Sustaining Collusion in Growing Markets

The impact of demand growth on the collusion possibilities is investigated in a Cournot supergame where market growth may trigger future entry and the collusive agreement is enforced by the most profitable ‘grim trigger strategies’ available. It is shown that even in situations where perfect collusion can be sustained after entry, coping with a potential entrant in a market which is growing over time may completely undermine any pre‐entry collusive plans of the incumbent firms. This is because, before entry, a deviation and the following punishment phase may become more attractive thanks to their additional effect in terms of delaying entry.     

Social norms,costly punishment and the evolution of cooperation

Within a co-evolutionary framework of reputations, strategies and social norms, we study the role of punishment in the promotion of cooperation. Norms differ according to whether they allow or do not allow the punishment action to be a part of the strategies, and, in the case of the former, they further differ in terms of whether they encourage or do not encourage the punishment action. In such a framework, depending on the applied social norm, players are first given different reputations based on their employed strategies. Players then update their strategies accordingly after they observe the payoff differences among different strategies. Finally, over a longer horizon, the evolution of the social norms may be driven by the average payoffs of all members of the society. The strategy dynamics are articulated under different social norms. It is found that costly punishment does contribute to the evolution toward cooperation. Not only does the attraction basin of the cooperative evolutionary stable state become larger, but the speed of convergence to the CESS also becomes faster. These two properties are further enhanced if the punishment action is encouraged by the social norm.     

OLIGOPOLY GAMES AND THE COURNOT–BERTRAND MODEL: A SURVEY

Traditional oligopoly models hold that firms compete in the same strategic variable, output (Cournot) or price (Bertrand). Alternatively, a hybrid model allows some firms to compete in output and other firms to compete in price, also known as the Cournot–Bertrand model. When the choice of strategic variable is endogenous, the established dominant strategy is output competition. A growing body of work demonstrates, however, that the Cournot–Bertrand outcome can be a subgame‐perfect Nash equilibrium in the presence of market asymmetries. Observations of real‐world markets consistent with Cournot–Bertrand behavior bolster justification for the model and have stimulated an impressive and evolving literature on advances and applications. We lay out the roots of the Cournot–Bertrand model and explore a number of model developments. We categorize 12 primary models in the literature based on alternative assumptions. In particular, some authors consider when the timing of play as well as the choice of strategic variable are endogenous. Altogether, this research identifies when Cournot–Bertrand behavior can emerge in a dynamic setting and under alternative market conditions. We also review the Cournot–Bertrand model applications in the fields of international economics, industrial organization, labor, and public economics. We expect the literature to continue to expand in the future.     

Disclosure Policy in a Mixed Market

This paper investigates the optimal disclosure strategy for private information in a mixed duopoly market, where a state-owned enterprise (SOE) and a joint-stock company compete to supply products. I construct a model where the two firms compete in either quantity or price, and uncertainty is associated with either marginal cost or market demand. The model identifies the optimal disclosure strategies that constitute a perfect Bayesian equilibrium by type of competition and uncertainty. In Cournot competition, both firms disclose information under cost uncertainty, while only the SOE or neither firm discloses information under demand uncertainty. Alternatively, in Bertrand competition, only the joint-stock company discloses information under cost uncertainty or demand uncertainty. Recently, developed countries have required the same level of disclosure standards for SOEs as for ordinary joint-stock companies. The findings described in this paper warn that such mandatory disclosure by SOEs can trigger a reaction by joint-stock companies, putting the economy at risk of a reduction in welfare.     

How does investors' heterogeneous trust affect the complexity of financial products? A look into the development of online finance

We introduce “trusting effects” to market complexity strategy and, through modeling, measure the decision‐making behavior of financial institutions' complexity choices as online and offline finance develops into different stages. We find that the complexity of financial products is not only determined by the intrinsic value and structure of products but also largely influenced by the behavior of investors. In addition, the characteristics of financial institutions, as well as different investor structures, also affect the complexity of the products and the equilibrium. Therefore, financial institutions attempt to exploit investors' biases and cognitive limitations through complexity strategies and ultimately obtain excess returns.     

