Do Strategic Substitutes Make Better Markets A Comparison

Do Strategic Substitutes Make Better Markets? A Comparison of Bertrand Cournot Markets as Trading Institutions Douglas Davis October 10, 2008 Thanks to Bob Reilly, Roger Sherman, Oleg Korenok and Asen Ivanov

Motivation: This paper examines the relation of strategic complements and strategic substitutes in a market context. Some definitions: Suppose we have a strategic context, and that possible actions (e. g. , choices by the players) can be rank-ordered from lowest to highest. Actions are strategic complements when high action choices by one player induces others to also make high action choices. Actions are strategic substitutes when high action choices by one player induces others to make low action choices.

To make this concrete, consider the two standard models of oligopoly interactions. Cournot Interactions: Sellers pick quantities. Once all quantity choices are complete, a market clearing price is determined, and all offered units are sold at the market clearing price. Bertrand Interactions: Sellers pick prices. Once all price choices are complete, sales are determined, with the low pricing seller selling the most units. (A number of variants are possible. ) In a Bertrand Game, actions are strategic complements. High price choices by rival sellers induce a seller to post a high price, just a little below that (s)he expects rivals to post. In a Cournot Game, actions are strategic substitutes. Low quantity choices by rival sellers induce a seller to post a large quantity, to take most of the market.

Cournot games are a little institutionally artificial. It is most natural to think of sellers competing on the basis of price. However, Cournot interactions have a number of desirable properties that theorists find useful. -Historically, it was the first model of strategic interdependence. -The equilibrium price cost markup varies inversely with the number of sellers. More recently, however, some economists have argued that Cournot games might actually be a desirable form of organization. Some of the reasoning follows from the relation of strategic substitutes and strategic complements.

A series of recent experimental papers suggest that contexts where actions are strategic substitutes have important properties relative to contexts where actions are strategic complements. Heemeijer, Hommes, Sonnemans and Tuinstra (2007) report that markets where actions are strategic substitutes converge more quickly and more completely to static Nash (here competitive) conditions. Fehr and Tyran (2008) find that contexts where actions are strategic substitutes respond much more quickly to a fully announced nominal shock than contexts where actions are strategic complements. Potters and Suetens (2008) find that contexts where actions are strategic substitutes are less susceptible to tacit collusion than contexts where actions are strategic complements.

Why? These authors all explain convergence differences in terms of a bounded rationality argument by Haltiwanger and Waldman (1985, 1989). Idea: Suppose the rationality of some players is limited in the sense that some sellers expectations are adaptive (e. g, not forward looking). In a context where actions are strategic substitutes, rational players have an incentive to move away from the rational players. A balance of the rational and boundedly rational action choices drives markets to an equilibrium. In a context where actions are strategic complements, rational players have an incentive to copy the actions of the boundedly rational players, resulting in slow convergence, limited adaptability and, in a repeated context, susceptibility to tacit collusion.

Startlingly different responses to a fully announced nominal shock observed by Fehr and Tyran (2008) motivate these authors to go a step further. They argue that institutions where actions are strategic substitutes endogenously induce rationality. To see this, consider the best reply functions of sellers in Bertrand Cournot games. In response to a shock an adaptive player will move from action A to action B, resulting in a group response of action C. The distance A-C is much larger in a quantity context (on the right) than in a price context (on the left), which should induce more rapid responses.

These implications come as something of a surprise to those familiar with the behavioral industrial organization literature. -Although Cournot markets are not explosively unstable, several investigators have observe the slow and incomplete convergence of Cournot markets, particularly when compared to Bertrand markets. -In a meta analysis of experimental results Suetens and Potters (2007) conclude that Bertrand markets are more susceptible to tacit collusion than Cournot markets. However, their results are based primarily on duopoly results. Evidence from thicker markets (particularly markets with more than 3 sellers) is rather unconvincing.

Importantly, the environments in each of the environments reported above were very highly stylized. -In HHST – best responses to action choices were ‘hard wired’ into seller decisions. -In Fehr and Tyran and Potters and Suetens, agents made action choices in a bi-matrix game format, where all factors other than the sign on the slope of the best reply function are held constant. Project: Address this curious inconsistency in the literature between results regarding strategic substitutes and strategic complements, and Cournot/Bertrand oligopoly performance. Approach: Rather than hold all things constant except the sign on the slope of the best reply function, we examine behavior in a differentiated product oligopoly, where underlying cost and the demand system are held constant.

