Local stability under evolutionary game dynamics

We prove that any regular ESS is asymptotically stable under any impartial pairwise comparison dynamic, including the Smith dynamic; under any separable excess payoff dynamic, including the BNN dynamic; and under the best response dynamic. Combined with existing results for imitative dynamics, our analysis validates the use of ESS as a blanket sufficient condition for local stability under evolutionary game dynamics.Evolutionary game dynamics, ESS

Some Relationships Between Evolutionary Stability Criteria in Games

The relationships between five stability criteria for evolutionary games are studies.Noncooperative games;

Language, meaning and games A model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to two-sided preplay communication in finite and symmetric two-player games and we establish that, in generic and symmetric n × n - coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We extend the approach to one-sided communication in finite, not necessarily symmetric, two-player games.

The explanatory relevance of Nash equilibrium: one-dimensional chaos in boundedly rational learning

Game theory is often used to explain behavior. Such explanations often proceed by demonstrating that the behavior in question is a Nash equilibrium. Agents are in Nash equilibrium if each agent’s strategy maximizes her payoff given her opponents’ strategies. Nash equilibriums are fundamentally static, but it is usually assumed that equilibriums will be the outcome of a dynamic process of learning or evolution. This article demonstrates that, even in the most simple setting, this need not be true. In two-strategy games with just a single equilibrium, a family of imitative learning dynamics does not lead to equilibrium

Replicator Dynamics and Correlated Equilibrium: Elimination of All Strategies in the Support of Correlated Equilibria

Nous donnons un exemple de jeu pour lequel, sous la dynamique des réplicateurs et pour un ensemble ouvert de conditions initiales, toutes les stratégies jouées en équilibre corrélé sont éliminées.

Veblen, Sen, and the formalization of evolutionary theory

It has been suggested that economics could benefit greatly from recent developments in evolutionary game theory. In fact, key authors in the study of the role of ethical norms in economic behavior like Amartya Sen argue that evolutionary game theory could contribute much to the study of social norms and behavior. Others have suggested that evolutionary game theory could be most helpful for formalizing the work of classic authors in evolutionary and institutional economics like Thorstein Veblen. Here I discuss the behavioral assumptions of evolutionary game theory models, and Jorgen Weibull's approach in particular. I will argue that Weibull's models, and evolutionary game theory in general, pose overly strong restrictions on the explanation of human behavior, which limit the potential of evolutionary explanation. I also suggest Tony Lawson's population-variety-reproduction-selection (PVRS) model as an alternative evolutionary framework that can successfully accommodate developments in behavioral economics, while also providing a solution to important critiques of Darwinian evolutionary analysis made by Richard Nelson, among others.info:eu-repo/semantics/publishedVersio

Robust Evolution Of Contingent Cooperation In Pure One-Shot Prisoners' Dilemmas. Part I: Vulnerable Contingent Participators Versus Stable Contingent Cooperators

ROC curves from the signal detection literature are used in an evolutionary analysis of one-shot and repeated prisoners' dilemmas: showing if there is any discounting of future payoffs, or any cost of searching for an additional partner, then cooperative players who contingently participate - in terms of who to play with or when to exit - cannot survive when most other players unconditionally defect; even when contingent participators only interact with themselves by perfectly detecting their own type. However, quite different results hold for players who act contingently, not in terms of whether to play or exit, but rather in terms of how to act with any given partner. There is a form of contingent cooperation in one-shot prisoners' dilemmas (called CD behavior) that will robustly evolve through any payoff monotonic process, such as replicator dynamics. That is, whenever CD-players can detect their own type better than pure chance, they are guaranteed to evolve from any initial population - eventually to a unique evolutionarily stable population composed entirely of contingent cooperators - provided the fear payoff difference is less than the sum of greed and cooperation payoff differences. The adaptive capabilities just described hold for pure one-shot prisoners' dilemmas: meaning no repeated interactions or pairings in any generation are involved; no information or third party reports about past behavior are involved, all signal information arises only from symptoms detected after two strangers meet for the first time; and no subjective preferences for altruism, fairness, equity, reciprocity, or morality affect the raw evolutionary dynamics. Testable predictions are also derived that agree with a large body of experimental data built up since the prisoners dilemma was first introduced in 1950. They describe how the CD-players' equilibrium probability of cooperating changes: depending on the relative size of fear, greed, and cooperation payoff differences; and depending on the players' history of communication, especially when face-to-face discussion is involved. --prisoners? dilemma,cooperation,Nash equilibrium,evolutionary stability,replicator dynamics,signal detection,ROC curves,experiment

Epistemically stable strategy sets

This paper provides a definition of epistemic stability of sets of strategy profiles, and uses it to characterize variants of curb sets in finite games, including the set of rationalizable strategies and minimal curb sets.Epistemic game theory; epistemic stability; rationalizability; closedness under rational behavior; mutual p-belief.