Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

We investigate the farsighted stable set in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players’ payoffs for any given strategies of other players. We particularly investigate a special class of the farsighted stable sets each of which consists of strategy profiles yielding a single payoff vector. We call such farsighted stable sets as the single-payoff farsighted stable sets. We propose a concept called the inclusive set that completely characterizes the single-payoff farsighted stable sets in the strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by the single-payoff farsighted stable sets is closely related to the strict -core in strategic games. Further, we apply the results to the strategic games where each player has two strategies and　strategic games associated with some market models.First version: September 30, 2016Revised version: October 24, 201