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.

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...

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,...

Theoretical Computer Science classically aimed to develop a mathematical understanding of capabilities and limits of traditional computing architecture (Boole, von Neuman, Turing, Church, Godel), investigating in computability, complexity theory and algorithmics. Now it seems more natural to...

We present the Progressive Second Price auction, a new decentralized mechanism for allocation of variable-size shares of a resource among multiple users. Unlike most mechanisms in the economics litterature, PSP is designed with a very small message space, making it suitable for real-time market...

We propose a quantum-like description of markets and economics. The approach has roots in the recently developed quantum game theory. Quantum Zeno paradoxes and noncomutative quantum mecanics are also discussed.