Essays on Nash equilibrium refinements

This thesis introduces, as major contribution, a new definition of strategically stable set of equilibria by considering a new class of perturbed games obtained by adding a set of irrelevant players and a collection of dominated strategies to the initial game. Both variations have no effect on the set of equilibria of the original game but allow to widen the resulting stable sets of equilibria up to satisfy all the properties proposed in Kohlberg and Mertens [1986] and in Mertens [1989]. Besides a new fictitious game is proposed to define a new single valued Nash equilibrium refinement, namely refined equilibria, and to extend strategic stability to correlated equilibria. In both cases the desired goals are not reached even if there are significant positive results: a refined equilibrium satisfies the invariance property improving on the concept of proper equilibrium. This result stems from a setting that is closer to the forward induction than the backwards induction approach: a single valued solution concept that always conforms with backwards induction cannot verify the property of invariance. Similarly the concept of stable correlated equilibria improve on both perfect and acceptable correlated equilibria since it can be applied to nplayer games and it excludes equilibria that are not perfect.(POLS - Sciences politiques et sociales) -- UCL, 201