Periodic Strategies II: Generalizations and Extensions

TL;DR

This paper extends the concept of periodic strategies to multi-player and incomplete information games, proving their existence and exploring their properties within a non-cooperative framework and epistemic game theory.

Contribution

It generalizes periodic strategies to multi-player and Bayesian games, demonstrating their existence and analyzing their mathematical and strategic properties.

Findings

Periodic strategies exist in multi-player perfect information games.

Periodic strategies can be found in Bayesian games with incomplete information.

Periodic strategies are non-cooperative but exhibit cooperative-like features.

Abstract

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.