References

ON SOME APPLICATIONS OF KAKUTANI€™S FIXED POINT THEOREM IN GAME THEORY


[1] K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy, Econometrica: Journal of the Econometric Society 22(3) (1954), 265-290.
DOI: https://doi.org/10.2307/1907353

[2] K. C. Border, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, 1985.
DOI: https://doi.org/10.1017/CBO9780511625756

[3] L. E. J. Brouwer, Ãœber abbildung von mannigfaltigkeiten, Mathematische Annalen 71(1) (1911), 97-115.
DOI: https://doi.org/10.1007/BF01456931

[4] C. Buxton, Brouwer Fixed-Point Theorem, 2016.

[5] S. CobzaÅŸ, Fixed point theorems in locally convex spaces: The Schauder mapping method, Fixed Point Theory and Applications 1 (2006); Article 57950.
DOI: https://doi.org/10.1155/FPTA/2006/57950

[6] S. Eilenberg and D. Montgomery, Fixed point theorems for multi-valued transformations, American Journal of Mathematics 68(2) (1946), 214-222.
DOI: https://doi.org/10.2307/2371832

[7] K. Fan, Fixed-point and minimax theorems in locally convex topological linear spaces, Proceedings of the National Academy of Sciences of the United States of America 38(2) (1952), 121-126.
DOI: https://doi.org/10.1073/pnas.38.2.121

[8] I. L. Glicksberg, A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points, Proceedings of the American Mathematical Society 3(1) (1952), 170-174.
DOI: https://doi.org/10.2307/2032478

[9] S. Kakutani, A generalization of Brouwer’s fixed point theorem, Duke Mathematical Journal 8(3) (1941), 457-459.
DOI: https://doi.org/10.1215/S0012-7094-41-00838-4

[10] R. Kannan, Some results on fixed points, Bulletin Calcutta Mathematical Society 60 (1968), 71-76.

[11] Z. Lin, Essential components of the set of weakly Pareto-Nash equilibrium points for multiobjective generalized games in two different topological spaces, Journal of Optimization Theory and Applications 124(2) (2005), 387-405.
DOI: https://doi.org/10.1007/s10957-004-0942-0

[12] J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences 36(1) (1950), 48-49.
DOI: https://doi.org/10.1073/pnas.36.1.48

[13] J. F. Nash, Non-cooperative Games, Ph.D. Thesis, Mathematics Department, Princeton University, 1950b.

[14] J. Nash, Non-cooperative games, Annals of Mathematics 54(2) (1951), 286-295.
DOI: https://doi.org/10.2307/1969529

[15] J. Von Neumann, Zur theorie der gesellschaftsspiele, Mathematische Annalen 100(1) (1928), 295-320.
DOI: https://doi.org/10.1007/BF01448847

[16] G. Owen, Teoria Jocurilor, Bucureşti, Romania: Editura Tehnică, 1974.

[17] A. Rubinstein, Experience from a course in game theory: Pre- and postclass problem sets as a didactic device, Games and Economic Behavior 28(1) (1999), 155-170.
DOI: https://doi.org/10.1006/game.1999.0723

[18] H. Scarf, The approximation of fixed points of a continuous mapping, SIAM Journal on Applied Mathematics 15(5) (1967), 1328-1343.
DOI: https://doi.org/10.1137/0115116

[19] G. van der Laan, A. J. J. Talman and Z. Yang, Combinatorial integer labeling theorems on finite sets with applications, Journal of Optimization Theory and Applications 144(2) (2010), 391-407.
DOI: https://doi.org/10.1007/s10957-009-9603-7

[20] R. V. Vohra, Advanced Mathematical Economics, Routledge, 2004.
DOI: https://doi.org/10.4324/9780203799956

[21] J. Von Neumann, Uber ein okonomisches gleichungssystem und eine verallgemeinerung des brouwerschen fixpunktsatzes, In Ergebnisse eines Mathematischen Kolloquiums 8 (1937), 73-83.

[22] J. Von Neumann, O. Morgenstern and H. W. Kuhn, Theory of Games and Economic Behavior (Commemorative Edition), Princeton University Press, 2007.

[23] H. Yang and J. Yu, Essential components of the set of weakly Pareto-Nash equilibrium points, Applied Mathematics Letters 15(5) (2002), 553-560.
DOI: https://doi.org/10.1016/S0893-9659(02)80006-4

[24] J. Yu and H. Yang, The essential components of the set of equilibrium points for set-valued maps, Journal of Mathematical Analysis and Applications 300(2) (2004), 334-342.
DOI: https://doi.org/10.1016/j.jmaa.2004.06.042