A tractable analysis of contagious equilibria

This paper studies contagious equilibrium in infinitely repeated matching games. The innovation is to identify a key statistic of contagious punishment that, used together with a recursive formulation, generates tractable closed-form expressions for continuation payoffs, off equilibrium. This allows a transparent characterization of the dynamic incentives created by contagious punishment schemes.     

-learning agents in a Cournot oligopoly model

Q-learning is a reinforcement learning model from the field of artificial intelligence. We study the use of Q-learning for modeling the learning behavior of firms in repeated Cournot oligopoly games. Based on computer simulations, we show that Q-learning firms generally learn to collude with each other, although full collusion usually does not emerge. We also present some analytical results. These results provide insight into the underlying mechanism that causes collusive behavior to emerge. Q-learning is one of the few learning models available that can explain the emergence of collusive behavior in settings in which there is no punishment mechanism and no possibility for explicit communication between firms.     

Cournot vs. Walras: A reappraisal through simulations

Best-reply behavior in Cournot oligopolies generally leads to Cournot-Nash equilibrium, but imitative behavior selects the Walrasian equilibrium as the unique stochastically stable state. Previous work (Alós-Ferrer, 2004) showed that in the presence of memory, imitative behavior leads to a non-trivial dynamics selecting all quantities between the Cournot and Walrasian outcomes. However, the scope of previous results was limited to specific assumptions on demand and cost functions, and did not provide information on the shape of the distribution of outcomes. We use computational simulations to address these limitations. We show that the selection result for non-trivial memory holds beyond the set of well-behaved Cournot games previously analyzed. Further, we find that, in Cournot games, the limit distribution of long-run outcomes is highly skewed towards the Walrasian quantity. Although longer memory increases the importance of the Cournot equilibrium, the competitive outcome remains the dominant prediction.     

An evolutionary model with best response and imitative rules

We formulate an evolutionary oligopoly model where quantity setting players produce following either the static expectation best response or a performance-proportional imitation rule. The choice on how to behave is driven by an evolutionary selection mechanism according to which the rule that brought the highest performance attracts more followers. The model has a stationary state that represents a heterogeneous population where rational and imitative rules coexist and where players produce at the Cournot–Nash level. We find that the intensity of choice, a parameter representing the evolutionary propensity to switch to the most profitable rule, the cost of the best response implementation as well as the number of players have ambiguous roles in determining the stability property of the Cournot–Nash equilibrium. This marks important differences with most of the results from evolutionary models and oligopoly competitions. Such differences should be referred to the particular imitative behavior we consider in the present modeling setup. Moreover, the global analysis of the model reveals that the above-mentioned parameters introduce further elements of complexity, conditioning the convergence toward an inner attractor. In particular, even when the Cournot–Nash equilibrium loses its stability, outputs of players little differ from the Cournot–Nash level and most of the dynamics is due to wide variations of imitators’ relative fraction. This describes dynamic scenarios where shares of players produce more or less at the same level alternating their decision mechanisms.     

Pure strategy equilibria in games with private and public information

We introduce a new game form which allows the players’ strategies to depend on their strategy-relevant private information as well as on some publicly announced information. The players’ payoffs depend on their own payoff-relevant private information and some payoff-relevant common information. Under the assumption that the players’ strategy-relevant private information is diffuse and their private information is conditionally independent given the public and payoff-relevant common information, we prove the existence of a pure strategy equilibrium for such a game by developing a distribution theory of correspondences via vector measures.     

