Discovering Theorems in Game Theory: Two-Person Games with Unique Pure Nash Equilibrium Payoffs

In this paper we provide a logical framework for using computers to discover theorems in two-person finite games in strategic form, and apply it to discover classes of games that have unique pure Nash equilibrium payoffs. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program rediscovered Kats and Thisse’s class of weakly unilaterally competitive two-person games, and came up with several other classes of games that have unique pure Nash equilibrium payoffs. It also came up with new classes of strict games that have unique pure Nash equilibria, where a game is strict if for both player different profiles have different payoffs.