Collusion in Price-Setting Duopoly Markets: Experimental Evidence * Lisa R. Anderson College of William and Mary

Transcription

1 Collusion in Price-Setting Duopoly Markets: Experimental Evidence * Lisa R. Anderson College of William and Mary Beth A. Freeborn College of William and Mary Charles A. Holt University of Virginia May 2008 Abstract We experimentally study the degree of collusion in differentiated Bertrand duopoly markets. In addition to the standard substitutes treatment, we also include a treatment in which the goods are complements. A recent paper surveys experimental evidence and reports that there is more collusion in Bertrand price-setting games than in Cournot quantity-setting games (Suetens and Potters, 2007). Our research adds to the literature by examining how collusive behavior may differ within the price-setting model. One hundred and two undergraduate students participated in the experiment; 54 subjects played the Bertrand complements game and 48 played the Bertrand substitutes game. We find evidence of collusion in the complements treatment, but no evidence of collusion in the substitutes treatment. This finding is in contrast with Potters and Suetens (2007) who find collusion in both treatments and more collusion in the case of substitutes. A notable difference between our experimental design and that of Potters and Suetens (2007) is that our game is described in a market context while their design is contextfree. * Financial support from the National Science Foundation (SBR ) is gratefully acknowledged.

2 1. Introduction The study of oligopoly behavior has received a great deal of attention in experimental economics. Specifically, much attention has been devoted to studying factors that facilitate tacit collusion. Recent research has focused on how the degree of collusion varies with context. Suetens and Potters (2007) surveyed five experimental studies and concluded that subjects collude more when the decision task was choosing price versus quantity. A possible explanation for this finding is that the Nash choice was below the collusive choice in the price setting games and above the collusive choice in the quantity setting games. Potters and Suetens (2007) investigate this explanation in context free experiments that vary in both the slope of the reaction functions and the relative position of the Nash and collusive choices. They conclude that the slope of subjects reaction functions is an important determinant of collusion. Specifically, the degree of collusion is higher with upward sloping reaction functions. However, the relative position of the Nash and collusive choices did not affect collusion. We study how collusive behavior may differ within the price-setting model by considering Bertrand substitutes and Bertrand complements. We find evidence of collusion in the complements treatment, but no evidence of collusion in the substitutes treatment. This finding is in contrast with Potters and Suetens (2007) who find collusion in both treatments and more collusion in the case of substitutes. Possible explanations for this difference in findings include context and culture. We review the related literature in the next section. Section 3 describes our experimental design, Section 4 presents our results, and Section 5 concludes. 2. Related Literature 1

3 A number of market experiments have focused on identifying conditions that are favorable to seller collusion. These studies vary in terms of the number of firms per market, the number of rounds played, whether or not subjects know the endpoint of the game, whether or not subjects are matched with the same rival across rounds and the amount of information subjects receive about rivals decisions and earnings. In a recent survey, Suetens and Potters (2007) compare measures of collusion in Bertrand and Cournot games from five separate experimental studies. All of the studies included Bertrand games and Cournot games. The five studies included various group sizes (2, 3 and 4) and number of rounds (15, 20, 22 and 40), known and unknown endpoints, and both fixed and random matchings. In addition, the five papers all studied the effect of information feedback on behavior. Specifically, each paper included one treatment where subjects were provided with aggregate information about price and quantity and no information on competitors profit. A second treatment provided individual information about competitors prices, quantities and profit. All of the five studies modeled competition for substitute goods. 1 Overall, Suetens and Potters (2007) report some evidence for collusion in Bertrand markets, but no such evidence in Cournot markets. As a possible explanation for this finding, they discuss the location of the Nash equilibrium relative to the collusive outcome. Specifically, the prior work in this area focuses on substitute goods where the Nash prediction is higher than the collusive outcome for Cournot quantities (with downward sloping reaction functions), and the Nash prediction is lower than the collusive outcome for Bertrand prices (with upward sloping reaction functions). 1 Note that we refer to goods from a consumption perspective rather than a production perspective. Specifically, we use the term substitute goods to refer to goods with a positive cross price elasticity of demand. Some studies in this area define the relationship between goods based on producer s reaction functions. For example, the term strategic substitutes refers to downward sloping reaction functions. Strategic complements refers to upward sloping reaction functions. 2

