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...

Unique-lowest sealed-bid auctions are auctions in which participation is endogenous and the winning bid is the lowest bid among all unique bids. Such auctions admit very many Nash equilibria (NEs) in pure and mixed strategies. The two-bidders' auction is similar to the Hawk-Dove game, which...

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,...

Altruists and envious people who meet in contests are symbionts. They do better than a population of narrowly rational individuals. If there are only altruists and envious individuals, a particular mixture of altruists and envious individuals is evolutionarily stable.

This paper studies an evolutionary model of network formation with endogenous decay, in which agents benefit both from direct and indirect connections. In addition to forming (costly) links, agents choose actions for a coordination game that determines the level of decay of each link. We address...

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 call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has (1) a product structure, is (2) upper semi-continuous, (3) always includes a best reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each...

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 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...

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...