Personality-Based Representations of Imperfect-Recall Games

Games with imperfect recall are a powerful model of strategic interactions that allows agents to forget less important details of the past. Nevertheless, the computational treatment of imperfect-recall games is largely unexplored so far, and no efficient strategy representation for this setting is known. In this paper, we focus on general imperfect-recall games without absentmindedness, and we study how to produce a perfect-recall representation of these games using personalities. In particular, a valid personality assignment is a decomposition of an imperfect-recall player such that she does not exhibit memory losses within the same personality. Given a valid personality assignment, we can build an auxiliary team game where a team of perfect-recall players---sharing the same objectives---replaces a player with imperfect recall. Our primary goal is the construction of a compact representation in terms of number of personalities. We study the (iterated) inflation operation as a way to simplify the information structure of a game with imperfect recall. We show that the complete (i.e., maximal) inflation of a game can be found in polynomial time. We also show that finding the valid personality assignment minimizing the number of personalities is NP-hard, and also hard to approximate, unless P=NP, even in a completely inflated game.