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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jmateco.2004.09.003 Byline: Dries Vermeulen, Mathijs Jansen Keywords: Bimatrix games; Stable sets; Computation Abstract: In this paper, an alternative definition of stable sets, defined by Mertens [Mertens, 1989. Stable equilibria - a reformulation. Part I. Definitions and basic properties. Mathematics of Operations Research 14, 575-625], is given where perturbations are interpreted as restrictions on the strategy space instead of perturbations of the payoffs. This alternative interpretation is then used to compute a special type of stable sets -called standard stable sets - in the context of bimatrix games, exclusively using linear optimization techniques and finite enumerations. Author Affiliation: Department of Quantitative Economics, University of Maastricht, PO Box 616, MD-6200 Maastricht, The Netherlands Article History: Received 6 March 2003; Revised 10 June 2004; Accepted 25 September 2004

The structure of the set of equilibria for two person multicriteria games is analyzed. The set of equilibria for bimatrix games was found to be a finite union of polytopes and is only valid for multicriteria games if one of the players only has two pure strategies.

In this paper we derive characterizations of egalitarian solutions on two subclasses of the class of balanced games. Firstly we show that the Dutta–Ray solution is the only solution that satisfies symmetry, independence of irrelevant core allocations, and continuity on the class of convex games. Secondly, together with the other two requirements, a strengthening of continuity to monotonicity in the value of the grand coalition turns out to be sufficient for the characterization of the lexicographically maximal solution on the class of large core games. [Copyright &y& Elsevier]