We examine dynamic models of evolutionary selection processes on asymmetric two-player games. Conditions are established under which dynamic selection processes will yield outcomes that respect iterated strict dominance. The addition of a stability requirement ensures that outcomes will be Nash equilibria. However, we find that stable outcomes need not respect weak dominance, and hence need not...

In evolutionary game theory, the main interest is normally on the investigation of how the distribution of strategies changes along time and whether an stable strategy arises. In this paper we compare the dynamics of two games in which three populations of agents interact: a three-player version of matching pennies and a game with several Nash equilibria. We do this comparison by three methods:...

A evolutionary game is introduced which explicitly models states and actions in the strategies of the organisms of the evolving population. The game principally features actions that result in demographic flow between states that may not conserve organism numbers. The game’s formalism is expounded and the nature of the game’s equilibrium is discussed. This discussion leads to an algorithm for n...

The purpose of the course is to study several dynamics generated by strategic interactions in games. Among the topics are adaptive dynamics in evolutionary game theory, robust procedures for on-line algorithms and stochastic approximation. 1. Fictitious play Discrete time Continuous time and best reply dynamics 2. Replicator dynamics n populations One population Evolutionary Stable Strategies 3...

Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and...

Consider an oligopolistic industry composed of two groups (or populations) of firms, the low cost firms and the high cost firms. The firms produce a homogeneous good. I study the finite population evolutionarily stable strategy defined by Schaffer (1988), and the long run equilibrium in the stochastic evolutionary dynamics based on imitation and experimentation of strategies by firms in each gr...

One of the best examples of traditional analysis of evolutionary stable strategies (ESS) is provided by the so called Dove-Hawk model. In this paper we present several enhancements to the model aimed at describing the evolution of cooperative behavior. In addition to Doves and Hawks we introduce several groups of Cooperators, who act as Doves within their own group, but as Hawks outside it. Thi...

Schaffer [Schaffer, M.E., 1988. Evolutionarily stable strategies for a finite population and a variable contest size. Journal of Theoretical Biololgy 132, 469–478] proposed a concept of evolutionary stability for finite-population models that has interesting implications in economic models of evolutionary learning, since it is related to perfectly competitive equilibrium. The present paper expl...

Animals can often coordinate their actions to achieve mutually beneficial outcomes. However, this can result in a social dilemma when uncertainty about the behavior of partners creates multiple fitness peaks. Strategies that minimize risk ("risk dominant") instead of maximizing reward ("payoff dominant") are favored in economic models when individuals learn behaviors that increase their payoffs...