Potential Games

Abstract

This chapter introduces a special class of N-player games, the so-called potential games, for which the Nash equilibrium is guaranteed to exist and is generally easy to find. It begins by considering a game with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies from the action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N), respectively. The notation is given for the outcome of the game for the player Pᵢ and all players wanting to minimize their own outcomes. The chapter goes on to discuss identical interests games, minimum vs. Nash equilibrium in potential games, bimatrix potential games, characterization of potential games, and potential games with interval action spaces. It concludes with practice exercises and their corresponding solutions, along with an additional exercise.