Incomplete Potential Game
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- 英文论文题名：Incomplete Potential Game
- 论文作者：Xiao Zhang ; Yaqi Hao ; Daizhan Cheng
- 英文论文作者：Xiao Zhang ; Yaqi Hao ; Daizhan Cheng ; School of Control Science and Engineering ; Shandong University ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences
- 年：2017
- 作者机构：School of Control Science and Engineering,Shandong University;Academy of Mathematics and Systems Science,Chinese Academy of Sciences;
- 英文论文关键词：Incomplete normal form game ; Potential game ; Feasible profile ; Semi-tensor product of matrices
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O225
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：249k
- 原文格式：D
- 会议级别：全国
摘要
The incomplete normal form game(INFG), in which there are some infeasible profiles, is considered. The structures of INFG and the dynamics of evolutionary INFG are investigated via semi-tensor product(STP) of matrices. First, the dynamics of evolutionary INFG is presented. Then a method is provided to verify whether an INFG is potential. Certain properties of potential INFGs are revealed. Finally, an algorithm is provided to search the feasible set to ensure the corresponding INFG is potential.
The incomplete normal form game(INFG), in which there are some infeasible profiles, is considered. The structures of INFG and the dynamics of evolutionary INFG are investigated via semi-tensor product(STP) of matrices. First, the dynamics of evolutionary INFG is presented. Then a method is provided to verify whether an INFG is potential. Certain properties of potential INFGs are revealed. Finally, an algorithm is provided to search the feasible set to ensure the corresponding INFG is potential.
The incomplete normal form game(INFG), in which there are some infeasible profiles, is considered. The structures of INFG and the dynamics of evolutionary INFG are investigated via semi-tensor product(STP) of matrices. First, the dynamics of evolutionary INFG is presented. Then a method is provided to verify whether an INFG is potential. Certain properties of potential INFGs are revealed. Finally, an algorithm is provided to search the feasible set to ensure the corresponding INFG is potential.
引文
[1]O.Candogan,I.Menache,A.Ozdaglar,P.A.Parrilo,Flows and decompositions of games:harmonic and potential games,Math.Operat.Research,36(3):474–503,2011.
[2]O.Candogan,A.Ozdaglar,P.A.Parrilo,Near-potential games:geometry and dynamics,ACM Trans.Econom.Comput.,1(2):Article 11,2013.
[3]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach,London:Springer,2011.
[4]D.Cheng,H.Qi,Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications,Singapore:World Scientific,2012.
[5]D.Cheng,On finite potential games,Automatica,50(7):1793–1801,2014.
[6]D.Cheng,T.Xu,H.Qi,Evolutionarily stable strategy of networked evolutionary games,IEEE TNNLS,25(7):1335–1345,2014.
[7]D.Cheng,F.He,H.Qi,T.Xu,Modeling,Analysis and control of networked evolutionary games,IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[8]D.Cheng,T.Liu,K.Zhang,et al.,On decomposed subspaces of finite games,IEEE Trans.Aut.Contr.,61(11):3651–3656,2016.
[9]P.Guo,Y.Wang,H.Li,Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method,Automatica,49(11):3384–3389,2013.
[10]S.Hart,A.Mas-Colell,Potential,value,and consistency,Econometrica,57(3):589–614,1989.
[11]T.Heikkinen,A potential game approach to distributed power control and scheduling,Computer Networks,50(13):2295–2311,2006.
[12]Y.Hino,An imporved algorithm for detecting potential games,Int.J.Game Theory,40(1):199–205,2011.
[13]C.G.Khatri,C.R.Rao,Solutions to some function equations and their applications to characterization of probability distributions,Sankhy:The Indian Journal of Statistics,Series A(1961-2002),30(2):167–180,1968.
[14]X.Liu,J.Zhu,On potential equations of finite games,Automatica,68(C):245–253,2016.
[15]J.R.Marden,G.Arslan,J.S.Shamma,Cooperative control and potential games,IEEE Trans.Sys.,Man,Cybernetcs,Part B,39(6):1393–1407,2009.
