On the computation of stable sets for bimatrix games

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.

Universality of Nash components

“…Since a success set is cubistic, it is polyhedral. Therefore, by Lemma 4 of Vermeulen and Jansen [13], any success set is also simplicial.…”