A generalization of an oddness-theorem for bimatrix games
Tóm tắt
It is a well-known result of Lemke and Howson that the number of Nash-equilibria of a bimatrix game is odd in a nondegenerate case. In this paper a generalized version of this theorem will be proved. It will be shown that in case of finiteness of the number of Nash-equilibria the number of nondegenerate Nash-equilibria is always odd. Consequences of this fact are nondegeneracy for unique Nash-equilibria and some results of Jansen.
Tài liệu tham khảo
Aubin JP (1979) Mathematical methods of game and economic theory. In: Studies in Mathematics and its Applications, vol 7. North Holland, Amsterdam New York Oxford
Bastian M (1976) Lineare Komplementaritätsprobleme im Operations Research und in der Wirtschaftstheorie. In: Mathematical Systems in Economics 25. Verlag Anton Hain, Meisenheim am Glan
Mangoldt H v (1974) Einführung in die Höhere Mathematik, Band 2, 14. Aufl. S. Hirzel, Stuttgart
Lemke CE, Howson JT jr (1964) Equilibrium points of bimatrix games. SIAM J Appl Math 12:413–423
Lüthi HJ (1976) Komplementaritäts- und Fixpunktalgorithmen in der mathematischen Programmierung, Spieltheorie und Ökonomie. In: Lecture Notes in Economics and Mathematical Systems, vol 129. Springer, Berlin Heidelberg New York
Jansen MJM (1981) Regularity and stability of equilibrium points of bimatrix games. Math Oper Res 6:530–550