4 To explore this issue, Potters and Suetens (2007) studied four experimental treatments that varied in terms of the slope of the reaction functions and the relative positions of the Nash prediction and the collusive solution in the strategy space. Two treatments, refereed to as strategic complements, had upward sloping reaction functions. And the other two treatments, referred to as strategic substitutes, had downward sloping reaction functions. Each of those pairs had a treatment with the Nash prediction above the collusive solution, which they refer to as the negative externality treatment, and a treatment with the Nash below the collusive outcome, which they refer to as a positive externality treatment. The subjects in Potters and Suetens (2007) were Dutch college students. They played in fixed pairs and were given a payoff table listing only even strategy choices and an earnings calculator for all possible combinations. They were told there would be 30 rounds and were given all information about their opponent s choices and earnings. Unlike the previous work in this area, the experiment had no context. Subjects did not choose prices or quantities, rather they picked a number between 0 and 28. The Nash choice was 14 across all treatments, and the collusive choice was either 2.5 or 25.5 depending on the treatment. Potters and Suetens (2007) report subjects choices are generally between the Nash prediction and the collusive outcome in all four treatments, regardless of whether the Nash is above or below the collusive outcome. They calculate the degree of collusiveness as ρ = (P actual P Nash )/(P collude P Nash ) and report that the two treatments with upward sloping reaction functions had the highest degree of collusion (ρ =.49 when Collusive < Nash and ρ =.42 when Collusive > Nash). The two treatments with downward sloping reaction functions also provided evidence, albeit weaker, for collusion (ρ =.24 with Collusive < Nash, and ρ =.17 with Collusive > Nash). In summary, Potters and Suetens (2007) reported that the slope of the reaction function was an 3

5 important determinant in the degree of collusion. Behavior did not vary significantly depending on whether or not the collusive outcome was higher or lower than the Nash prediction. We can compare results from Potters and Suetens (2007) to those reviewed in Suetens and Potters (2007) to gain some insight into the effect of context. Since those studies only considered substitute goods, all of the Cournot games had downward sloping reactions functions and a Nash prediction that was higher than the collusive prediction. The survey of five studies with context included in the experiment reported ρ s ranging from to compared to the comparable context-free treatment in Potters and Suetens which reported ρ = From these numbers, it appears that providing context to the choice problems (specifically, the context of choosing quantity) makes subjects less cooperative. Turning to the Bertrand setting, we focus on the treatment with upward sloping reaction functions and a Nash prediction that is lower than the collusive choice. The survey of five studies with context reported ρ s of -0.05, 0.04, 0.08, 0.18 and 0.52, compared to the comparable context free treatment in Potters and Suetens which reported ρ = Hence, context also appears to depress cooperation in a price-choice setting. 3. Experimental Design Given this evidence that context matters for cooperation, we take a different approach to studying this issue. We consider only Bertrand price-choice games, but we examine substitute goods and complementary goods. If context affects behavior, we would expect to see differences in the ability of subjects to collude across these two treatments. Many people are familiar with the idea of sellers offering competing products, which might lead to aggressive 2 Here we report results from the Extra treatments in which subjects were provided detailed information about competitors choices and earnings. 4

