∧ t ∈  T , T  between “show” and “No-Show” groups. 27 28 3  Graphics 1 and 2 show the differences respect to the “Nash Cournot” equilibrium, in the first and last stages of the game for all of the 16 experimental markets:

(Q/Nash)-1

G1: Difference respect to the NashCournot equilibrium "Show" groups 0,50 0,40 0,30 0,20 0,10 0,00 -0,10 -0,20 -0,30 -0,40

First Third [1,1/3T] Last Third (2/3T,T]

1

2

3

4

5

6

7

8

(Q/Nash)-1

G2: Difference respect to the NashCournot equilibrium groups "no - show" 2,40 2,10 1,80 1,50 1,20 0,90 0,60 0,30 0,00 -0,30

First Third [1,1/3T] Last Third (2/3T,T]

1

2

3

4

5

6

7

8

27

Note that if it was this way, the ratio would have been larger for the “no-show” groups. The only exception that was found (consistent with the results obtained by H-N.-O.) appeared in the last period of the game. About this, the reason of that result responded punctually to the group 1’s behavior of the “show” category. This group began producing significantly low quantities and assimilable to the one of a cooperative structure. After a defection, the quantities triggered to a market of Walrasian characteristics. 28

10

Note that in concordance to Fajfar, P. (2004), the markets performance in the game’s terminal steps happen to be closer to the subgame perfect equilibrium with independence to the level of information.29

For studying the dynamic adjustment in individual’s quantities, the following model was estimated: 6

max π t-1 i ,t −1

10. qit − qi ,t −1 = β 0, i + β1 ( BRFi ,t −1 − qi ,t −1 ) + β 2 (q

− qi ,t −1 ) + β3 (

qit − qi ,t −1 = β 0, i + β1 (lbest ) + β 2 (lsim) + β3 (lme dim) .

∑q j =1

6

j ,t −1

− qi ,t −1 ) , or:

The lbest variable indicates that adjustment’s dynamics in t , t − 1 for a firm i can be explained in terms of the difference between the optimal quantities that this firm had to have produced and the quantity that firm effectively produced in t – 130. The variable lsim expresses that the dynamic adjustment in t , t − 1 of the company is explained by the difference between the quantity produced by “the company with larger profit in t − 1 ” and the quantity that i have effectively produced in t − 1 . 31 Finally, Imedim variable supports that the dynamic adjustment in t , t − 1 for a firm i is explained by the difference between the mean quantity produced by its rivals in t − 1 and the effectively produced quantity i in t − 1 32. Tables 2 and 3 show the estimation results by the fixed effects method in OLS. The first one details the values adopted by the coefficients in the 8 markets for both groups (show and noshow) for the total played periods. The second presents the same data for the last two thirds of the game.

29

Only 2 of the 16 groups experienced markets (pertaining to the category "show") displayed discrepancies. 30 Best myopic response without inertia 31 Note that this variable is solely relevant for “show” groups. . 32 This variable, which is common for both groups, it’s incorporated as a product of the ad hoc hypothesis proposed by the author. It must be added that was included, also, in H–N.–O.

11

Table 2; OLS- fixed effects, Show & No-Show t ∈ [1, T ] : Parameters Groups and periods studied:

β1

β2

β3

Constant

R2

Show; t ∈ [1, T ] : Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Market 7 Market 8

0.034 (0.032) P-Value=0.29 0.256 (0.052) P-Value=0.00 0.234 (0.07) P-Value=0.001 0.105 (0.057) P-Value=0.06 0.34 (0.073) P-Value=0.00 0.17 (0.105) P-Value=0.105 0.163 (0.101) P-Value=0.108 0.022 (0.10) P-Value=0.826

0.09 0.122 -0.12 (0.035) (0.051) (0.26) P-Value=0.011 P-Value=0.018 P-Value=0.64 0.065 0.49 0.076 (0.038) (0.064) (0.3) P-Value=0.089 P-Value=0.00 P-Value=0.8 0.095 0.337 -0.063 (0.06) (0.06) (0.38) P-Value=0.114 P-Value=0.00 P-Value=0.87 0.088 0.45 0.187 (0.05) (0.3) (0.07) P-Value=0.108 P-Value=0.00 P-Value=0.54 0.128 0.018 1.44 (0.041) (0.43) (0.05) P-Value=0.66 P-Value=0.022 P-Value=0.001 0.036 0.49 1.22 (0.072) (0.084) (0.56) P-Value=0.672 P-Value=0.00 P-Value=0.031 0.054 0.52 0.56 (0.07) (0.09) (0.54) P-Value=0.574 P-Value=0.00 P-Value=0.302 0.277 0.33 -1.00 (0.07) (0.07) (0.58) P-Value=0.00 P-Value=0.00 P-Value=0.087

