In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.

In this paper we examine a number of different definitions of strategic stability and the relations among them. In particular, we show that the stability requirement given by Hillas (1990) is weaker than the requirements involved in the various definitions of stability in Mertens' reformulation of stability (Mertens 1989, 1991). To this end, we introduce a new definition of stability and show that it is equivalent to (a variant of ) the definition given by Hillas (1990). We also use the equivalence of our new definition with the definition of Hillas to provide correct proofs of some of the results that were originally claimed (and incorrectly “proved”) in Hillas (1990).

This paper deals with regular equilibrium points. Using properties of such equilibrium points, it is possible to give short proofs of known facts about completely mixed bimatrix games and bimatrix games with a unique equilibrium point. We prove that a bimatrix game with a convex equilibrium point set or with a finite number of equilibrium points has a regular equilibrium point. We shall show, moreover, that the class of all m × n-bimatrix games (m, n ∈ ℕ) for which all the equilibrium points are regular, is an open and dense subset of the class of all m × n-bimatrix games. Furthermore, it is shown that an isolated equilibrium point of a bimatrix game is stable if and only if it is a regular one. Here, we call an equilibrium point of a bimatrix game stable if, roughly speaking, all bimatrix games in a neighborhood of the game in question have an equilibrium point close to it.

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A symmetrization for finite two-person gamesJurg, A.P.; Jansen, M.J.M.; Potters, J.A.M.; Tijs, S.H. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policyIf you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Absrracr: The symmetrization method of Galq Kuhn and Tucker for matrix games is eatended (or bimatrix games. It is shown that the equilibria of a bimatrix game end its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.

On the structure of the set of perfect equilibria in bimatrix games Borm, Peter; Jansen, M.J.M.; Potters, J.A.M.; Tijs, S.H.

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