Nash refinements of equilibria (Q1338559)

The multiplicity of Nash equilibria in strategic form games restricts the predictive power of the Nash equilibrium concept. In the literature many attempts are made to reduce the set of (Nash) equilibria by keeping the more desirable equilibria (refinements) or to make a convincing unique choice out of the set of Nash equilibria (equilibrium selection). In this paper, the authors start from any refinement and make a choice out of the lotteries over the refinement equilibria, all with the same payoff vector. The method they use to find such lotteries is borrowed from Nash bargaining theory. The set of lotteries is a convex compact set. A map assigning to each strategic game a disagreement point, is introduced (a typical example is the vector of max-min-values for each for the players) and the Nash (bargaining) solution is applied. From the axioms for the Nash bargaining solution an axiomatization of the Nash refinements is deduced.