0.51 (0.086) P-Value=0.00 0.29 (0.043) P-Value=0.00 0.226 (0.06) P-Value=0.00 0.45 (0.07) P-Value=0.00 0.44 (0.06) P-Value=0.00 0.24 (0.06) P-Value=0.00 0.26 (0.1) P-Value=0.009 0.42 (0.07) P-Value=0.00

0.473 (0.09) P-Value=0.00 0.48 (0.064) P-Value=0.00 0.413 (0.076) P-Value=0.00 0.44 (0.08) P-Value=0.00 0.31 (0.08) P-Value=0.00 0.33 (0.08) P-Value=.00 0.253 (0.1) P-Value=0.011 0.36 (0.08) P-Value=0.00

0.15 0.45 0.42 0.35 0.28 0.36 0.38 0.39

No Show; t ∈ [1, T ] : Market 1 Market 2 Market 3 Market 4 Market 5 Market 6 Market 7 Market 8

1.79 (0.65) P-Value=0.007 -1.197 (0.17) P-Value=0.261 0.97 (0.5) P-Value=0.056 1.75 (0.613) P-Value=0.005 1.92 (0.46) P-Value=0.00 0.5 (0.6) P-Value=0.406 4.5 (1.92) P-Value=0.02 0.86 (0.59) P-Value=0.148

0.5 0.41 0.32 0.46 0.37 0.29 0.25 0.4

12

1 3

 

Table 3; OLS- fixed effects, Show & No-Show t ∈  T , T  : Parameters Groups and periods studied:

β1

β2

β3

Constant

R2

0.0526 (0.08)

0.108 (0.047)

0.098 (0.063)

0.102 (0.48)

0.18

Show; t ∈  1 T , T  : 3  Market 1

P-Value=0.519 P-Value=0.025 P-Value=0.125

Market 2 Market 3 Market 4

0.345 (0.66)

0.054 (0.046)

0.489 (0.08)

0.325 (0.388)

P-Value=0.00

P-Value=0.243

P-Value=0.00

P-Value=0.405

0.26 (0.06)

0.0005 (0.0618)

0.47 (0.08)

0.17 (0.33)

P-Value=0.00

P-Value=0.99

P-Value=0.00

P-Value=0.604

0.15 (0.06)

-0.007 (0.06)

0.513 (0.08)

0.39 (0.34)

P-Value=0.00

P-Value=0.248

0.463 (0.07)

0.858 (0.39)

P-Value=0.00

P-Value=0.029

0.448 (0.8)

0.52 (0.61)

P-Value=0.00

P-Value=0.394

P-Value=0.015 P-Value=0.913

Market 5

0.21 (0.08)

0.019 (0.044)

P-Value=0.008 P-Value=0.661

Market 6

0.023 (0.13)

0.16 (0.099)

P-Value=0.859 P-Value=0.116

Market 7 Market 8

P-Value=0.83

0.26 (0.07)

0.033 (0.07)

0.62 (0.09)

0.366 (0.38)

P-Value=0.001

P-Value=0.64

P-Value=0.00

P-Value=0.347

0.28 (0.08)

0.071 (0.053)

0.248 (0.08)

0.26 (0.44)

P-Value=0.002 P-Value=0.184 P-Value=0.002

0.52

0.39

0.32

0.38

0.36

0.48

0.37

P-Value=0.56

No Show; t ∈  1 T , T  : 3  Market 1 Market 2 Market 3

0.63 (0.11)

0.46 (0.11)

1.77 (0.82)

P-Value=0.00

P-Value=0.00

P-Value=0.033

0.22 (0.049)

0.435 (0.07)

-0.052 (0.14)

P-Value=0.00

P-Value=0.00

P-Value=0.708

0.295 (0.04)

0.173 (0.07)

0.14 (0.26)

P-Value=0.00

Market 4 Market 5 Market 6 Market 7 Market 8

0.482 (0.09)

1.255 (0.46)

P-Value=0.00

P-Value=0.00

P-Value=0.008

0.16 (0.06)

0.36 (0.07)

0.52 (0.31)

P-Value=0.008

P-Value=0.00

P-Value=0.101

0.23 (0.04)

0.29 (0.05)

-0.275 (0.18)

P-Value=0.00

P-Value=0.00

P-Value=0.133

0.5 (0.14)

0.235 (0.13)

6.27 (1.98)

0.29 (0.05) P-Value=0.00

0.35

0.32

P-Value=0.014 P-Value=0.588

0.473 (0.08)

P-Value=0.00

0.55

0.49

0.25

0.38

0.37

P-Value=0.076 P-Value=0.002

0.074 (0.046)

-0.071 (0.19)

