It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric...

We present two new notions of evolutionary stability, the truly evolutionarily stable state (TESS) and the generalized evolutionarily stable equilibrium (GESE). The GESE generalizes the evolutionarily stable equilibrium (ESE) of Joosten [1996]. An ESE attracts all nearby trajectories...

This paper studies the evolution of peoples' models of how other people think - their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found...

Nash proposed an interpretation of mixed strategies as the average pure-strategy play of a population of players randomly matched to play a normal-form game. If populations are finite, some equilibria of the underlying game have no such corresponding "mass-action" equilibrium. We show that for...

We apply the dynamic stochastic framework proposed by recent evolutionaryliterature to the class of strict supermodular games when two simplebehavior rules coexist in the population, imitation and myopic optimization.We assume that myopic optimizers are able to see how well their payoff...

We apply the stochastic evolutionary approach of equilibrium selection tomacroeconomic models in which a complementarity at the macro level ispresent. These models often exhibit multiple Pareto-ranked Nash equilibria,and the best response-correspondence of an individual increases with ameasure...

Second price allpay auctions (wars of attritions) have an evolutionarily stable equilibrium in pure strategies if valuations are private information. I show that for any level of uncertainty there exists a pure deviation strategy close to the equilibrium strategy such that for some valuations...

We present attractiveness, a refinement criterion for evolutionary equilibria. Equilibria surviving this criterion are robust to small perturbations of the underlying payoff system or the dynamics at hand. Furthermore, certain attractive equilibria are equivalent to others for certain...

Motivated by trying to better understand the norms that govern pedestrian traffic, I study symmetric two-player coordination games with independent private values. The strategies of "always pass on the left" and "always pass on the right" are always equilibria of this game. Some such games,...