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 present a new and simple mechanism for repeated public good environments. In the Conditional Contribution Mechanism (CCM), agents send two message of the form, "I am willing to contribute x units to the public good if in total y units are contributed." This mechanism offers agents risk-free...

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 observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for...

We show that for many classes of symmetric two-player games, the simple decision rule 'imitate-if-better' can hardly be beaten by any strategy. We provide necessary and sufficient conditions for imitation to be unbeatable in the sense that there is no strategy that can exploit imitation as a...

One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a...

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this restriction is in most cases unnecessary. We give a mild condition under which the continuous time replicator dynamics are well defined for infinite strategy spaces....

Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' which is based on the...

We use an experiment to explore how subjects learn to play against computers which are programmed to follow one of a number of standard learning algorithms. The learning theories are (unbeknown to subjects) a best response process, fictitious play, imitation, reinforcement learning, and a trial...

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinte strategy...