Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoﬀ diﬀerences and beliefs. Some “potential game” arguments (cf. Monderer and Shapley, 1996, Games. Econ. Behav. 14, 124-143) rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended.
Morris, Stephen and Ui, Takashi, "Best Response Equivalence" (2002). Cowles Foundation Discussion Papers. 1641.