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. It is considered the variational inequality for two sets of Cournot oligopoly games. As a consequence of well known facts, the existence and uniqueness of the Nash equilibrium point are guaranteed and also the Tykhonov and Hadamard well-posedness of the game. We prove that the game is well posed with respect to its variational inequality.
Variational Inequalities in Cournot Oligopoly
PIERI, GRAZIANO
2007-01-01
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. It is considered the variational inequality for two sets of Cournot oligopoly games. As a consequence of well known facts, the existence and uniqueness of the Nash equilibrium point are guaranteed and also the Tykhonov and Hadamard well-posedness of the game. We prove that the game is well posed with respect to its variational inequality.
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