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...

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....

The backward induction (or subgame-perfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large.

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,...

A large and growing literature on reputation in games builds on the insight that the possibility of one or more players being other than fully rational can have significant effects on equilibrium behavior. This literature leaves unexplained the presence of behavioral players in the first place,...

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...

Random Boolean Network has been used to find out regulation patterns of genes in organism. This approach is very interesting to use in a game such as N-Person Prisoner’s Dilemma. Here we assume that agent’s action is influenced by input in the form of choices of cooperate or defect she...

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 present a simple model of spatial evolution that avoids several problems that arise with more complex networks of players. We consider a world where pairs of players are matched forever. These players learn from the whole population but they are more likely to learn to strategies used by...