Abstract. In this paper we consider a two-stage three players game: in the first stage one of the players chooses an optimal strategy knowing that, at the second stage, the other two players react by playing a noncooperative game which may admit more than one Nash equilibrium. We investigate continuity properties of the set-valued function defined by the Nash equilibria of the (second stage) two players game and of the marginal functions associated to the first stage optimization problem. By using suitable approximations of the mixed extension of the Nash equilibrium problem, we obtain without convexity assumption the lower semicontinuity of the set-valued function defined by the considered approximate Nash equilibria and the continuity of the associate approximate average marginal functions when the second stage corresponds to a particular class of noncooperative games called antipotential games.

On approximate mixed Nash equilibria and average marginal functions for two-stage three players games

MALLOZZI, LINA;MORGAN, JACQUELINE
2006

Abstract

Abstract. In this paper we consider a two-stage three players game: in the first stage one of the players chooses an optimal strategy knowing that, at the second stage, the other two players react by playing a noncooperative game which may admit more than one Nash equilibrium. We investigate continuity properties of the set-valued function defined by the Nash equilibria of the (second stage) two players game and of the marginal functions associated to the first stage optimization problem. By using suitable approximations of the mixed extension of the Nash equilibrium problem, we obtain without convexity assumption the lower semicontinuity of the set-valued function defined by the considered approximate Nash equilibria and the continuity of the associate approximate average marginal functions when the second stage corresponds to a particular class of noncooperative games called antipotential games.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/203022
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