Finite-population evolution with rare mutations in asymmetric games

Finite-population evolution with rare mutations in asymmetric games

We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these mutations occur sufficiently infrequently, the dynamics over all population states simplify to an ergodic Markov chain over just the pure population states (where e...

Evolutionary Stability in Asymmetric Population Games¤

We extend the notions of evolutionary stability and neutral stability to asymmetric games played between two populations. Assuming that a single strategy is initially played in each population, we consider the simultaneous entry of small proportions of mutants into both populations. The originally played strategy pair is called neutrally stable if the mutants cannot spread. For bimatrix games, ...

Nash Equilibria for Stochastic Games with Asymmetric Information-Part 1: Finite Games

A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information among the controllers makes it difficult to compute or characterize Nash equilibria. Using common information among the controllers, the game with asymmetric...

Evolution of Decisions in Population Games with Sequentially Searching Individuals

In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium ...

Asymmetric population games and the legacy of Maynard Smith: From evolution to game theory and back?