We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of...

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 provide an evolutionary foundation to evidence that in some situations humans maintain optimistic or pessimistic attitudes towards uncertainty and are ignorant to relevant aspects of the environment. Players in strategic games face Knightian uncertainty about opponents' actions and maximize...

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a...

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a...

We provide an evolutionary foundation to evidence that in some situations humans maintain optimistic or pessimistic attitudes towards uncertainty and are ignorant to relevant aspects of the environment. Players in strategic games face Knightian uncertainty about opponents' actions and maximize...

Neuroeconomics focuses on brain imaging studies mapping neural responses to choice behavior. Economic theory is concerned with choice behavior but it is silent on neural activities. We present a game theoretic model in which players are endowed with an additional structure - a simple ``nervous...

We show that in symmetric two-player exact potential games, the simple decision rule "imitate-if-better" cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2...

We characterize the class of symmetric two-player games in which tit-for-tat cannot be beaten even by very sophisticated opponents in a repeated game. It turns out to be the class of exact potential games. More generally, there is a class of simple imitation rules that includes tit-for-tat but...

We show that in symmetric two-player exact potential games, the simple decision rule imitate-if-better cannot be beaten by any strategy in a repeated game by more than the maximal payoff difference of the one-period game. Our results apply to many interesting games including examples like 2x2...