Research on Equilibrium Solutions for Incomplete Information Games Considering Both Expectation and Variance

WANG Guoling, YANG Hui, WANG Chun, YANG Guanghui, TANG Wei

Journal of Systems Science and Mathematical Sciences ›› 2024, Vol. 44 ›› Issue (12) : 3573-3585.

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Journal of Systems Science and Mathematical Sciences ›› 2024, Vol. 44 ›› Issue (12) : 3573-3585. DOI: 10.12341/jssms23830

Research on Equilibrium Solutions for Incomplete Information Games Considering Both Expectation and Variance

  • WANG Guoling1,2, YANG Hui1,2, WANG Chun3, YANG Guanghui1,2, TANG Wei1,2,3
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Abstract

In this paper, variance is introduced into incomplete information static games. By setting the upper bound of variance, the feasible strategy set is obtained for each player, then Nash equilibria are defined by maximizing expected payoffs within the feasible strategy sets. First, the existence of Nash equilibria for such games is proved by Kakutani fixed point theorem. Second, the stability of Nash equilibria for such games is studied. The results show that most games are essential when payoff functions are disturbed. Finally, an example namely incomplete information static Cournot game is given to verify the existence of Nash equilibria for such games.

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Incomplete information games / expectation / variance / Nash equilibria / existence / stability

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WANG Guoling , YANG Hui , WANG Chun , YANG Guanghui , TANG Wei. Research on Equilibrium Solutions for Incomplete Information Games Considering Both Expectation and Variance. Journal of Systems Science and Mathematical Sciences, 2024, 44(12): 3573-3585 https://doi.org/10.12341/jssms23830

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