非合作博弈中扩张Nash均衡点的存在性
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摘要
以不动点定理为主要研究工具,考虑非货币化非合作博弈中扩张Nash均衡点的存在性问题.首先引入一个不连续集值算子的不动点定理,然后将该不动点定理运用于非货币化非合作博弈,获得了一个扩张Nash均衡点的存在性定理.由于该博弈模型中局中人的支付函数是不连续的,且支付函数值是向量值,因此所得的扩张Nash均衡点的存在性定理更具有普遍性和广泛的应用性.
In this paper we consider extended Nash equilibriums of the nonmonetized noncooperative game.We first introduce a fixed point theorem of discontinuous multivalued operators and then use it to establish an existence result of the extended Nash equilibriums.As each player's payoff function is discontinuous and the outcome space is poset,the existence theorem of the extended Nash equilibriums is more universal and practical.
In this paper we consider extended Nash equilibriums of the nonmonetized noncooperative game.We first introduce a fixed point theorem of discontinuous multivalued operators and then use it to establish an existence result of the extended Nash equilibriums.As each player's payoff function is discontinuous and the outcome space is poset,the existence theorem of the extended Nash equilibriums is more universal and practical.
引文
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[2]MCLENNAN A,MONTEIRO P K,TOURKY R.Games with discontinuous payoffs:a strengthening of Reny's existence theorem[J].Econometrica,2011,79(5):1643-1664.
[3]LI J L.Several extensions of the Abian-Brown Fixed Point Theorem and their applications to extended and generalized Nash equilibria on chain-complete posets[J].Journal of Mathematical Analysis and Applications,2014,409(2):1084-1092.
[4]LI J L,Park S.Generalized Nash equilibria of nonmonetized noncooperative games on lattices[J].British Journal of Economics,Management&Trade,2014,4(1):97-110.
[5]XIE L S,LI J L,WEN C F.Applications of fixed point theory to extended Nash equilibriums of nonmonetized noncooperative games on posets[J].Fixed Point Theory and Applications,2013,2013(2):746-746.
[6]HONG S H,QIU Z Y.Fixed points of discontinuous multivalued operators in ordered spaces with applications[J].Fixed Point Theory and Applications,2010,11(2):395-400.
[7]时宝,王兴平,盖明久,等.泛函分析引论及其应用[M].北京:国防工业出版社,2006:123-127.
[8]DINESH N,JOSHI A K,LEE I,et al.A Default Temporal Logic for Regulatory Conformance Checking[J].A Default Temporal Logic for Regulatory Conformance Checking,2008.
[9]ZHAO C X,HONG S H,LI C H.Existence of extended Nash equilibriums of nonmonetized noncooperative games[J].Fixed Point Theory and Applications,2015,2015(1):65-73.