Temporal Logic with Preferences and Reasoning About Games

Abstract

Game theory based semantics has provided good insights into the decidabilityand completeness of several modal logics [24]. On the other hand,we can formalise the language and reasoning used in game theory usingappropriate types of modal logic [1, 3, 12–15, 23, 25]. This paperis concerned with the latter issue. The starting point in games isa set of players (agents) having certain strategies (decisions) andpreferences on the game’s outcomes. Hence we have to represent boththe game structure and the agents’ preference relations. When reasoningabout the games, we wish to determine the properties that hold inthe equilibrium to which the game naturally evolves.