Abstract
Abstract : This paper develops in an abstract way the theory of infinite games. The kernel is replaced by an operator and the distributions by suitably chosen Banach spaces and the complete theory of the determiteness of a game is studied. Both weak and uniform upper and lower values are introduced and are related. A study of Bayes solutions are given and an analysis of the change of the value under pertubation of the operator is pursued. Some new examples of determinate games are presented to illustrate the general theory. A further discussion on non-linear games and the Wald Theory is also given. Games invariant under groups of transformations are also discussed. The usual terminology of the theory of games developed in the Annals of Mathematics Studies 24 is freely employed. A future paper on the applications of this theory to statistical decision functions is intended. (Author)
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