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Binary 2 × 2 games
Authors:Peter C. Fishburn  D. Marc Kilgour
Affiliation:(1) AT&T Bell Laboratories, Murray Hill, 07974, NJ, U.S.A.;(2) Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada
Abstract:The 2 × 2 game is the simplest interactive decision model that portrays concerned decision makers with genuine choices. There are two players, each of whom must choose one of two strategies, so that there are four possible outcomes. Binary 2 × 2 games are 2 × 2 games with no restrictions on the players' preference relations over the outcomes. They therefore generalize the strict ordinal 2 × 2 games and the ordinal 2 × 2 games, classes which have already been studied extensively. This paper enumerates the strategically distinct binary 2 × 2 games. It also identifies important subsets defined by the number of pure Nash equilibria and the occurrence of dominant strategies.
Keywords:Noncooperative game theory  2 ×   2 games  nontransitive preferences  Nash equilibria  dominant strategy
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