References
- Bertrand J. Théorie mathématique de la richesse sociale. J Savants. 1883;67:499–508.
- Hotelling H. Stability in competition. Econ J. 1929;39(153):41–57.
- Nash JF. Equilibrium points in n-person games. Proc Natl Acad Sci USA. 1950;36(1):48–49.
- Nash JF. Non-cooperative games. Ann Math. 1951;54(2):286–295.
- Debreu G. A social equilibrium existence theorem. Proc Natl Acad Sci USA. 1952;38(10):886–893.
- Glicksberg IL, Burgess D, Gochberg IC. A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc Amer Math Soc. 1952;3(1):170–174.
- Reny PJ. On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica. 1999;67(5):1029–1056.
- Morgan J, Scalzo V. Pseudocontinuous functions and existence of Nash equilibria. J Math Econ. 2007;43(2):174–183.
- Scalzo V. Equilibrium existence in games: slight single deviation property and Ky Fan minimax inequality. J Math Econ. 2019;82:197–201.
- Tian GQ, Zhou JX. Transfer continuities, generalizations of the Weierstrass and maximum theorems: a full characterization. J Math Econ. 1995;24(3):281–303.
- Wu WT, Jiang JH. Essential equilibrium points of n-person noncooperative games. Sci Sin. 1962;11:1307–1322.
- Fort MK. Essential and non essential fixed points. Amer J Math. 1950;72(2):315–322.
- Yu J. Essential equilibria of n-person noncooperative games. J Math Econ. 1999;31(3):361–372.
- Carbonell-Nicolau O. Essential equilibria in normal-form games. J Econ Theory. 2010;145(1):421–431.
- Scalzo V. Continuity properties of the Nash equilibrium correspondence in a discontinuous setting. J Math Anal Appl. 2019;473(2):1270–1279.
- Reny PJ. Further results on the existence of Nash equilibria in discontinuous games. University of Chicago, Mimeo; 2009.
- Scalzo V. Essential equilibria of discontinuous games. Econ Theory. 2013;54(1):27–44.
- Scalzo V. Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games. Econ Theory. 2016;61(3):571–586.
- Carbonell-Nicolau O. Further results on essential Nash equilibria in normal-form games. Econ Theory. 2015;59(2):277–300.
- Carbonell-Nicolau O, Wohl N. Essential equilibrium in normal-form games with perturbed actions and payoffs. J Math Econ. 2018;75:108–115.
- Shapley LS, Rigby FD. Equilibrium points in games with vector payoffs. Nav Res Logist Q. 1959;6(1):57–61.
- Corley HW. Games with vector payoffs. J Optim Theory Appl. 1985;47(4):491–498.
- Wang SY. Existence of a Pareto equilibrium. J Optim Theory Appl. 1993;79(2):373–384.
- Ding XP. Pareto equilibria for generalized constrained multiobjective games in FC -spaces without local convexity structure. Nonlinear Anal. 2009;71(11):5229–5237.
- Yang H, Yu J. Essential components of the set of weakly Pareto-Nash equilibrium points. Appl Math Lett. 2002;15(5):553–560.
- Qiu XL, Peng DT, Yu J. Berge's maximum theorem to vector-valued functions with some applications. J Nonlinear Sci Appl. 2017;10:1861–1872.
- Jia WS, Xiang SW, He JH, et al. Existence and stability of weakly Pareto-Nash equilibrium for generalized multiobjective multi-leader-follower games. J Glob Optim. 2015;61(2):1–9.
- Hung NV, Tam VM, O'Regan D, et al. A new class of generalized multiobjective games in bounded rationality with fuzzy mappings: structural ( λ,ε)-stability and ( λ,ε)-robustness to ε-equilibria. J Comput Appl Math. 2020;372:112735.
- Aliprantis CD, Border KC. Infinite dimensional analysis. Berlin: Springer; 2006.
- Fan K. A generalization of Tychonoff's fixed point theorem. Math Ann. 1961;142(3):305–310.
- Fort MK. Points of continuity of semi-continuous functions. Publ Math. 1951;2:100–102.