Consider a -player game in strategic form = where, for any , the set is a closed interval of real numbers and the payoff function is differentiable with respect to the related variable . If they are also concave, with respect to the related variable, then it is possible to associate to the game a variational inequality which characterizes its Nash equilibrium points. We have find appropriate conditions on the payoff functions under which the well-posedness with respect to the related variational inequality is equivalent to the formulation of the Tykhonov well-posedness in a game context. The idea of the proof is to appeal to a third equivalence, which is the well-posedness of an appropriate minimum problem.
On the Variational Inequality and Tykhonov Well-Posedness in Game Theory
PIERI, GRAZIANO
2010-01-01
Abstract
Consider a -player game in strategic form = where, for any , the set is a closed interval of real numbers and the payoff function is differentiable with respect to the related variable . If they are also concave, with respect to the related variable, then it is possible to associate to the game a variational inequality which characterizes its Nash equilibrium points. We have find appropriate conditions on the payoff functions under which the well-posedness with respect to the related variational inequality is equivalent to the formulation of the Tykhonov well-posedness in a game context. The idea of the proof is to appeal to a third equivalence, which is the well-posedness of an appropriate minimum problem.
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