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

Toshiyuki Hirai ()
Toshiyuki Hirai: University of Toyama

International Journal of Game Theory, 2018, vol. 47, issue 4, 1087-1111

Abstract: Abstract We investigate farsighted stable sets 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 chosen by these other players. We particularly investigate a special class of farsighted stable sets, each of which consists of strategy profiles yielding a single payoff vector. We call such a farsighted stable set as a single-payoff farsighted stable set. We propose a concept called an inclusive set that completely characterizes single-payoff farsighted stable sets in strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by single-payoff farsighted stable sets is closely related to the strict $$\alpha$$ α -core in a strategic game. Furthermore, we apply the results to strategic games where each player has two strategies and strategic games associated with some market models.

Keywords: Farsighted stable set; Dominant punishment strategy; Inclusive set; Strict $$\alpha$$ α -core (search for similar items in EconPapers)
JEL-codes: C70 C71 (search for similar items in EconPapers)
Date: 2018
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