6 price slashing behavior. Alternatively, with complementary goods subjects might view their experimental rival as more of a partner, thus fostering cooperation. Mathematically, the Bertrand complements problem is identical to a Cournot substitutes game in the sense that reaction functions are downward sloping and the competitive level of the choice variable is greater than the collusive level. Hence, we can compare our results to the Cournot and Bertrand results (with context) that are reviewed in Suetens and Potters (2007). This will provide insight about how the choice of quantity versus price affects collusive behavior. Finally, we can compare our results to two of the (context-free) treatments from Potters and Suetens (2007). This will provide insight about how context in general affects collusive behavior. We recruited 102 subjects from undergraduate classes at the College of William and Mary. Subjects participated in a repeated duopoly price-setting game using the Veconlab website developed by Charles Holt at the University of Virginia. Each subject participated in either a complements treatment or a substitutes treatment. The complements design is based on the following demand curve: Q 1 = P 1 0.5P 2, where Q 1 represents the quantity sold by firm 1, P 1 represents the price set by firm 1, and P 2 represents the price set by firm 2. The individual profit maximizing Nash equilibrium price is $2.40 in this treatment. The substitutes design is based on the following demand curve: Q 1 = P 1 + P 2 and the Nash price is $1.20. In both designs there is no marginal cost of production and a fixed cost of $2.18 per round. The collusive price is the same for both designs and is $1.80. Note that these designs were chosen such that the difference between the collusive price and Nash price is the same (60 cents) in both designs. 3 3 Suetens and Potters (2007) report a Friedman Index to measure the sustainability of collusion. It is calculated as the collusive profit minus the Nash profit (the potential gain from colluding) divided by the profit from defecting 5

7 The Appendix contains instructions for the experiment. Each pricing decision was repeated for either 10 or 20 rounds, but subjects were not told the number of rounds in the experiment. Subjects were told that they were matched with the same partner each round. Students were told the equation for demand and, at the end of each round subjects were told the price charged by their partner. Average earnings were $6.51 in the sessions with 10 rounds and $11.01 in the sessions with 20 rounds. Subjects were paid $5 for showing up to the experiment. Earnings also varied significantly based on the treatment as described below. 4. Results Figure 1 shows the average price per round for both treatments. In the complements treatment, the average price starts slightly above the midpoint between the collusive price and the Nash price. The average price climbs closer to the Nash price with repetition and oscillates around the Nash price after 13 rounds of play. Recall that the Bertrand complements problem is mathematically identical to a Cournot substitutes problem. Both problems have downward sloping reaction functions and the position of the collusive solution is below the Nash solution. Thus we can compare our Bertrand complements results to the five Cournot studies reviewed in Suetens and Potters (2007). All five of the Cournot studies report subjects making supra competitive choices when subjects are provided with full information about partners choices and earnings. One reason for the difference in results might be the specific context presented to subjects. In the five Cournot studies, subjects were informed that they were choosing their own quantity, and the price consumers pay was determined by the total quantity chosen (the sum of minus the collusive profit (the potential gain from defecting on a collusive agreement). The five studies they reviewed have indexes ranging from 0.32 to The parameters in our experiment generate a Friedman Index of 0.88 in both treatments, which is higher than three of the five studies reviewed in Suetens and Potters (2007). 6

8 their own quantity and quantity of their rival firm). A higher quantity chosen by the rival increased total quantity and decreased overall price. In our Bertrand complements treatment, subjects were told they were choosing their own price and the quantity they sold depended on their own price and the price of their rival. A higher price by the rival reduced the quantity they sold, since the two goods are used together. $2.60 Figure 1: Average Price per Round $2.40 Price $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 $ Round Complements Price Substitutes Price Complements Nash Substitutes Nash Joint Profit Maximizing Price In our substitutes treatment, the average price rises and falls over time but is always below the Nash prediction. This is also in contrast to the studies reviewed in Suetens and Potters (2007) which reports average prices are higher than the Nash prediction in 4 out of 5 studies of Bertrand substitutes. Overall, Figure 1 shows that the average price in the complements treatment is closer to the collusive price than the average price in the substitutes treatment. It is possible, however, that subjects are under pricing relative to the Nash prediction in both treatments and this under pricing only appears to be cooperative behavior in the complements treatment because the collusive price is below the Nash price. 7

