大博弈中Nash均衡的存在性

杨哲;蒲勇健

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (12) : 1606-1612.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (12) : 1606-1612. DOI: 10.12341/jssms09432
论文

大博弈中Nash均衡的存在性

    杨哲, 蒲勇健
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On the Existence of Nash Equilibrium Points in Large Games

    YANG Zhe, PU Yongjian
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摘要

研究了具有任意多个局中人的非合作博弈(大博弈)中Nash均衡的存在性.将1969年Ma的截口定理推广得到新的截口定理.用这个新的截口定理进一步证明了:1)大博弈中Nash均衡的存在性;2)纯策略集为紧度量空间而且支付函数为连续函数时,连续大博弈中混合策略Nash均衡的存在性.并且存在性定理推出了2010年Salonen的结果,即此研究结果较Salonen的结论更具普遍意义.

Abstract

In this paper, noncooperative game with an infinite number of players is considered. By generalizing section theorem, we show that 1) there exists one Nash equilibrium point in large games at least; 2) there exists a mixed strategy Nash equilibrium point in continuous large game such that pure strategy
sets are nonempty compact metric space and payoff functions are continuous. The results can imply the existence theorem of Salonen in 2010.

关键词

大博弈 / 连续大博弈 / 截口定理 / Nash均衡 / 存在性.

Key words

Large games / continuous large game / Nash equilibrium points / section theorem / existence.

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杨哲 , 蒲勇健. 大博弈中Nash均衡的存在性. 系统科学与数学, 2010, 30(12): 1606-1612. https://doi.org/10.12341/jssms09432
YANG Zhe , PU Yongjian. On the Existence of Nash Equilibrium Points in Large Games. Journal of Systems Science and Mathematical Sciences, 2010, 30(12): 1606-1612 https://doi.org/10.12341/jssms09432
中图分类号： 91A10    91A40    91A44   
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