A Model. To see the differences induced by shifting the form of strategic interactions for a given demand system, consider the following model. Consider a market with four firms, constant unit costs, c, differentiated products and a symmetrical demand system for all sellers. For a quantity setting game, write inverse demand for seller i as For a price setting game, write demand as These expressions are equivalent when and Each firm acts to optimize

a) Static Considerations: In such game, it is easy to show that in the Cournot game, the static equilibrium price will be higher and the static equilibrium quantity will be lower than in the comparable Bertrand game (Vives, 1999). More interesting for us are the best response functions. In the Cournot game, the best response function is In Bertrand game, we have Taking the ratio of the slopes (q to p), observe that as long as 0< <1, the slope of the best reply function will be flatter in the Bertrand game than in the Cournot game Further, this difference increases with differentiation.

In the background papers, these slopes were held constant across games. As we can see, this is impossible for a given demand system. What does this difference mean? It strengthens the ‘endogeneous rationality argument of Fehr and Tyran. Just compare adaptive expectation differences across markets in the upper panel ( =. 5) and the lower panel ( =. 9).

This result suggests our first two conjectures, regarding stability and convergence. First, recalling HHST and Fehr and Tyran Conjecture 1: Convergence levels and speeds are higher in Cournot markets than in comparable Bertrand markets Second, to the extent the ‘endogenous rationality argument is pertinent, we have a second conjecture. Conjecture 2: The difference in convergence levels and speeds across Bertrand Cournot markets is larger when products are close substitutes ( =. 9) than when they are more differentitated ( =. 5)

Potentially countering this effect are the costs of a given deviation. Consider for example, the costs of a small deviation from the best reply in Cournot and Bertrand markets. In the Cournot market, In contrast, in the Bertrand market Notice that these deviations are always larger in the Bertrand markets, and become increasingly so as differentiation increases. Not only may this affect convergence speeds in Bertrand markets, it may affect incentives to tacitly collude, because the profit losses of deviations from the best reply reflect the costs of both signaling and responding to signals.

Some Dynamic Considerations. Economists typically evaluate incentives to tacitly collude in terms of the ‘Friedman Coefficient’ Lower values suggest that a tacit collusion is more easily sustained. Notice that for a given demand system, these values are higher for Bertrand games than Cournot games, with the difference increasing as product differentiation falls ( rises). Observations: 1) Suetens and Potters (2007) suggest that institutional effects dominate the effects of tacit incentives to collude. 2) In a Price setting game Davis (2007) finds that tacit collusion does move inversely with . However, is a coincident explainer of tacit collusion.

These observations suggest two additional behavioral conjectures. The first regards an extension of Potters and Suetens to the current context. Conjecture 3. Tacit collusion, measured as the mean deviation from the static Nash equilibrium price is higher in Bertrand markets than in Cournot markets. A second conjecture regards the collusion damping effects of increased signalling costs in the Bertrand markets. Conjecture 4, Increasing the rate of substitutability from =. 5 to =. 9 reduces the incidence of tacit collusion in Bertrand games relative to Cournot games.

Experiment Design. To test these four conjectures, we conducted the following experiment. -24 sessions. Each session consisted of two 40 period sequences. -Sessions are combinations of two treatment variables, the institution (‘C’ Cournot or ‘B’ Bertrand) and, given the impact of product differentiation on predictions, the degree of substitutability (‘L’ =. 5 and ‘H’ =. 9). We refer to treatments as combinations of these variables (e. g, ‘BL’ is the bertrand markets with =. 5) -The experiment is conducted in a simple 2 x 2 design, with 6 markets in each cell.

Experiment Procedures -Participants were 96 undergraduate students enrolled in business and economics courses in the Spring semester of 2008. No person participated in more than one market. -In each period, sellers make a simultaneous action choice (price or quantity) as well as a forecast of the average of their rivals’ action choices. After all action choices were complete, sellers see their own sales and earnings, as well the average of rivals’ action choices. Each period lasted up to 90 seconds. -To assist players, they were given a profit calculator, that showed the profit consequences of own choices, given the presumed average actions of rivals. -At the end of the first sequence, the session is paused, and both supply and demand are shifted downward. To keep earnings constant (and make the shift nominal) the U. S. currency/Lab exchange rate is quadrupled. -Participant earnings for the 70 minute sessions ranged from $13 to $40 and averaged $23. 75.