9 0.35 Figure 2: Percentage of Pairs of Subjects with Prices in the Collusive Region % Comps Subs Round To further investigate the amount of collusion across the two treatments, we defined the collusive region as the range of prices within 30 cents of the collusive price. 4 Then we identified matched pairs of subjects who priced in this region. We focused 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. Figure 2 shows the percentage of pairs in the collusive region by round and treatment. In all but 2 rounds of play there is more collusive behavior in the complements treatment than in the substitutes treatment. Figure 3 shows average prices for the pairs of subjects who priced in the collusive range. Overall, subjects in the complements treatment price significantly closer to the collusive price than subjects in the substitutes treatment. 5 4 We chose 30 cents as the boundary of the collusive region because it is the midpoint between the collusive price and the Nash price. The general shape and relative position of the lines in Figure 2 do not change when we reduce the range of prices to be within 20 cents of the collusive price or increase the range of prices to be within 40 cents of the collusive price. Graphs using ranges other than 30 cents are available from the authors upon request. 5 Note that in the substitutes treatment, there are zero pairs that choose a collusive region price for rounds 1,2,4, and There is at least one pair that prices in the collusive region for all rounds of the complements treatment. 8

10 Turning our attention to competitive behavior, we defined the Nash region to be prices within 30 cents of the Nash price. Figure 4 shows that there are also significant differences in the proportion of pairs who priced in this region. Over 70% of pairs in the substitutes treatment priced in the Nash region in the first round of decision making compared to only 22% in the complements treatment. In every round more pairs were in the Nash region under substitutes than under complements. If we look at the average over rounds, over 75% of the pairs of subjects in the substitutes treatment priced in the Nash region while only 45% of the pairs in the complements treatment priced in the Nash region. 6 6 Note that Figures 2 and 4 are limited to the pairs of subjects that price within the collusive or Nash region, respectively. Some pairs of subjects are not included in these graphs because either both subjects priced outside of the specified region, or one subject priced within the region while the other subject priced outside of the region. 9

11 Figure 4: Percentage of Pairs of Subjects in the Nash Region % Comps Subs Round As a final check on how behavior differs across the two treatments, we calculated a standard measure of collusiveness: ρ = (P actual P Nash ) / (P collude P Nash ). Note that positive values of ρ indicate collusive behavior, zero indicates pricing at the Nash prediction, and negative values indicate supra-competitive pricing. Overall, we found ρ = 0.17 in the complements treatment and ρ = in the substitutes treatment. These values are significantly different from each other at the 5 % level using a 2-sample Wilcoxon rank-sum test. Table 1 shows that this difference is not sensitive to the number of rounds subjects played. The average ρ for the substitutes treatment is negative for all sets of rounds played and the average ρ for the complements treatment is positive for all sets of rounds. The final column of Table 1 provides the t-statistic to test for equality between ρ substitutes and ρ complements. The two are always statistically different from one another. 10

12 Table 1. Substitutes Rho versus Complement Rho for Subsets of Rounds Played Mean Rho Substitutes Standard Deviation Mean Rho Complements Standard Deviation t-test for Equality Rounds ONLY Rounds 1-10 Played ONLY Rounds 1-20 Played ALL Obs of Rounds Rounds We can compare these results to those reported in the context free experiments of Potters and Suetens (2007). They refer to the treatment with downward sloping reaction functions and the collusive choice lower than the Nash choice as SUBSTneg. This is comparable to our complements treatment. They refer to the treatment with upward sloping reaction function and the collusive choice greater than the Nash choice as COMPLpos. This is comparable to our substitutes treatment. Potters and Suetens (2007) find collusion in both treatments, but more collusion in the COMPLpos (rho =.42) than in the SUBSTneg (rho =.24). This is the opposite of our finding of collusion with complementary goods (rho = 0.17) but supra-competitive pricing with substitute goods (rho = -0.13). This also suggests that context about the choice problem tends to depress cooperative behavior. 5. Conclusion We compare collusive behavior in Bertrand duopoly experiments with substitute goods versus complementary goods. We find moderate collusion with complementary goods but no collusion with substitute goods. This resulted in significantly higher earnings for subjects in the 11