Stopping with congestion and private payoffs

This paper analyses a two-player stopping game with multiarmed bandits in which each player chooses between learning about the quality of her private risky arm and competing for the use of a single shared safe arm. The qualities of the players’ risky arms are independent. A player whose risky arm produces a success no longer competes for the safe arm. We assume that a player observes her opponent’s actions but not his realised payoffs. She is therefore never certain whether her opponent is still competing for the safe arm. When the players’ prior probabilities of success are sufficiently close, there exists no pure strategy equilibrium, and we characterise the unique mixed strategy equilibrium. Otherwise, the unique equilibrium is in pure strategies. The amount of experimentation performed in equilibrium is inefficiently low but, for many priors, higher than if successes are publicly observed.     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Correcting for bias in retrospective data

When panel data are not available, retrospective data are used in the estimation of dynamic choice models. However, retrospective data are not reliable. Previous studies of voting choices, for example, have shown that respondents misreport their past choices in order to appear more consistent with their current choice. Such retrospective bias leads to inconsistent estimates, especially when there is state dependence in choices. Specifically, observed persistence in retrospective data may be due to (a) true state dependence, (b) unobserved heterogeneity, and (c) retrospective bias in reporting previous choices. Whereas Heckman in his 1981 study deals with (a) and (b), we introduce a method to estimate true state dependence while accounting for both unobserved heterogeneity and retrospective reporting bias. Our method is based on modeling the reporting behavior and integrating it into the estimation. The identification strategy is based on the correlation between the reported previous choices and current exogenous variables. Using data on Israeli voters, we find that the probability that a respondent whose vote intention in 1991 differed from his or her past voting choices would lie about their past choices is 0.23. Copyright © 2007 John Wiley & Sons, Ltd.     

Simple collective equilibria in stopping games

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class of problems as stopping games. Collective choice games, quitting games, and coalition formation games are particular examples. When the core of a stopping game is non-empty, a subgame perfect equilibrium in pure stationary strategies is shown to exist. But in general, even subgame perfect equilibria in mixed stationary strategies may not exist. We show that aggregate voting behavior can be summarized by a collective strategy. We insist on pure strategies, allow for simple forms of punishment, and provide a constructive proof to show that so-called two-step simple collective equilibria always exist. This implies the existence of a pure strategy subgame perfect equilibrium. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to a model of redistributive politics.     

Menu-dependent self-control

The literature on self-control problems has typically put forth models that imply behavior that is consistent with the weak axiom of revealed preference (WARP). We argue that when choice is the outcome of some underlying internal conflict, the resulting choices may not be perfectly consistent across choice problems: an agent’s ability to resist temptation may well depend on what alternatives are available to him. We generalize Gul and Pesendorfer (2001) so that self-control weakens in the presence of temptation. To model choices from menus explicitly, we consider a choice correspondence as well as a preference over menus and relax both the Independence axiom for the preference and the WARP condition for the choice correspondence. The model is shown to unify a range of well-known findings in the experimental literature on choice under risk and over time within a single specification.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

Inferring strategies from observed actions: a nonparametric, binary tree classification approach

This paper introduces a non-parametric binary classification tree approach to inferring unobserved strategies from the observed actions of economic agents. The strategies are in the form of possibly nested if–then statements. We apply our approach to experimental data from the repeated ultimatum game, which was conducted in four different countries by Roth et al. (Am. Econ. Rev. 81 (1991) 1068). We find that strategy inference is consistent with existing inference, provides new explanations for subject behavior, and provides new empirically based hypotheses regarding ultimatum game strategies. We conclude that strategy inference is potentially useful as a complementary method of statistical inference in applied research.     

Robust results on the sharing of firm-specific information: Incentives and welfare effects

Contrary to much of the existing literature, we obtain robust and clear-cut results for the incentives and welfare effects of information sharing when information is firm-specific. We show that firms’ incentives to share this type of information are aligned with social welfare. Whenever revealing information is the dominant strategy (such as for Cournot firms revealing costs or Cournot and Bertrand firms revealing demand), it is socially beneficial. Only cost information in Bertrand competition will not be revealed but this is socially desirable, too. These findings are independent of distributional assumptions on random shocks and signals and hold for general asymmetric oligopoly with any mixture of substitute, complementary and independent goods.