Juegos con matrices infinitas

We study the games with an infinite matrix. Then, we consder two extension of the game with finitely additive probabilities, according to the selected order of integration. It is showed, Theorem 1, that the first extension has a value and that the player 1 has, at least, an optimal finitely additive strategy, which is the limit in a definite sense of σ-additive probabilities defined on a countable field properly chosen. The same can be said of player 2, regarding the second extension. Theorem 2 and its corollary relate the values of the these two extensions to the value of the σ-additive extension and show that the latter has a value if and only if the both finitely additive extensions have the same value. In theorem 3 we find a sufficient condition so that the σ-additive extension has a value. Finally, two examples are presented.