# «Price competition and market concentration: an experimental study Martin Dufwenberg a, Uri Gneezy b, * a Department of Economics, Stockholm ...»

International Journal of Industrial Organization

18 (2000) 7–22

www.elsevier.com / locate / econbase

Price competition and market concentration: an

experimental study

Martin Dufwenberg a, Uri Gneezy b, *

a

Department of Economics, Stockholm University, SE-10691 Stockholm, Sweden

b

Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology,

Technion City, Haifa 32000, Israel

Received 31 March 1999; received in revised form 31 May 1999

Abstract

The classical price competition model (named after Bertrand), prescribes that in equilibrium prices are equal to marginal costs. Moreover, prices do not depend on the number of competitors. Since this outcome is not in line with real-life observations, it is known as the ‘Bertrand Paradox.’ In experimental price competition markets we ﬁnd that prices do depend on the number of competitors: the Bertrand solution does not predict well when the number of competitors is two, but (after some opportunities for learning) predicts well when the number of competitors is three or four. A bounded rationality explanation of this is suggested. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Bertrand model; Price competition; Experiment; Market concentration; Bounded rationality;

Noise-bidding JEL classiﬁcation: C92; L13

1. Introduction The investigation of oligopolistic markets is central in economics. It is often assumed that ﬁrms in such markets compete in prices (see e.g. Tirole, 1994, p.

* Corresponding author.

E-mail address: gneezy@econ.haifa.ac.il (U. Gneezy) 0167-7187 / 00 / $ – see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S0167-7187( 99 )00031-4 M. Dufwenberg, U. Gneezy / Int. J. Ind. Organ. 18 (2000) 7 –22 224). In the classical model of price competition (named after Bertrand, 1883), the equilibrium entails that price is equal to marginal cost whenever at least two ﬁrms are in the market. In effect, each ﬁrm makes zero proﬁts even in a duopoly situation. Since observations from real markets are not in line with this result, it is referred to as the ‘Bertrand Paradox.’ In this paper we report experimental results of markets in which participants compete in prices. In particular, we consider the effect of changing the number of competitors on market outcome. We study the following game, which corresponds

**to a discrete version of the Bertrand model:**

Each of N players simultaneously chooses an integer between 2 and 100. The player who chooses the lowest number gets a dollar amount times the number he bids and the rest of the players get 0. Ties are split among all players who submit the corresponding bid.

N is a control variable in the experiment, which in different treatments take the respective values 2, 3, and 4. The unique Nash equilibrium in each treatment is a bid of 2 by all players, and each player gets a payoff of only 2 /N.1 The equilibrium payoffs are not zero, as in the standard Bertrand model, but they are almost zero and very low relative to what is otherwise available in the game.

This game has several attractive features that obviate some common critiques of the Bertrand model. Economists have addressed the Bertrand paradox along two different lines. First, it has been argued that certain assumptions that underlie the Bertrand model are not realistic. Edgeworth (1925), Hotelling (1929), Kreps and Scheinkman (1983), and Friedman (1977) respectively point out that the Bertrand paradox goes away if the assumption of constant return to scale is relaxed, if goods are not homogeneous, if capacity constraints are introduced, or if ﬁrms compete repeatedly. The ﬁrms may furthermore have incomplete information about cost functions or demand (as Bertrand models resemble ﬁrst-price auctions, Vickrey, 1961 is relevant), and, with reference to Cournot (1960); model, one may also argue that ﬁrms compete in quantities rather than prices. The second line of attack is aimed at the game-theoretic foundations of the Bertrand reasoning. The assumption of Nash conjectures has been criticized (this type of objection has pre-Nash roots; see Bowley, 1924), and the use of weakly dominated strategies in equilibrium is problematic if ‘admissibility’ is viewed as a reasonable decisiontheoretic requirement to impose on strategic choices (see, e.g., Luce and Raiffa, 1957 (Chapter 13) for supporting arguments). Canoy (1993) discusses many of these references in more depth.

The game we investigate is designed to give the Bertrand model its best shot at The reason that we do not include 0 and 1 in the strategy sets is that the equilibrium would then not be unique.

M. Dufwenberg, U. Gneezy / Int. J. Ind. Organ. 18 (2000) 7 –22 9 not being rejected by the data. If the Bertrand model would fail to perform well under such circumstances, there would be good cause to reject it. The game can be derived from an economic model of price competition with constant returns, homogeneous goods, no capacity constraints, no repeated interaction, and no incomplete information about demand (which is completely inelastic) or costs. The unique Nash equilibrium is strict, and hence does not involve the use of weakly dominated strategies. A bid of 2 is furthermore the unique rationalizable strategy of the game, so the solution has a strong decision-theoretic foundation and Nash conjectures need not be assumed.

We wish to study the behavior of experienced participants, and so must let them play the game several times. Following the classic contribution by Fouraker and Siegel (1963), most other studies of experimental price competition cater for experience by letting a ﬁxed group of participants interact repeatedly.2 However, a drawback with this approach is that a confounding effect is introduced. Since the same ﬁrms interact repeatedly. opportunities for cooperation of the kind studied in the theory of repeated games (see Pearce (1992) for a general overview, and Friedman (1977) for the application to oligopoly) may be created. We wish to isolate the effects of experience from repeated game effects, and therefore let participants play the game several times but not facing the same rivals in each round.