Results. Mean transaction prices provide an overview of results Observe that the relative stability of the Bertrand markets contrasts sharply with that in the Cournot markets. -Observe also that the only obvious evidence of tacit collusion comes in the BL treatment.

To evaluate convergence levels, we follow Chen and Gazzale (2004) and examine the percentage of decisions within =5% of the static NE action choice.

To gain more insight into convergence levels and to evaluate convergence speeds, we analyze a linear probability model.

This analysis suggests an initial pair of findings, regarding convergence. Finding 1. Neither convergence levels nor convergence speeds are significantly higher in Cournot markets than in comparable Bertrand markets. In fact, in most instances, the opposite is true. Finding 2. Increasing differentiation improves convergence levels and speeds in Bertrand markets relative to Cournot markets. Notes: -Finding 1 runs exactly counter to both HHST and Fehr and Tyran. -Finding 2 runs flatly against the ‘endogenous rationality’ argument of Fehr and Tyran. We’ll consider reasons for this momentarily. First, however, consider tacit collusion.

Tacit Collusion. Following Potters and Suetens (2008) we analyze tacit collusion in terms of a cooperativeness index Mean cooperation rates are not significant higher in BH markets than in CH mkts. BL markets are more cooperative (less uncooperative) than CL markets.

This yields two additional results, each of which pertains to tacit collusion Finding 3. Tacit collusion is not uniformly more pervasive in Bertrand Markets than in Cournot Markets. When =. 9 the effects of tacit collusion are no more pronounced in Bertrand markets than in Cournot markets. Finding 4. Reducing substitutability from =. 9 to =. 5 increases the incidence of tacit collusion in Bertrand markets relative to Cournot markets.

Tacit Collusion and Institutions. There is little organized activity in any of the markets. Sellers, however, do engage in signaling activity. Consider the signals sent. Data are only suggestive, but signaling levels are higher in Bertrand markets than in Cournot markets. High prices appear to be driven by ‘surges’ rather than ‘spikes’.

6. Bounded Rationality and Market Convergence. Why don’t Cournot markets converge more quickly than Bertrand markets? We consider this question in terms of response to the nominal shock. Consider first how sellers update expectations Cournot sellers (hollow bars) do not update expectations more quickly than Bertrand sellers (solid bars).

More problematic: Cournot sellers do not appear to best respond to their forecasts. Figure 6 a. Price (Quantity) Choices given forecasts, periods 41 -46.

Time does not eliminate this problem. Consider the final 20 periods post-shock.

This would seem to suggest that it is the Bertrand Institution rather than the Cournot institution that fosters rationality. Bertrand sellers are absolutely closer to BR than Cournot sellers But, we suspect that the pertinent rationality bound here regards action responses. In addition to making best replies, sellers use rules of thumb, such as the own action choice of the preceding period (‘inertia’) or the anticipated actions of rivals (‘herding’) as anchors. Notice that in relative terms these choice frequencies are quite similar for all sellers.

Interestingly, the relative incidence of these rules is remarkably similar across treatments. Observe also that few individuals select a ‘pure’ rule.

Institutions interact with the use of these anchors in that the distance between these anchors varies substantially. To see this, consider again figure 1. The distance between an ‘inertia’ choice, for example, and an adaptive best reply is much smaller in Bertrand markets than in Cournot markets.

A simple simulation represents one method that might support the plausibility of a conjecture that the increased differences between rules of thumb and best replies in the Cournot game explains the observed relative instablity of Cournot markets. Suppose that sellers use a mechanical rule. They anchor action choices on best reply, inertia and herding with equal probabilities. That is, Initial choices are randomly selected over the action space range. In a subsequent periods, sellers reduce the markup of price over cost, or their quantity by half until they hit the market once. Then they follow the above rule.

Observe: Simulated absolute mean transaction price deviations look pretty similar to observed results (smoothed for purposes of presentation to a MA(5) process). Results are particularly close if ‘cooperative’ sessions are excluded.

Conclusions Our Cournot markets neither converge more quickly or completely, nor are they uniformly more susceptible to tacit collusion than Bertrand markets Importance - For IO this calls into question the relative preferability of Cournot markets. The answer turns on whether the pertinent rationality bound regarding updating expectations, or submitting best responses. -More generally, suggests a caution about making broad inferences about performance in natural contexts from highly stylized experiments. This is particularly true when the motivation driving the result is a form of bounded rationality. -In moving from a simple context to a relatively more complicated one, other rationality limitations may arise, and may exert dominating effects.