Ramanujam, Ramaswamy and Simon, Sunil, A Logical Structure for Strategies

Abstract We consider a logic for reasoning about composite strategies in games, where players’ strategies are like programs, composed structurally. These depend not only on conditions that hold at game positions but also on properties of other players’ strategies. We present an axiomatization for the logic and prove its completeness.

Builds a logic that creates an arena, identifies win conditions in it, strategy specifications that describe what players test before selecting a move, and game formulas describe the game as a whole in modal logic terms accounting for all the player strategies taken together.