13 complements treatment relative to the substitutes treatment (70 cents per round versus 45 cents per round). These results are in contrast to previous studies and provide evidence that context affects behavior in important ways. Within our experiment, subjects facing a competing producer rather than a complementary producer were significantly more likely to price near the Nash equilibrium. Comparing our results to Potters and Suetens (2007), we provide context and find less overall cooperation in our experiments. This is consistent with research from ultimatum game experiments. Hoffman et al. (1994) found that offers were closer to the Nash prediction when the game was presented in a market context as opposed to a bargaining context. Another possible explanation for the difference in results might be cultural, because our subjects were largely American students as opposed to Dutch students. Our results suggest that the specific context of price-choice influences the degree of collusiveness in duopoly markets. Future research will extend this study to include quantitychoice context, and compare the amount of collusion observed in Cournot substitute and complement goods. References Hoffman, Elizabeth, Kevin McCabe, Keith Shachat and Vernon Smith (1994). Preferences, Property Rights, and Anonymity in Bargaining Games, Games and Economic Behavior, 7(3): Potters J. and S. Suetens (2007). Cooperation in Experimental Games of Strategic Complements and Substitutes, CentER Discussion Paper , University of Tilburg. Suetens, S. and J. Potters (2007). Bertrand Colludes More than Cournot, Experimental Economics, 10:

14 Appendix A: Instructions for Complements Treatment (copied from Veconlab.Econ.Virginia.edu/admin.htm) Page 1 Rounds and Matchings: The experiment sets up markets that are open for a number of rounds. Note: You will be matched with the same person in all rounds. Interdependence: The decisions that you and the other person make will determine your earnings. Price Decisions: Both you and the other person are sellers in the same market, and you will begin by choosing a price. You cannot see the other's price while choosing yours, and vice versa. Sales Quantity: A lower price will tend to increase your sales quantity, and a higher price charged by the other seller will tend to lower your sales quantity. This is because consumers use your product together with the other's product, so an increase in their price will reduce your sales. Page 2 Price and Sales Quantity: Your price decision must be between (and including) $1.50 and $3.00; use a decimal point to separate dollars from cents. Production Cost: Your cost is $0.00 for each unit that you sell. However, you must pay a fixed cost of $2.18 for a license to operate, regardless of your sales quantity. So your total cost is $2.18, regardless of how many or few units you produce. Consumer Demand: The quantity that consumers purchase depends on all prices. Your sales quantity will be determined by your price (P) and by the other seller's price (A): Sales Quantity = *P *A Negative quantities are not allowed, so your sales quantity will be 0 if the formula yields a negative quantity. Sales Revenue: Your sales revenue is calculated by multiplying your production quantity and the price. Since your sales are affected by the other's price, you will not know your sales revenue until market results are available at the end of the period. Page 3 Earnings: Your profit or earnings for a round is the difference between your sales revenue and your production cost. If Q is the quantity you sell, then total revenue is (Q*price), total cost is $ fixed cost of 2.18, so earnings = Q*(price) - $2.18. Cumulative Earnings: The program will keep track of your total (cumulative) earnings. Positive earnings in a round will be added, and negative earnings will be subtracted. Working Capital: Each of you will be given an initial amount of money, $0.00, so that gains will be added to this amount, and losses will be subtracted from it. This initial working capital will show up in your cumulative earnings at the start of round 1, and it will be the same for everyone. There will be no subsequent augmentation of this amount. 13

15 Page 4 In the following examples, please use the mouse button to select the best answer. Remember, your sales quantity = *Price -0.50*(Other Price) Question 1: Suppose that both sellers choose equal prices and that the total sales for both sellers combined is Q units, then each seller has a sales quantity of: a) 2Q b) Q/2. Question 2: A higher price will increase both the price-cost margin and the chance of having a positive sales quanitity.(true/false) a) True. b) False. Page 5 Question 1: Suppose that both sellers choose equal prices and that the total sales for both sellers combined is Q units, then each seller has a sales quantity of: (a) 2Q (b) Q/2 Your answer, (b) is Correct. The sales quantity formula divides sales equally when prices are equal. Question 2: A higher price will increase both the price-cost margin and the chance of having a positive sales quanitity.(true/false) (a) True. (b) False. Your answer, (b) is Correct. The chances of making sales go down as price is increased. Page 6 Matchings: Please remember that you will be matched with the same person in all rounds. Earnings: All people will begin a round by choosing a number or "price" between and including $1.50 and $3.00. Remember, your sales quantity = *Price *(Other Price) Your total cost is $0.00 times your sales quantity, plus your fixed cost $2.18, and your total sales revenue is the price times your sales quantity. Your earnings are your total revenue minus your total cost. Positive earnings are added to your cumulative earnings, and losses are subtracted. Rounds: There will be a number of rounds, and you are matched with the same person in all rounds. 14

