This chapter of the Handbook of Game Theory (Vol. 3) provides an overview of the theory of Nash equilibrium and its refinements. The starting-point is the rationalistic approach to games and the question whether there exists a convincing, self-enforcing theory of rational behavior in...

We consider a basic stochastic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. Following Young's papers, we call a state stochastically stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases...

We consider a co-evolutionary model of social coordination and network formation where agents may decide on an action in a 2x2 - coordination game and on whom to establish costly links to. We find that a payoff dominant convention is selected for a wider parameter range when agents may only...