0.26

P-Value=0.112 P-Value=0.708

13

In the case of groups with smaller amounts of information about rivals, “no show groups”, the results show that for the total of periods played, t ∈ [1, T ] , the dynamics through which firms adjust their individual quantities is explained by both variables. That is to say, firms observe both the optimum quantity they should have produced in t − 1 and the mean quantity produced by their opponents. Here, two points must be made clear. First, in every case the sign of the estimated coefficients was the one expected, and estimated coefficients were significant at 1%. Second, the Wald test did not allow us to reject the hypothesis of equality

1 3

 

of the coefficients for markets 1, 4, 5, 6, 7 and 8.33 Regarding the adjustment in t ∈  T , T  , the coefficients tend once again to be globally significant but the relative weight of the best myopic response (without inertia) grew bigger.34 Thus, coefficient β1 was significant at 1% in the 8 markets included in the experiment; while β3 was significant in six out of eight markets at 1% and in one at 7.6%. In the case of groups with greater amounts of information about the opponents, “show groups”, the results tended to be somewhat ambiguous in reference to the best myopic response (without inertia), but exhaustive in terms of the hypothesis of imitation. Nevertheless, the behavioral pattern that best explains the dynamic of adjustment is the one that consists in following the mean. For the total of periods played, that is, t ∈ [1, T ] , the most explanatory variable is the following the mean, for which coefficients adopted the expected sign and were significant at 2%. Following right behind, adjustment regarding the best myopic response (without inertia) was significant in four of the eight markets under 1% and 6% of significance respectively.35 Finally, the behavior of “imitation of the best” was only significant in three markets at 1% and 9% of significance.

1 3

 

When analyzing the dynamics in t ∈  T , T  , results stress once again the feature of following the mean36, but with the following considerations: a) Adjustment regarding the best myopic response (without inertia) turns to be significant in six markets out of eight at 1%, that is, it’s explanatory power increases. b) Adjustment regarding imitation of the best turns to be an exception to the rule. Its explanatory power is limited to just one of the eight markets tested in the experiment. In this last one, a mono-dependent behavior is observed.

33 34

The mentioned hypothesis states that

β1 = β 3 , versus the alternative β1 ≠ β 3 .

Notwithstanding, note that there is no case in which the dynamic adjustment’s was explained solely by one variable. 35 In three markets it was significant at 1% and in one at 6%. 36 Coefficients turn to be significant at 1% in 7 out of the 8 markets.

14

V. Conclusions In the evolutionary approach of game theory, agents try to maximize their relative payments rather than the absolute ones. This fact entails that many standardized results in economics are subject to a restate37. In this aspect, Vega Redondo (1997) demonstrates that the performance of an oligopolic market with Cournotians characteristics may converge to the Walrasian equilibrium, when the companies have enough information about the quantities produced by their competitors. The Huck, S.; Normann, H., and Oechssler, J. (1998), & (1999) experimental results happened to be consequent to the Vega – Redondo’s theoretical model, in a context where the companies can’t adjust the production in all the periods. In this paper a reproduction of the H.-N.-O.'s experiment was attempted, in a scenario where the companies can adjust their production in all periods38. After 16 repetitions with different groups, the results obtained substantially differed from the H.-N.-O.’s ones. In the first place, the quotient between the mean aggregated quantity produced by the companies and the Nash-Cournot equilibrium were not significantly different in groups “show” and “no –show” 39. Respect to this last fact, notice that in case there was a difference, the “no-show” groups would have adopted larger levels40. In second place, the dynamic adjustment of individual quantities produced by the companies in the “show” groups was far from being explained by the hypothesis of imitation of the best. As a final note, the main conclusion obtained from this paper is that, experimentally, the companies tend unfailingly to observe the mean behavior of the market41. In addition to this fact, the strategies usually adopted during the game show to be a mix between the best myopic answer (with no inertia) and the “following the mean” one. Acknowledgements: 1. To Maria Teresa Casparri, for the financial support surrounding the incentives in the game; as well as for her daily stimulus on my research. 2. To Nicholas Aguelakakis, for the unconditional collaboration in the making of this work. 3. To Luis Trajtemberg, for his suggestions regarding the econometrical model used. 4. To Gonzalo Wolfenson for processing the data.

