Tacit collusion in price-setting duopoly markets: experimental evidence with complements and substitutes.

• Author: Anderson, Lisa R.

1. Introduction

   For decades, economists have studied oligopoly behavior using laboratory experiments. Much attention has been devoted to identifying factors that facilitate tacit collusion. We contribute to this literature by studying the effect of demand structure on the ability of subjects to collude within the price-setting model. Specifically, we consider Bertrand substitutes and Bertrand complements. (1) In the case of substitutes, the model generates upward-sloping reaction functions in prices. Hence, theory predicts that if one seller moves away from the Nash solution toward the collusive outcome, the other seller has a unilateral incentive to respond by raising price toward the collusive outcome. Alternatively, in the case of complements, the model generates downward-sloping reaction functions. So a unilateral deviation from the Nash solution toward the collusive outcome will provide a unilateral incentive for the other seller to adjust price in the opposite direction. Based on the slopes of the reaction functions, it is reasonable to expect that sellers of substitute goods might find it easier to collude tacitly than do sellers of complement goods (Holt 1995). This argument is not entirely compelling because the incentives are in terms of myopic best responses to past decisions of the other seller.

   Moreover, the idea is somewhat at odds with economic intuition because sellers offering competing (substitute) products could reasonably be expected to engage in aggressive price-slashing behavior. In contrast, sellers of complementary goods might view the other person as more of a partner than a rival, thus fostering cooperation.

   Two related articles suggest that subjects in experiments find it easier to tacitly collude when market structure generates upward-sloping reaction functions. In a recent survey, Suetens and Potters (2007) compare results from a series of Bertrand and Cournot experiments and conclude that subjects colluded more when the decision task was choosing price versus choosing quantity. One possible explanation for this finding is that reaction functions are upward sloping in Bertrand (substitutes) games and downward sloping in Cournot games. However, the different market choice variables (price versus quantity) cannot be ruled out as an explanation for the observed differences in collusion. As a follow up to this survey, Potters and Suetens (2008) conducted experiments with no market framing. They included treatments with upward-sloping and downward-sloping reaction functions. Consistent with the survey in their previous work, they conclude that there is more collusion with upward-sloping reaction functions in their experiment without market framing.

   Many market experiments have focused on identifying other conditions that are favorable to seller collusion. Engel (2007) organizes the results from this vast literature in a meta-analysis that covers 107 articles. These studies span a wide range of experimental design features, including the number of firms per market, whether or not subjects have multiple interactions with the same rival, whether or not subjects face capacity constraints, whether or not firms offer more than one product, the degree of product differentiation, and the amount of information subjects receive about rivals' decisions and earnings. (2) Our design differs from all of the previous studies on collusion in the sense that we focus on the effect of market structure (substitutes versus complements) within the price-setting model. Hence, we eliminate any differences in behavior that might result from choosing quantity rather than price. Further, we include market framing in our experiments because tacit collusion is generally a market phenomenon. Our experimental design is described in detail in the next section, section 3 presents our results, and section 4 concludes.

2. Experimental Design

   We recruited 128 subjects from undergraduate classes at the College of William and Mary. Subjects participated in a repeated symmetric duopoly price-setting game in either a complements treatment or a substitutes treatment. (3) Table 1 summarizes the equilibrium values derived from the experimental parameters. The complements design is based on the following demand curve: [Q.sub.1] = 3.60 - 0.5[P.sub.1] - 0.5[P.sub.2], where [Q.sub.1] represents the quantity sold by firm 1, [P.sub.l] represents the price set by firm 1, and [P.sub.2] represents the price set by firm 2. The Nash equilibrium price is $2.40 in this treatment. The substitutes design is based on the following demand curve: [Q.sub.1] = 3.60 - 2[P.sub.1] + [P.sub.2], and the Nash price is $1.20. In both designs, there is no marginal cost of production, and there is a fixed cost of $2.18 per round. With this fixed cost, earnings from collusion are 50% higher than earnings at the Nash equilibrium. Subjects earn $0.70 per person at the Nash equilibrium, and they earn $1.06 per person at the collusive outcome. Another important feature of this set of parameters is that the difference between the collusive price and Nash price is the same ($0.60) in both designs. In addition, the collusive price is the same for both designs and is $1.80. (4) Figure 1 presents the best-response functions for the two treatments. Notice that the collusive (joint profit maximizing) price is below the Nash price in the complements case on the left side, and it is above the Nash price in the substitutes case, shown on the right.

