N-Player Games

Abstract

This chapter extends several of the concepts for two-player games to games with N-players. It begins by considering general games with N players P₁, P₂, . . ., P(subscript N), which are allowed to select policies within action spaces Γ‎₁, Γ‎₂, . . ., Γ‎(subscript N). Each player wants to minimize their own outcome, and does not care about the outcome of the other players. The chapter proceeds by discussing the security level, security policy, and Nash equilibrium for N-player games, pure N-player games in normal form, mixed policy for N-player games in normal form, and computation of the completely mixed Nash equilibrium for N-player games. A mixed Nash equilibrium is computed for a different game in which some (or all) players want to maximize instead of minimize the outcome.