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Competition among Conventions

Description:

A convention can be seen as the standard way of playing a game. If different conventions exist in various geographical, social or other entities (called "towns") and if there is some mobility between these towns, which conventions, if any, will emerge as the successful ones? A simple evolutionary process is suggested and it is shown that the pro...

A convention can be seen as the standard way of playing a game. If different conventions exist in various geographical, social or other entities (called "towns") and if there is some mobility between these towns, which conventions, if any, will emerge as the successful ones? A simple evolutionary process is suggested and it is shown that the process converges to a Nash equilibrium for all games satisfying weak acyclity or a condition called evolutionary stable with respect to pure strategies (ESPS). Further, if the process converges, it converges to an efficient convention for all games in which the Pareto optimal symmetric equilibria are strict. Hence, the paper presents an explanation for the endogenous evolution of efficiency. In contrast to most recent studies in evolutionary game theory, the conclusions do not rely on random "mutations". Instead, the driving force is the tendency of players to have increased interaction with member of their own group (viscosity). Minimize

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AN EVOLUTIONARY INTERPRETATION OF MIXED-STRATEGY EQUILIBRIA

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One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a good story about how the population arrives at the ap...

One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a good story about how the population arrives at the appropriate distribution over pure strategies. In this paper I attempt to give an explanation based on an evolutionary, stochastic learning process. Convergence properties of these processes have been studied extensively but almost exclusively for the case of convergence to pure Nash equilibria. Here I study the conditions under which an evolutionary process converges to population mixed-strategy equilibria. I find that not all mixed equilibria can be justified as the result of the evolutionary learning process even if the equilibrium is unique. For symmetric 2x2 and 3x3 games I give necessary and sufficient conditions for convergence and for n*n games I give a sufficient condition. For cases in which the conditions are not satisfied counterexamples are given, in which the process enters a limit cycle. Minimize

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Decentralization and the Coordination Problem

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This paper addresses the relation between the degree of decentralization in a population and the probability of coordinating on an efficient outcome. An evolutionary learning mechanism with a group structure that allows players to "vote with their feet" is introduced. In contrast to most of the recent literature (e.g. Kandori, Mailath and Rob, 1...

This paper addresses the relation between the degree of decentralization in a population and the probability of coordinating on an efficient outcome. An evolutionary learning mechanism with a group structure that allows players to "vote with their feet" is introduced. In contrast to most of the recent literature (e.g. Kandori, Mailath and Rob, 1993) in which the risk dominant equilibrium is shown to prevail in the long run, in this paper it is demonstrated that given a general probability distribution over initial states the evolutionary learning process converges almost always to the efficient equilibrium if interaction is decentralized enough. Furthermore, it is shown how the model can be applied to the problem of product standardization. Minimize

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Cooperation as a Result of Learning with Aspiration Levels

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It is shown that a win-stay, lose-hift behavior rule with endogenous aspiration levels yields cooperation in a certain class of games. The aspiration level in each round equals the current population average. The class of games includes the prisoner's dilemma and Cournot oligopoly and thus yields an explanation for cooperation and collusion. ; c...

It is shown that a win-stay, lose-hift behavior rule with endogenous aspiration levels yields cooperation in a certain class of games. The aspiration level in each round equals the current population average. The class of games includes the prisoner's dilemma and Cournot oligopoly and thus yields an explanation for cooperation and collusion. ; cooperation Minimize

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Evolutionary Dynamics on Infinite Strategy Spaces

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The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this restriction is in most cases unnecessary. We give a mild condition under which the continuous time replicator dynamics are well defined for infinite strategy spaces. Furthermore, we provide conditions for stability of rest p...

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this restriction is in most cases unnecessary. We give a mild condition under which the continuous time replicator dynamics are well defined for infinite strategy spaces. Furthermore, we provide conditions for stability of rest points. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, Cournot and Bertrand oligopoly games, and mixed strategies. ; replicator dynamics, evolutionary stability, continuous strategy spaces, oligopoly Minimize

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The Indirect Evolutionary Approach to Explaining Fair Allocations

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Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' which is based on the assumption that players behave rationally for given ...

Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' which is based on the assumption that players behave rationally for given preferences but that their preferences change through an evolutionary process. We prove that despite anonymous interaction a preference for punishing unfair offers is an evolutionarily successful strategy if players interact in small groups. This leads players to split the resource equally almost always. However, the equal split is not due to 'true fairness' (or 'altruism') but is entirely caused by the (justified) fear that unfair offers might be rejected. ; evolutionary game theory, ultimatum game, punishment. Minimize

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The Absent-minded Centipede (revision)

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In this note we apply the notion of absent-mindedness (see Piccione and Rubinstein, 1994), which is a form of imperfect recall, to Rosenthal's (1981) centipede game. We show that for standard versions of the centipede game a subgame perfect equilibrium exists in which play is continued almost to the end if one player is known to be absent-minded...

In this note we apply the notion of absent-mindedness (see Piccione and Rubinstein, 1994), which is a form of imperfect recall, to Rosenthal's (1981) centipede game. We show that for standard versions of the centipede game a subgame perfect equilibrium exists in which play is continued almost to the end if one player is known to be absent-minded. In fact, it is sufficient that one player is known to be absent-minded with sufficiently high probability. Minimize

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Informational Cascades with Continuous Action Spaces

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The recent literature on informational cascades has nurtured the impression that cascades can occur only if the action space is coarser than the signal space. In particular, it is sometimes claimed that with continuous action spaces cascades are impossible. In this note we present a simple counter-example showing that this conclusion is not nece...

The recent literature on informational cascades has nurtured the impression that cascades can occur only if the action space is coarser than the signal space. In particular, it is sometimes claimed that with continuous action spaces cascades are impossible. In this note we present a simple counter-example showing that this conclusion is not necessarily warranted. ; herding, cascades, information Minimize

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On the Dynamic Foundation of Evolutionary Stability in Continuous Models

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We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the ...

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games. ; replicator dynamics, evolutionary stability, ESS, CSS Minimize

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Does Rationing of Shares Increase Revenues in Initial Public Offerings?

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We provide a new explanation for the apparent underpricing of initial public offerings applicable to large, regulated firms like telecommunications companies. Under the assumption that regulation is subject to political pressure by voters we demonstrate that it may be rational for issuers to ration investors in order to insure a broad distributi...

We provide a new explanation for the apparent underpricing of initial public offerings applicable to large, regulated firms like telecommunications companies. Under the assumption that regulation is subject to political pressure by voters we demonstrate that it may be rational for issuers to ration investors in order to insure a broad distribution of shares in the population. At the same time we explain the common practice of bonus systems designed to prevent investors from taking profits immediately. Minimize

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