ON GAMES IN WHICH BOTH PLAYERS EITHER HAVE OR FAIL TO HAVE WINNING STRATEGIES

Abstract

The result of a true strategy applied by a (perfectly informed) player in positional games represents a sequence of consecutive choices from a given set. It is, therefore, subject to the axiom of choice or some equivalent selection principle. Our attention in this study is focused on the existence of finite sequences associated with winning strategies. It will be shown in the sequel that the use of the axiom of choice may lead to sets devoid of winning strategies, while the negation of this axiom produces winning strategies for both players. A modified axiom, the axiom of determination, is discussed which no longer admits such “paradoxes” in virtue of certain inherent restrictions.

Citation

KAAZ, M.A. (1975), "ON GAMES IN WHICH BOTH PLAYERS EITHER HAVE OR FAIL TO HAVE WINNING STRATEGIES", Kybernetes, Vol. 4 No. 4, pp. 233-237. https://doi.org/10.1108/eb005399