References
- Nash JF. Equilibrium points in N-person games. Proc Natl Acad Sci USA. 1950;36:48–49.
- Nash JF. Non-cooperative games. Ann Math. 1951;54:286–295.
- Tan KK, Yu J, Yuan XZ. Existence theorems of Nash equilibria for non-cooperative n-person games. Int J Game Theor. 1995;24(3):217–222.
- Yu J. Essential equilibria of n-person noncooperative games. J Math Econ. 1999;31(3):361–372.
- Yu J, Yuan XZ. The study of Pareto equilibria for multiobjective games by fixed point and Ky fan minimax inequality methods. Comp Math Appl. 1998;35(9):17–24.
- Yang H, Yu J. On essential components of the set of weakly Pareto-Nash equilibrium. Appl Math Lett. 2002;15:553–560.
- Park S. The Fan minimax inequality implies the Nash equilibrium theorem. Appl Math Lett. 2011;24:2206–2210.
- Park S. On S.-Y. Chang's inequalities and Nash equilibria. J Nonlinear Convex Anal. 2011;12(3):455–471.
- Park S. A simple proof of the sion minimax theorem. Bulletin Korean Math Soc. 2010;47:1037–1040.
- Park S. Some general fixed point theorems on topological vector spaces. Appl Set-Valued Anal Optim. 2019;1:19–28.
- Yao JC. Nash equilibria in n-person games without convexity. Appl Math Lett. 1992;5:67–69.
- Yang Z, Zhang HQ. Essential stability of cooperative equilibria for population games. Optim Lett. 2019;13(7):1573–1582.
- Pang JS, Fukushima M. Quasi-variational inequalities, generalized Nash equilibria, and multi-leader–follower games. Comput Manag Sci. 2005;2(1):21–56.
- Yu J, Wang HL. An existence theorem of equilibrium points for multi-leader–follower games. Nonlinear Anal. 2008;69:1775–1777.
- Ding XP. Equilibrium existence theorems for multi-leader–follower generalized multiobjective games in FC-spaces. J Global Optim. 2012;53(3):381–390.
- Jia WS, Xiang SW, He JH, et al. Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader-follower games. J Global Optim. 2015;61(2):397–405.
- Yang Z, Ju Y. Existence and generic stability of cooperative equilibria for multi-leader–multi-follower games. J Global Optim. 2016;65(3):563–573.
- Yang Z, Wang AQ. Existence and stability of the α-core for fuzzy games. Fuzzy Sets Syst. 2018;341:59–68.
- Yu J, Peng DT. Generic stability of Nash equilibria for noncooperative differential games. Oper Res Lett. 2020;48(2):157–162.
- Vincenzo S. Equilibrium existence in games: slight single deviation property and Ky Fan minimax inequality. J Math Econ. 2019;82:197–201.
- Renou L, Schlag KH. Minimax regret and strategic uncertainty. J Econ Theory. 2010;145:264–286.
- Yang Z, Pu YJ. Existence and stability of minimax regret equilibria. J Global Optim. 2012;54(1):17–26.
- Cuong TH, Yao JC, Yen ND. Qualitative properties of the minimum sum-of-squares clustering problem. Optimization. 2020; doi:https://doi.org/10.1080/02331934.2020.1778685.
- Gong XH. The strong minimax theorem and strong saddle points of vector-valued functions. Nonlinear Anal. 2008;68:2228–2241.
- Li XB, Li SJ, Fang ZM. A minimax theorem for vector valued functions in lexicographic order. Nonlinear Anal. 2010;73:1101–1108.
- Yang Z, Meng DW, Wang AQ. On the existence of ideal Nash equilibria in discontinuous games with infinite criteria. Operations Res Lett. 2017;45(4):362–365.
- Yang Z, Pu YJ. Generalized Knaster–Kuratowski–Mazurkiewicz theorem without convex hull. J Optim Theory Appl. 2012;154(1):17–29.
- Takashi M. On characterization of Nash equilibrium strategy in bi-matrix games with set payoffs. Set optimization and applications the state of the art. Heidelberg: Springer; 2015. p. 313–331. (Springer Proc. Math. Stat.; 151).
- Luc DT, Vargas C. A saddlepoint theorem for set-valued maps. Nonlinear Anal. 1992;18:1–7.
- Li SJ, Chen GY, Lee GM. Minimax theorems for set-valued mappings. J Optim Theory Appl. 2000;106:183–200.
- Li SJ, Chen GY, Teo KL, et al. Generalized minimax inequalities for set-valued mappings. J Math Anal Appl. 2003;281:707–723.
- Ram T. On existence of operator solutions of generalized vector quasi-variational inequalities. Commun Optim Theor. 2015;2015: Article ID 1.
- Zhang Y, Li SJ, Zhu SK. Mininax problems for set-Valued mappings. Numer Funct Anal Optim. 2012;33(2):239–253.
- Zhang Y, Li SJ. Minimax theorems for scalar set-valued mappings with nonconvex domains and applications. J Global Optim. 2013;57(4):1359–1373.
- Anh LQ, Khanh PQ. Continuity of solution maps of parametric quasiequilibrium problems. J Global Optim. 2010;46(2):247–259.
- Anh LQ, Tam TN. Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems. Top. 2016;24(1):242–258.
- Anh LQ, Hung NV. Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems. J Indust Manag Optim. 2018;14:65–79.
- Anh LQ, Hung NV. Levitin–Polyak well-posedness for strong bilevel vector equilibrium problems and applications to traffic network problems with equilibrium constraints. Positivity. 2018;22:1223–1239.
- Jahn J. Vector optimization: theory, applications, and extensions. Berlin, Germany: Springer; 2004.
- Aubin JP, Ekeland I. Applied nonlinear analysis. New York: John Wiley and Sons; 1984.
- Zhang Y, Li SJ. Generalized Ky Fan minimax inequalities for set-valued mappings. Fixed Point Theor. 2014;15:609–622.
- Gerth C, Weidner P. Nonconvex separation theorems and some applications in vector optimization. J Optim Theory Appl. 1990;67:297–320.
- Fan K. Fixed-point and minimax theorems in locally convex topological linear spaces. Proc Natl Acad Sci USA. 1952;38:121–126.
- Kakutani S. A generalization of Brouwer's fixed point theorem. Duke Math J. 1941;8:457–459.
- Tan KK, Yu J, Yuan XZ. Existence theorems for saddle points of vector-valued maps. J Optim Theory Appl. 1996;89:731–747.