Strategy Elimination in Games with Interaction Structures

Abstract

Abstract. We study games in the presence of an interaction structure, which allows players to communicate their preferences, assuming that each player initially only knows his own preferences. We study the outcomes of iterated elimination of strictly dominated strategies (IESDS) that can be obtained in any given state of communication. We also give epistemic foundations for these "intermediate" IESDS outcomes. This involves firstly describing the knowledge that the players would have in any state of communication, using the framework from Apt et al. [3]. We then prove that when there is common knowledge of rationality, each intermediate outcome is entailed by the knowledge in the relevant state of communication.