2014/02/20 by Yakov Babichenko, Babichenko, Yakov
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems #Opinion Dynamics and Social Influence
paper · pdf · doi:10.48550/arxiv.1402.5165
openalex publication_date 2014/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest notion of individual rationality restricts the set of solutions to be equilibria. This observation holds for all types of solutions: in pure-strategies, in mixed strategies, and in correlated strategies where the corresponding notions of equilibria are pure-Nash, Nash and coarse-correlated. An action profile is (strict) simultaneous maximizer if it simultaneously globally (strictly) maximizes the payoffs of all players. - If we require that a simultaneous maximizer (if it exists) will be a solution, then the solution contains the set of pure Nash equilibria. - There is no solution for which a strict simultaneous maximizer (if it exists) is the unique solution.