Acta mathematica scientia, Series B >
EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES
Received date: 2013-12-03
Revised date: 2014-05-05
Online published: 2015-03-20
Supported by
Project was supported by the Scientific Research Fun of Sichuan Normal University (11ZDL01) and the Sichuan Province Leading Academic Discipline Project (SZD0406).
In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.
Xieping DING . EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES[J]. Acta mathematica scientia, Series B, 2015 , 35(2) : 339 -347 . DOI: 10.1016/S0252-9602(15)60005-4
[1] Nash J F. Equilibrium points in n-person games. Proc Natl Acad Sci USA, 1950, 36: 48-49
[2] Nash J F. Non-cooperative games. Ann Math, 1951, 54: 286-295
[3] Bai X, Shahidehpour S M, Ramesh V C, Yu E. Transmission analysis by Nash game method. IEEE Trans Power Syst, 1997, 12: 1046-1052
[4] Song H, Liu C C, Lawarre J, Bellevue W A. Nash equilibrium didding strategies in a bilateral electricity market. IEEE Trans Power Syst, 2002, 17: 73-79
[5] Chinchuluun A, Paradalos P M, Migdalas A, Pitsoulis L. Pareto Optimality, Game Theory and Equilibria. Springer, Optimization and its application, 2008, 17
[6] Chinchuluun A, Paradalos P M, Huang H X. Multilevel (hierarchical) optimization, complexity issues, optimality conditions, algorithms//Cao D, Sherali H. Advances in Applied Mathematics and Global Opti- mization. Berlin: Springer, 2009: 197-221
[7] Migdalas A, Paradalos P M, Varbrand P. Multilevel Optimization: Algorithm and Applications. Dordrecht: Kluwer Acad Publ, 1997
[8] Basar T, Srikant, R. A stackelberg network game with a large number of followers. J Optim Theory Appl, 2002, 115(3): 479-490
[9] Pang J S, Fukushima M. Quasi-variational inequalities, generalized Nash equilibria and multi-follower game. Computational Management Science, 2005, 1: 21-56
[10] Outrata J V. A note on a class of equilibrium problems with equilibrium constraints. Kybernetika, 2004, 40: 585-594
[11] Hu M, Fukushima M. Variational inequality formulation of a class of multi-leader-follower games. J Opyim Theory Appl, 2011, 151: 455-473
[12] Yu J, Wang H L. An existence theorem of equilibrium points for multi-leader-follower games. Nonlinear Anal, 2008, 69(5/6): 1775-1777
[13] Ding X P. Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces. J Global Optim, 2012, 53(3): 381-390
[14] Wang S Y, Li Z. Pareto equilibria in multicriteria metagames. Top, 1995, 3(2): 247-263
[15] Ding X P. Parteo equilibria of multicriteria games without compactness, continuity and concavity. Appl Math Mech, 1996, 17(9): 847-854
[16] Yuan X Z, Tarafdar E. Non-compact Pareto equilibria for multiobjective games. J Math Anal Appl, 1996, 204: 156-163
[17] Yu J, Yuan X Z. The study of Pareto equilibria for multiobjective games by fixed point and Ky Fan minimax inequality methods. Comput Math Appl, 1998, 35(9): 17-24
[18] Ding X P. Existence of Pareto equilibria for constrained multiobjective games in H-spaces. Comput Math Appl, 2000, 39(9): 125-134
[19] Ding X P, Park J Y, Jung I H. Pareto equilibria for constrained multiobjective games in locally L-convex spaces. Comput Math Appl, 2003, 46(10/11): 1589-1599
[20] Yu H. Weak Pareto equilibria for multiobjective constrained games. Appl Math Lett, 2003, 16(5): 773-776
[21] Lin Z, Yu J. The existence of solutions for the system of generalized vector quasi-equilibrium problems. Appl Math Lett, 2005 18(4): 415-422
[22] Ding X P, Yao J C. Maximal element theorems with applications to generalized games and a system of generalized vector quasi-equilibrium problems in G-convex spces. J Optim Theory Appl, 2005, 126(2): 571-588
[23] Ding X P. Weak Pareto equilibria for generalized constrained multiobjective games in locally FC-uniform spaces. Nonlinear Anal, 2006, 65(3): 538-545
[24] Ding X P. Nonempty intersection theorems and generalized multiobjective games in product FC-spaces. J Global Optim, 2007, 37(1): 63-73
[25] Ding X P, Lee C S, Yao J C. Generalized constrained multiobjective games in locally FC-uniform spaces. Appl Math Mech, 2008, 29(3): 301-309
[26] Ding X P. Pareto equilibria for generalized constrained multiobjective games in FC-spaces without local convexity structure. Nonlinear Anal, 2009, 71: 5229-5237
[27] Ding X P. Maximal element theorems in product FC-spaces and generalized games. J Math Anal Appl, 2005, 305: 29-42
[28] Ding X P. The generalized game and system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces. Nonlinear Anal, 2008, 68(4): 1028-1036
[29] Aubin J P, Cellina A. Differential Inclusions. Berlin, Heidberg, New York: Springer, 1994
[30] Aliprantis C D, Border K C. Infinite Dimensional Analysis. New York: Springer-Verlag, 1994
[31] Aubin J P. Mathematical Methods of Game and Economic Theory. New York: North-Holland Publishing Company, 1979
[32] Ding X P. Collectively fixed point theorem in product locally FC-uniform spaces and applications. J Sichuan Normal Univ, 2008, 31(1): 1-5
/
| 〈 |
|
〉 |