37

A clear example of this can be found in the traditional “ultimatum game”. In formal terms, the fact that firms can’t adjust their production in every period is due to the fulfillment of equation 4. This behavior hypothesis is incorporated into several theoretical and experimental essays to enable Nash-Cournot equilibriums within limited rationality contexts. 39 “Show” groups had more information concerning the quantities produced by their opponents available to them. 40 Related to this fact, the markets’ performance in the final stages of the game was, independently to the level of information, nearer to a Nash-Cournot equilibrium. 41 This fact has no relation with the level of information regarding the opponents. 38

15

References Alós-Ferrer; C. (2004), “Cournot versus Walras in dynamic oligopolies with memory”, International Journal of Industrial Organization Vol. 22 (2004) pages 193-217. Fajfar, P. (2004), “Aprendizaje en un juego repetido de Cournot: Un experimento de laboratorio”. Asociación Argentina de Economía Política, document nº 1896. Fouraker, L. Siegel, S. (1963), Bargaining Behavior McGraw –Hill, New York. Huck, S.; Normann, H.; Oechssler, J. (1998), “Does information about competitors’ actions increase or decrease competition in experimental oligopoly markets’?” Department of Economics, Humboldt University, Berlin. Huck, S.; Normann, H.; Oechssler, J. (1999), “Learning in Cournot oligopoly – An experiment”, The Economic Journal, vol.109 March 1999; Department of Economics, Humboldt University, Berlin (1997). Huck, S.; Normann, H.; Oechssler, J. (2002), “Stability of the Cournot process – experimental evidence”, International Journal of Game Theory Vol. 31 pages 123-136. Huck, S.; Normann, H.; Oechssler, J. (2004) “Two are few and four are many: number effects in experimental oligopolies”, Journal of Economic Behavior & Organization Vol. 53 (2004) pages 435-446. Rassenti, S.; Reynolds, S.; Smith, V.; Szidarovszky, F. (2000), “Adaptation and convergence of behavior in repeated experimental Cournot games”, Journal of Economic Behavior & Organization Vol. 41 (2000) pages 117-146. Reichmann, Thomas. (2002), “Cournot oder Walras? Agentenbasiertes Lernern, Rationalität und langfristige Resultate in Oligopspielen“, Discussionpapier Nr 261, Universität Hannover. Schipper, B. (2004), “Imitators and Optimizers in Cournot Oligopoly”, Department of Economics, University of Bonn. Stigler, G. (1964), “A Theory of Oligopoly”, Journal of Political Economy 12, pages 44-61. Szidarovszky, F.; Rassenti, S.; Yen, J., (1994) “The stability of the Cournot solution under adaptive expectation”. International Review of Economic and Finance 3 (2). Vega-Redondo (1997), “The Evolution of Walrasian Behavior”, Econometrica, vol. 65 pages 375-384.

16

Appendix: Table 1.1 Experiment1

Total Sample2

First Third3

Second Third4

Last Third5

Mean

Q/Nash

Deviation Mean

Mean

Q/Nash

Deviation Mean

Mean

Q/Nash

Deviation Mean

Mean

Q/Nash

Deviation Mean

1_29

70.97

1.16

0.31

72.70

1.19

0.31

73.30

1.20

0.41

66.44

1.08

0.15

2_30

60.17

0.98

0.12

58.90

0.96

0.18

61.50

1.00

0.08

60.10

0.98

0.08

3_29

71.59

1.17

0.34

89.50

1.46

0.37

63.70

1.04

0.19

60.44

0.99

0.11

4_29

73.14

1.19

0.32

83.20

1.36

0.40

69.40

1.13

0.28

66.11

1.08

0.07

5_30

72.26

1.18

0.31

82.90

1.35

0.42

67.60

1.10

0.10

66.30

1.08

0.17

6_30

73.86

1.21

0.44

99.50

1.62

0.48

64.80

1.06

0.10

57.30

0.94

0.08

7_30

134.60

2.20

0.41

197.00

3.22

0.20

112.70

1.84

0.19

93.30

1.52

0.31

8_30

70.93

1.16

0.48

91.60

1.50

0.59

61.30

1.00

0.10

59.90

0.98

0.10

1_31

59.68

1.00

0.30

41.50

0.70

0.24

59.00

0.99

0.08

76.82

1.29

0.17

2_27

64.26

1.08

0.14

64.10

1.08

0.13

65.10

1.09

0.10

63.29

1.06

0.20

3_31

63.26

1.06

0.23

68.40

1.15

0.32

65.00

1.09

0.15

57.00

0.96

0.15

4_32

64.75

1.09

0.14

66.40

1.12

0.15

59.72

1.00

0.12

68.27

1.14

0.11

5_32

67.68

1.14

0.10

69.60

1.17

0.14

65.80

1.11

0.08

67.66

1.14

0.06

6_32

74.78

1.26

0.23

83.50

1.40

0.19

71.50

1.20

0.31

70.25

1.18

0.15

7_32

69.15

1.16

0.26

83.20

1.40

0.30

65.70

1.10

0.13

60.33

1.01

0.16

8_32

64.93

1.09

0.27

68.20

1.14

0.44

62.90

1.06

0.15

63.91

1.07

0.11

No Show

Show

1

The number after the dash in each market indicates the number of periods played.

2

Period t ∈ 1, T

[

]

 1    1 2  4 Period t ∈  T , T  3 3  2  5 Period t ∈  T , T  3  3

Period t ∈ 1, T  3

17