Computing the strong Nash equilibrium for Markov chains games: Convergence and uniqueness

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• 作者：Kristal K. Trejo ; ^a ; ^{ktrejo@ctrl.cinvestav.mx} ; ^{kristal_trejo@hotmail.com} ; Julio B. Clempner^b ; ^{julio@clempner.name} ; Alexander S. Poznyak^a ; ^{apoznyak@ctrl.cinvestav.mx}
• 关键词：Nash equilibrium ; Strong Nash equilibrium ; Lp- norm ; Strong Pareto policy ; Coalition
• 刊名：Applied Mathematical Modelling
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：41
• 期：Complete
• 页码：399-418
• 全文大小：1170 K
• 卷排序：41

文摘

We suggest a method for computing the strong Lp−Lp− Nash equilibrium for Markov chains games. There exists an optimal solution that is a strong Pareto optimal point and corresponds to the strong Nash equilibrium. We design the extraproximal method for the static strong Nash game in terms of nonlinear programming problems. For solving each equation of the extraproximal optimization approach we use the projection gradient method. We prove that the proposed method converges in exponential time to a unique strong Lp−Lp− Nash equilibrium.