Evolutive equilibrium selection I: symmetric two player binary choice games

The aim of the paper is the construction of a distributional model which enables the study of the evolutionary dynamics that arise for symmetric games, and the equilibrium selection mechanisms that originate from such processes. The evolution of probability distributions over the state variables is studied using the Fokker-Planck diffusion equation. Equilibrium selection using the ��basin of attraction�� approach, and a selection process suggested by Pontryagin are contrasted. Examples are provided for all generic 2-person symmetric binary choice games

Contagion and State Dependent Mutations

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected in the long run under the best-response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest response is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for a given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exist only in local interaction settings and favor the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theory.contagion, state dependent mutations, risk dominance, local interaction games

On the Evolutionary Selection of Nash Equilibrium Components

It is well known for the common multi-population evolutionary dynamics applied to normal form games that a pure strategy combination is asymptotically stable if and only if it is a strict equilibrium point. We extend this result to sets as follows. For certain regular selection dynamics every connected and closed asymptotically stable set of rest points containing a pure strategy combination is a strict equilibrium set and hence a Nash equilibrium component. A converse statement holds for two person games, for convex strict equilibrium sets and for the standard replicator dynamic.evolutionary dynamics, replicator dynamic, regular selection dynamics, strict equilibrium set, Nash equilibrium component.

Contagion and state dependent mutations

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected on the long run by the best response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest reply is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for a given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exists only in local interaction settings and favors the play of the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theor

The Evolution of Conflict under Inertia

In Norman (2003), the introduction of individual strategy switching costs, and thus inertia, into stochastic evolutionary coordination games was found inter alia to strengthen the mixed-strategy equilibrium as a short- to medium-run equilibrium. This paper considers the impact of such switching costs on the conflict scenario of Hawk-Dove games. The "attractive" mixed-strategy equilibrium of Hawk-Dove games represents a far better candidate for long-run equilibrium than its unstable counterpart in coordination games, and yet robust selection results have proved elusive, with conditions on the selection dynamics generally being required. Such a condition remains a necessity in the switching cost model with state-independent mutations. However, a more realistic model of state-dependent mutations driven by stochastic switching costs overcomes this problem, and identifies a threshold mean switching cost, above which the mixed-strategy equilibrium is selected in the long run for a wide class of switching cost distributions.

Contagion and state dependent mutations

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected on the long run by the best response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest reply is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for a given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exists only in local interaction settings and favors the play of the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theory

Drift and Equilibrium Selection with Human and Computer Players

The theory of drift (Binmore and Samuelson 1999) concerns equilibrium selection in which second order disturbances may have first-order effects in the emergence of one equilibrium over the other. We provided experimental evidence with human players supporting the model in Caminati, Innocenti and Ricciuti (2006). In this paper we test it with conditioning by computer players. When computers are removed and humans are matched against each other, the comparative static properties of the model are confirmed.drift, equilibrium selection, evolutionary games, experiments.

Evolutionary games and equilibrium selection

In dieser Dissertation werden mehrere Methoden zur Gleichgewichtsselektion f¨ur gewisse Klassen von Spielen studiert. Es wird untersucht, inwiefern diese Methoden zu ¨ahnlichen oder verschiedenen Resultaten f¨uhren. Die Dissertation besteht aus f¨unf Kapiteln. In Kapitel 1 werden die theoretischen Grundlagen einer Homotopiemethode entlang des Graphen der quantal response Gleichgewichte beschrieben. In Kapitel 2 wird diese Methodik im Detail auf 2 × 2 Bimatrixspiele angewendet. Kapitel 3 untersucht das Ultimatumspiel mittels eines Lern- und Mutationsprozesses. Kapitel 4 widmet sich zwei weiteren Methoden der Gleichgewichtsauswahl, die auf der Replikatorgleichung basieren. Kapitel 5 stellt ein ¨okonomisches Experiment vor, das zeigt, wie eine strafende Institution dem Problem der Trittbrettfahrer Herr werden kann.The object of this thesis is to study several equilibrium selection methods for certain classes of games and compare to what extent these selection methods lead to similar or different results. The thesis consists of five chapters. Chapter 1 describes a theoretical framework for equilibrium selection by tracing the graph of the quantal response equilibrium (QRE) correspondence. Chapter 2 analyzes the quantal response methods for equilibrium selection in detail for 2 × 2 bimatrix games. Chapter 3 investigates the ultimatum game by a learning-mutation process related to the quantal response equilibrium. Chapter 4 studies two equilibrium selection methods based on the replicator dynamics. Chapter 5 provides a economic experiment to show that social learning can lead to a spontaneously emerging social contract, based on a sanctioning institution to overcome the free rider problem

Evolutionary Learning in Signalling Games

We study equilibrium selection by evolutionary learning in monotone signalling games. The learning process is a development of that introduced by Young for static games extended to deal with incomplete information and sequential moves; it thus involves stochastic trembles. For vanishing trembles the process gives rise to strong selection among sequential equilibria. If the game has separating equilibria, then in the long run only play according to a specific separating equilibrium, the so-called Riley equilibrium, will be observed frequently. Also if the game has no separating equilibrium a particular behavior will emerge as the only one observed frequently in the long run. It may or may not correspond to a pooling equilibrium, but if it does, it is to one where both types of sender choose the signal that is best for the ''high'' type when all signals are responded to as if they came from the ''low'' type. This selection is stronger than, and only partly in accordance with, traditional selection based on restrictions on ''out-of-equilibrium'' beliefs.monotone signalling games; intuitive criterion; Riley equilibrium; evolutionary learning; separating equilibrium; pooling equilibrium

Global Analysis of an Expectations Augmented Evolutionary Dynamics

We consider a deterministic evolutionary model where players form expectations about future play. Players are not fully rational and have expectations that change over time in response to current payoffs and feedback from the past. We provide a complete characterization of the qualitative dynamics so induced for a two strategies population game, and relate our findings to standard evolutionary dynamics and equilibrium selection when agents have rational forward looking expectations.evolutionary games, dynamic systems, bounded rationality