EXISTENCE OF NASH EQUILIBRIUM IN A COMPACT ACYCLIC STRATEGIC GAME

Kim, Won Kyu (Department of Mathematics Education Chungbuk National University) ;
Kum, Sangho (Department of Mathematics Education Chungbuk National University)

In this note, we will prove a new equilibrium existence theorem for a compact acyclic strategic game by using Begle's fixed point theorem.

Supported by : Chungbuk National University

J. G. Becker and D.S. Damianov, On the existence of symmetric mixed strategy equilibria, Econom. Letters 90 (2006), 84-87. https://doi.org/10.1016/j.econlet.2005.07.005
E. G. Begle, A fixed point theorem, Ann. Math. 51 (1950), 544-550. https://doi.org/10.2307/1969367
G. Debreu, A social equilibrium theorem, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 386-393.
W. K. Kim and S. Kum, Best proximity pairs and Nash equilibrium pairs, J. Kor. Math. Soc. 45 (2008), 1297-1310. https://doi.org/10.4134/JKMS.2008.45.5.1297
H. Lu, On the existence of pure strategy Nash equilibrium, Econom. Letters 94 (2007), 459-462. https://doi.org/10.1016/j.econlet.2006.09.006
J. Nash, non-cooperative games, Annals of Math. 54 (1951), 286-295. https://doi.org/10.2307/1969529
H. Nikaido and K. Isoda, Note on non-cooperative convex games, Pacific J. of Math. 5 (1955), 807-815. https://doi.org/10.2140/pjm.1955.5.807
S. Park, Acyclic versions of the von Neumann and Nash equilibrium theorems, J. Comp. Appl. Math. 113 (2000), 83-91. https://doi.org/10.1016/S0377-0427(99)00246-0
S. Park, Remarks on acyclic versions of generalized von Neumann and Nash equilibrium theorems, Applied Math. Lett. 15 (2002), 641-647. https://doi.org/10.1016/S0893-9659(02)80018-0