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...

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...

Online and offline gaming has become a multi-billion dollar industry.However, games of chance are prohibited or tightly regulated in many jurisdictions. Thus, the question whether a game predominantly depends on skill or chance has important legal and regulatory implications. In this paper, we...

We introduce a generalized theoretical approach to study imitation models and subject the models to rigorous experimental testing. In our theoretical analysis we find that the different predictions of previous imitation models are due to different informational assumptions, not to different...

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a...

In this note we study a very simple trial & error learning process in the context of a Cournot oligopoly. Without any knowledge of the payoff functions players increase, respectively decrease, their quantity by one unit as long as this leads to higher profits. We show that this process converges...

In this note we apply the notion of absent-mindedness (see Piccione and Rubinstein, 1994), which is a form of imperfect recall, to Rosenthal's (1981) centipede game. We show that for standard versions of the centipede game a subgame perfect equilibrium exists in which play is continued almost to...

In this article we study a very simple trial and error learning process in the context of a Cournot oligopoly. Without any knowledge of the payoff functions players increase, respectively decrease, their quantity as long as this leads to higher profits. We show that despite the absence of any...

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept,...

This paper addresses the relation between the degree of decentralization in a population and the probability of coordinating on an efficient outcome. An evolutionary learning mechanism with a group structure that allows players to "vote with their feet" is introduced. In contrast to most of the...