A method for solving Nash equilibria of games based on public announcement logic

Abstract

Describing the interactional behavior of rational agents and seeking equilibria are two main domains of game theory. The epistemic foundation of the above two domains is based on the assumption that all players are rational. However, game theory itself cannot precisely model the higher-order information changes of mutual knowledge among players, so in the current studies of game theory the interpretations of rationality are vague. In this paper, a concept of the rationality is redefined through incorporating an epistemic ingredient. Then a method is proposed to solve and refine Nash equilibria which is grounded on public announcement logic, and it is proved that the iterated announcement of this rationality assertion characterizes the iterated admissibility algorithm in game theory, which offers a dynamic epistemic foundation for this algorithm. Finally, an implementation of this method, based on the extended DEMO, is shown to be correct.