Capacity precommitment and price competition yield the Cournot outcome

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14, 326–337]. We show that in this new model every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.     

Finitely Repeated Voluntary Provision of a Public Good

This paper theoretically explores the voluntary provision of a public good when either one of the following holds: (i) agents’ utility is the sum of their monetary earnings and a nonmaterial component, or (ii) agents’ exhibit satisficing behavior. We show that a small degree of either nonmaterial payoffs or satisficing behavior can generate large contributions in a finitely repeated game, even if the incentive to free‐ride on others’ contributions calls for negligible public good provision in the static game. The equilibrium is characterized by a sharp decline in contributions toward the end of the game. Several comparative results regarding group size and technology are consistent with laboratory data obtained in experimental studies. The model also predicts the restart effect observed in previous experiments.     

Imitation and the evolution of Walrasian behavior: Theoretically fragile but behaviorally robust

A well-known result by Vega-Redondo (1997) [18] implies that in symmetric Cournot oligopolies, imitation leads to the Walrasian outcome. We show that this result is not robust to the slightest asymmetry in costs, since every outcome where agents choose identical actions will be played some fraction of the time in the long run. We then conduct experiments to check this fragility. We obtain that, contrary to the theoretical prediction, the Walrasian outcome is a good predictor of market outcomes. Finally, we suggest a new theory based on a mix of imitation and other learning processes that explains subjects' behavior fairly well.     

The relationship between risk attitudes and heuristics in search tasks: A laboratory experiment

Experimental studies of search behavior suggest that individuals stop searching earlier than the optimal, risk-neutral stopping rule predicts. Two different classes of decision rules could generate this behavior: rules that are optimal conditional on utility functions departing from risk neutrality, or heuristics derived from limited cognitive processing capacities and satisficing. To discriminate between these possibilities, we conducted an experiment that consists of a search task as well as a lottery task designed to elicit utility functions. We find that search heuristics are not related to measures of risk aversion, but to measures of loss aversion.     

Capacity Choices and Price Competition in Experimental Markets

We report on experimental duopoly markets with heterogeneous goods. In these markets, sellers first choose capacities and then prices. While capacities remain fixed for either five or ten periods, prices have to be chosen in every period. The experiments starts with two sets of exogenously predetermined capacities. Independently of the distribution of capacities is, a unique pure-strategy in prices is subgame perfect. In equilibrium, capacities should correspond to the Cournot prediction. Given capacities, price-setting behavior is in general consistent with the theory. Average capacities converge above the Cournot level. Capacities converge at the industry level but are somewhat dispersed. Sellers rarely manage to cooperate.     

Bilateral oligopoly and quantity competition

Bilateral oligopoly is a market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, bilateral oligopoly approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one and investigate the differences in equilibria otherwise. These results lead to necessary and sufficient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied.     

Learning to collude: An experiment in convergence and equilibrium selection in oligopoly

The paper considers a simple oligopoly model where firms know their own and the average pay-off in the industry. Firms choose decision rules for trading. The theory predicts that there are three types of Nash equilibria in this game (collusive, Cournot and Stackelberg). Our experiments test the selection process. We find that there is clear evidence of convergence to an equilibrium, and whilst both Cournot and collusive outcomes were selected, the collusive equilibrium is more common. The experimental results also give insights into the process of individual learning, confirming that subjects follow aspiration rules rather than reinforcement rules.     

Competition and innovation: an experimental investigation

The paper analyzes the effects of more intense competition on firms’ investments in process innovations. More intense competition corresponds to an increase in the number of firms or a switch from Cournot to Bertrand competition. We carry out experiments for two-stage games, where R&D investment choices are followed by product market competition. An increase in the number of firms from two to four reduces investments, whereas a switch from Cournot to Bertrand increases investments, even though theory predicts a negative effect in the four-player case. The results arise both in treatments in which both stages are implemented and in treatments in which only one stage is implemented. However, the positive effect of moving from Cournot to Bertrand competition is more pronounced in the former case.     

Strategic interaction between futures and spot markets

We study an oligopolistic industry where firms are able to sell in a futures market at infinitely many moments prior to the spot market. A kind of Folk-theorem is established: any outcome between perfect competition and Cournot can be sustained in equilibrium. We then find that the Cournot outcome can be sustained by a renegotiation-proof equilibrium. However, this is not true for the competitive outcome. Furthermore, only the monopolistic outcome is renegotiation-proof if firms can buy and sell in the futures market. These results suggest, contrary to existing literature, that the introduction of futures markets may have an anti-competitive effect.     

Stackelberg Beats Cournot — On Collusion and Efficiency in Experimental Markets

We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.     

