\(p\)-dominance and equilibrium selection under perfect foresight dynamics. (Q1867552)

The author considers a class of evolutionary games with perfect foresight dynamics. A continuum of identical players is repeatedly and randomly matched to play a symmetric \(n \times n\) game. Time instants at which each player can switch actions follow a Poisson process, i.e. there are frictions in the game. The author establishes equivalence between linear stability and \(p\)-dominance of the pure strategy Nash equilibrium under a small friction and shows that \(p\)-dominance represents a sufficient condition for other stability concepts (accessible and absorbing equilibria) under similar assumptions. Some existence results for stability concepts are also presented in the set-valued case.