In three out of the four experimental treatments described in this paper, twelve bidders participated. These treatments differed only in terms of how many bidders were matched in each round (two, three, or four). Markets operated for ten rounds.

At the beginning of each round all twelve participants placed their bids. We then randomly matched N bidders together (N 5 2, 3, or 4), resulting in 12 /N different matchings per round. The actual matching and the entire bid vector were then posted on a blackboard. Note that it was relatively unlikely that two participants would run into each other in two consecutive rounds. The set-up is intended to reduce the impact of repeated game effects and to retain the one-shot character of the Bertrand game while allowing for learning over time.

In all these treatments, behavior differed greatly from the theoretical outcome in the ﬁrst round. In the N 5 2 treatment this was also the case in the last round.

However, in the N 5 3 and N 5 4 treatments the winning bids converged towards the competitive outcome by the 10th round. Somewhat surprisingly, these results are roughly consistent with those reported by Fouraker and Siegel (1963, Chapter

10) for the case of repeated experimental price competition within a ﬁxed group of participants. This suggests that it is experience that has the most important impact on price competition, rather than the build-up of reputation or mutual cooperation that may be possible when a given set of ﬁrms interact repeatedly.

However, there is a possible objection to this. Strictly speaking, our design For overviews of this literature. see Plott (1982, 1989) and Holt (1995).

M. Dufwenberg, U. Gneezy / Int. J. Ind. Organ. 18 (2000) 7 –22 creates a repeated game too, one with twelve ordinary players plus nature. Maybe the participants are concerned with building a reputation of not being interested in price wars even if the next-period match is stochastic? Maybe such an effect is relevant with a ‘small’ pool of randomly matched subjects, but not in a larger pool where others will ﬁnd the probability of being matched with the reputation-builder to be negligible? So, could it be that the results change if there is random matching in a larger group than one with twelve participants? In order to control for this, we include a fourth treatment in which N 5 2 but with random matching among 24 instead of twelve participants. It turns out that the results essentially do not change, so our aforementioned ﬁnding appears to be robust.

The theoretical literature on Bertrand competition does not offer an explanation of these observations. We suggest one that relies on bounded rationality. The idea is to illustrate the disruptive effect of ‘noise’ on the viability of the Bertrand outcome when there are sufﬁciently many ﬁrms. If with some ‘small’ probability any ﬁrm in the market may bid differently from what the Bertrand model prescribes, then deviations from the Bertrand outcome can depend on the number of ﬁrms.

**2. Experimental procedure 3**

We now refer to the four treatments as 2, 3, 4, and 2*. We ran two sessions of each treatment. In these sessions groups of respectively two, three, four, and two students were matched in each round, with random matching among twelve students in treatments 2, 3, and 4, and 24 students in treatment 2*.

The students received an introduction, were told they would be paid 7.50 Dutch guilders 4 for showing up, and were randomly assigned private ‘registration numbers’ with an additional student becoming a ‘Monitor’ 5 who checked that we did not cheat. They received instructions (see the Appendix) and ten coupons numbered 1,..., 10. Each student was asked to write on the ﬁrst coupon her registration number and bid for round 1. Bids had to be between 2 and 100 ‘points,’ with 100 points being worth 5 guilders. Each students put her coupon in a box carried by the Monitor. In treatments 2 and 2* the Monitor randomly took two coupons from the box and gave them to the experimenter, who announced the registration number and bid on each coupon. If the bids were different, the low bidder won as many points as her bid and the other bidder won 0 points. If the bids were equal, each bidder won half of the bid. The Monitor wrote this on a

blackboard, took out another two coupons, etc., until the box was empty. Then the second round was conducted the same way, etc. After round 10, payoffs were summed up and the students were paid privately.

Treatments 3 and 4 were carried out the same way, except the assistant each time matched three or four students, respectively, instead of two.

3. Results

3.1. The impact of market concentration (Sessions 2, 3, 4) We refer to the two sessions of treatment 2 as 2a and 2b, etc. To save space, we here report the complete data only from two illustrative sessions: 2a and 4b. See Tables 1 and 2. The complete raw data set from all sessions is given in Dufwenberg and Gneezy (1999) (along with a somewhat more detailed discussion of the results) and can also be obtained from the IJIO home page. Average winning bids and average bids for all session are plotted in Figs. 1–6.

We start by discussing the behavior in round 1, because at this stage no elements of learning or experience exist. It is clear that the Bertrand outcome was not achieved in this round in any session. The average bid (average winning bid) was 33.5 (29.7) and 41.8 (23) in sessions 2a and 2b; 26.4 (21.5) and 30.1 (16.5) in sessions 3a and 3b; and 33.1 (24) and 30.8 (6.3) in sessions 4a and 4b. We also perform a statistical test of whether the bids in different sessions come from the same distribution. We consider each of the (15) possible pairs of sessions separately, use the non-parametric Mann–Whitney U test based on ranks, and

cannot for any pair reject (at a 95% signiﬁcance level) the hypothesis that the observations come from the same distribution.