Do short-term laboratory experiments provide valid descriptions of long-term economic interactions? A study of Cournot markets

One key problem regarding the external validity of laboratory experiments is their duration: while economic interactions out in the field are often lengthy processes, typical lab experiments only last for an hour or two. To address this problem for the case of both symmetric and asymmetric Cournot duopoly, we conduct internet treatments lasting more than a month. Subjects make the same number of decisions as in the short-term counterparts, but they decide once a day. We compare these treatments to corresponding standard laboratory treatments and also to short-term internet treatments lasting one hour. We do not observe differences in behavior between the short- and long-term in the symmetric treatments, and only a small difference in the asymmetric treatments. We overall conclude that behavior is not considerably different between the short- and long-term.     

Information and learning in oligopoly: An experiment

This paper presents an experiment on learning in repeated games, which complements the analysis of playersʼ actual choices with data on the information acquisition process they follow. Subjects play a repeated Cournot oligopoly, with limited a priori information. The econometrics hinges on a model built upon Experience Weighted Attraction learning, and the simultaneous analysis of data on the information gathered and on actions taken by the subjects. Results suggest that learning is a composite process, in which different components coexist. Adaptive learning emerges as the leading element, but when subjects look at the strategies individually adopted by their competitors they tend to imitate the most successful behavior, which makes markets more competitive. Reinforcement learning also plays a role, as subjects favor strategies that have yielded higher profits in the past.     

License auctions with royalty contracts for (winners and) losers

This paper revisits the licensing of a non-drastic process innovation by an outside innovator to a Cournot oligopoly. We propose a new mechanism that combines a restrictive license auction with royalty licensing. This mechanism is more profitable than standard license auctions, auctioning royalty contracts, fixed-fee licensing, pure royalty licensing, and two-part tariffs. The key features are that royalty contracts are auctioned and that losers of the auction are granted the option to sign a royalty contract. Remarkably, combining royalties for winners and losers of the auction makes the integer constraint concerning the number of licenses irrelevant.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

On the economic theory of the labor-managed firm in the short run

This paper proposes a short-run utility-maximizing theory of the labor-managed firm (LMF), and shows how four previous theories can be derived from it. It is argued that one of the models, by Horvat, should be viewed as a type of satisficing theory for the LMF. In contrast to the theory of the conventional capitalist firm, it is the satisficing variant that provides efficient resource allocation. This paper also shows why comparative-static analysis may not be as accurate a predictor of short-run behavior of the LMF as it is for the profit-maximizing firm. Consideration is given to microeconomic policy in a socialist labor-managed economy.     

Optimal punishments in linear duopoly supergames with product differentiation

We analyze optimal penal codes in both Bertrand and Cournot supergames with product differentiation. We prove that the relationship between optimal punishments and the security level (individually rational discounted profit stream) depends critically on the degree of supermodularity in the stage game, using a linear duopoly supergame with product differentiation. The security level in the punishment phase is reached only under extreme supermodularity, i.e., when products are perfect substitutes and firms are price setters. Finally, we show that Abreu's rule cannot be implemented under Cournot behavior and strong demand complementarity between products.     

A Cournot Mechanism for Pollution Control under Asymmetric Information

The contribution of this paper is to show that a simple nonlinear tax can achieve a long-run socially optimal level of pollution without the regulator knowing marginal abatement costs. Firms are charged their differential contribution to total damages, evaluated at the upper margin of current emissions. This induces a Cournot game in pollution levels. We show that the Nash equilibrium exists, corresponds to the socially optimal long-run output and emission levels and number of firms, is stable, and can be reached by iterative computations where conjectures are formed using a linear estimator based on past emission levels.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Price formation in heterogeneous oligopoly

Conclusion An equilibrium price vector has been defined and its existence and function in static price formation in cases of heterogeneous oligopoly has been established. Hitherto, authors have been misled, we think, by misinterpreting the role of reaction functions, which are central to our argument. After defining and proving the existence and uniqueness of an equilibrium price vector, it is possible to construct a generalization of the wellknown equilibrium concept of the Nash-Cournot game solution. It has previously been thought that the restriction to the Cournot solution is one of the main drawbacks to using game theoretical solutions to the problem of oligopoly. We have developed a generalization of the Nash solution in order to deal with a type of reaction hypothesis which cannot be expressed in terms of the Cournot reaction function. The new set of reaction functions here introduced demonstrate conclusively that the so-called identity on a Nash and a Cournot equilibrium is only of a formal character.We would like to thank F. Delbaen, R. A. Hirschfeld and K. Okuguchi for useful comments on an earlier draft of this paper.