   The Appendix contains instructions for the experiment. Subjects selected prices, and pairs were able to go at their own pace. Half of the subjects in each treatment interacted for 10 rounds, and half interacted for 20 rounds. (5) To avoid end-game effects, subjects were not told the number of rounds in advance. (6) Subjects were told that they were matched with the same person for each round. In addition, subjects were told the equation for demand, and it was common knowledge that all subjects within a session faced the same demand curve and costs. Finally, at the end of each round, subjects were told the price charged by the other seller. Average earnings were $6.42 in the sessions with 10 rounds and $10.74 in the sessions with 20 rounds. Earnings also varied considerably based on the treatment, as described below.

   [FIGURE 1 OMITTED]

   [FIGURE 2 OMITTED]

3. Results

   Analysis of Price Levels

   Figure 2 shows the average price per round for both treatments separated by 10 and 20 round sessions. In the complements treatment, the average price starts between the collusive price and the Nash price. The average price rises and falls over time but generally climbs closer to the Nash price with repetition. It oscillates around the Nash price after 13 rounds of play. In the substitutes treatment, the average price also rises and falls over time but is generally below the Nash prediction. Notice that prices in the 10 round sessions appear to be slightly closer to the collusive price than prices in the 20 round sessions for both complements and substitutes. However, because subjects did not know the number of rounds they would play, there is no theoretical reason to believe that behavior would differ across those sessions. Hence, for much of the analysis that follows, we pool data for the first 10 rounds of play. Over all rounds, the average price is $1.12 in the substitutes treatment and $2.25 in the complements treatment. This difference in pricing behavior resulted in average earnings per subject of $0.74 per round in the complements treatment compared to $0.44 per round in the substitutes treatment. (7)

   Overall, Figure 2 suggests that the average price in the complements treatment is closer to the collusive price than the average price in the substitutes treatment. To further investigate the amount of collusion across the two treatments, we define the "collusive region" as the range of prices within $0.30 of the collusive price. (8) Next, we identify matched pairs of subjects who priced in this region. We focus on pairs of subjects rather than individuals who priced cooperatively because collusion in a duopoly setting is only relevant and more likely to be sustained when both players choose the cooperative outcome. Over all 20 rounds, the percentage of pairs in the collusive region is 20% for complements and 5% for substitutes. (9)

   Because subjects were paired for all rounds of the experiment, we can also examine how well pairs of subjects were able to sustain cooperation. When we consider a relatively strict definition of sustained cooperation as pricing in the cooperative region for at least 70% of the rounds played, 3 of the 32 pairs in the complements treatment and none of the 32 pairs in the substitutes treatment were able to sustain cooperation. When we consider a very liberal definition of sustained cooperation as maintaining prices in the cooperative region for at least 30% of the rounds played, 7 of the 32 pairs in the complements treatment and 3 of the 32 pairs in the substitutes treatment were able to sustain cooperation. (10) For each pair of subjects, we also calculate the percentage of rounds they priced in the collusive region. On average, pairs of subjects in the complements treatment priced in the collusive region in 23% of the rounds played. Pairs of subjects in the substitutes treatment priced in the collusive region in only 5% of the rounds played. Thus, subjects in the complements treatment were significantly more likely to price in this region than subjects in the substitutes treatment. (11)

   Within this collusive region, subjects in the complements treatment appear to price closer to the collusive price of $1.80 than subjects in the substitutes treatment. Figure 3 shows average prices by round for the pairs of subjects who priced in the collusive range. The average price in the collusive region is $1.78 for complements and $1.64 for substitutes. For each pair that priced in the collusive region, we...