16 Appendix B: Instructions for Substitutes Treatment (copied from Veconlab.Econ.Virginia.edu/admin.htm) Page 1 Rounds and Matchings: The experiment sets up markets that are open for a number of rounds. Note: You will be matched with the same person in all rounds. Interdependence: The decisions that you and the other person make will determine your earnings. Price Decisions: Both you and the other person are sellers in the same market, and you will begin by choosing a price. You cannot see the other's price while choosing yours, and vice versa. Sales Quantity: A lower price will tend to increase your sales quantity, and a higher price charged by the other seller will tend to raise your sales quantity. This is because consumers view the products as similar, so an increase in their price will increase your sales. Page 2 Price and Sales Quantity: Your price decision must be between (and including) $0.60 and $2.10; use a decimal point to separate dollars from cents. An increase in the other seller's price will tend to raise the number of units you sell. Production Cost: Your cost is $0.00 for each unit that you sell. However, you must pay a fixed cost of $2.18 for a license to operate, regardless of your sales quantity. So your total cost is $2.18, regardless of how many or few units you produce. Consumer Demand: The quantity that consumers purchase depends on all prices, with more of the sales going to the seller with the lowest (best available) price in the market. Your sales quantity will be determined by your price (P) and by the other seller's price (A): Sales Quantity = *P *A Negative quantities are not allowed, so your sales quantity will be 0 if the formula yields a negative quantity. Sales Revenue: Your sales revenue is calculated by multiplying your production quantity and the price. Since your sales are affected by the other's price, you will not know your sales revenue until market results are available at the end of the period. Page 3 Earnings: Your profit or earnings for a round is the difference between your sales revenue and your production cost. If Q is the quantity you sell, then total revenue is (Q*price), total cost is $ fixed cost of 2.18, so earnings = Q*(price) - $2.18. Cumulative Earnings: The program will keep track of your total (cumulative) earnings. Positive earnings in a round will be added, and negative earnings will be subtracted. Working Capital: Each of you will be given an initial amount of money, $0.00, so that gains will be added to this amount, and losses will be subtracted from it. This initial working capital will show up in 15

17 your cumulative earnings at the start of round 1, and it will be the same for everyone. There will be no subsequent augmentation of this amount. Page 4 In the following examples, please use the mouse button to select the best answer. Remember, your sales quantity = *Price *(Other Price) Question 1: Suppose that both sellers choose equal prices and that the total sales for both sellers combined is Q units, then each seller has a sales quantity of: a) 2Q b) Q/2. Question 2: A higher price will increase both the price-cost margin and the chance of having a positive sales quanitity.(true/false) a) True. b) False. Page 5 Question 1: Suppose that both sellers choose equal prices and that the total sales for both sellers combined is Q units, then each seller has a sales quantity of: (a) 2Q (b) Q/2 Your answer, (b) is Correct. The sales quantity formula divides sales equally when prices are equal. Question 2: A higher price will increase both the price-cost margin and the chance of having a positive sales quanitity.(true/false) (a) True. (b) False. Your answer, (b) is Correct. The chances of making sales go down as price is increased. Page 6 Matchings: Please remember that you will be matched with the same person in all rounds. Price Choice: All people will begin a round by choosing a number or "price" between and including $0.60 and $2.10. Demand: Remember, your sales quantity = *Price *(Other Price). Cost: Your total cost is $0.00 times your sales quantity, plus your fixed cost $2.18 Earnings: Your earnings are your total revenue (price times sales quantity) minus your total cost. Positive earnings are added to your cumulative earnings, and losses are subtracted. 16