[16]D.Monderer,L.S.Shapley,Potential games Games and Economic Behavior,14(1):124–143,1996.
[17]R.W.Rosenthal,A class of games possessing pure-strategy Nash equilibria,Int.J.Game Theory,2(1):65–67,1973.
[18]G.Szabó,Evolutionary potential games on lattices,Physics Reports,Vol.624,1-60,2016.
[19]J.von Neumann and O.Morgenstern,Theory of Games and Economic Behavior,Princeton:Princeton University Press,1944.
[20]Y.Wang,D.Cheng,Stability and stabilization of a class of finite evolutionary games,J.Franklin Inst.,354(3):1603–1617,2017.
[21]N.Wiener,Cybernetics,Or Control and Communication in the Animal and the Machine,Paris:Hermann&Camb.Press,1948.
[2]O.Candogan,A.Ozdaglar,P.A.Parrilo,Near-potential games:geometry and dynamics,ACM Trans.Econom.Comput.,1(2):Article 11,2013.
[3]D.Cheng,H.Qi,Z.Li,Analysis and Control of Boolean Networks:A Semi-tensor Product Approach,London:Springer,2011.
[4]D.Cheng,H.Qi,Y.Zhao,An Introduction to Semi-tensor Product of Matrices and Its Applications,Singapore:World Scientific,2012.
[5]D.Cheng,On finite potential games,Automatica,50(7):1793–1801,2014.
[6]D.Cheng,T.Xu,H.Qi,Evolutionarily stable strategy of networked evolutionary games,IEEE TNNLS,25(7):1335–1345,2014.
[7]D.Cheng,F.He,H.Qi,T.Xu,Modeling,Analysis and control of networked evolutionary games,IEEE Trans.Aut.Contr.,60(9):2402–2415,2015.
[8]D.Cheng,T.Liu,K.Zhang,et al.,On decomposed subspaces of finite games,IEEE Trans.Aut.Contr.,61(11):3651–3656,2016.
[9]P.Guo,Y.Wang,H.Li,Algebraic formulation and strategy optimization for a class of evolutionary networked games via semi-tensor product method,Automatica,49(11):3384–3389,2013.
[10]S.Hart,A.Mas-Colell,Potential,value,and consistency,Econometrica,57(3):589–614,1989.
[11]T.Heikkinen,A potential game approach to distributed power control and scheduling,Computer Networks,50(13):2295–2311,2006.
[12]Y.Hino,An imporved algorithm for detecting potential games,Int.J.Game Theory,40(1):199–205,2011.
[13]C.G.Khatri,C.R.Rao,Solutions to some function equations and their applications to characterization of probability distributions,Sankhy:The Indian Journal of Statistics,Series A(1961-2002),30(2):167–180,1968.
[14]X.Liu,J.Zhu,On potential equations of finite games,Automatica,68(C):245–253,2016.
[15]J.R.Marden,G.Arslan,J.S.Shamma,Cooperative control and potential games,IEEE Trans.Sys.,Man,Cybernetcs,Part B,39(6):1393–1407,2009.
[16]D.Monderer,L.S.Shapley,Potential games Games and Economic Behavior,14(1):124–143,1996.
[17]R.W.Rosenthal,A class of games possessing pure-strategy Nash equilibria,Int.J.Game Theory,2(1):65–67,1973.
[18]G.Szabó,Evolutionary potential games on lattices,Physics Reports,Vol.624,1-60,2016.
[19]J.von Neumann and O.Morgenstern,Theory of Games and Economic Behavior,Princeton:Princeton University Press,1944.
[20]Y.Wang,D.Cheng,Stability and stabilization of a class of finite evolutionary games,J.Franklin Inst.,354(3):1603–1617,2017.
[21]N.Wiener,Cybernetics,Or Control and Communication in the Animal and the Machine,Paris:Hermann&Camb.Press,1948.