SOLVABILITY OF 2-PLAYER GAME FORMS WITH INFINITE SETS OF STRATEGIES

A game form is N-solvable for a class of payoff functions, if for ever y pair of payoff functions of that class, the associated game in strat egic Form has a Nash equilibrium. A finite game farm is N-solvable (fo r the universal class of preferences) if and only if it is tight-that is if its alpha-effectivity function and its beta-effectivity function are equal. We extend this result to various models of two-player game forms with infinite sets of strategies and/or alternatives. This is d one by an appropriate definition of tightness relative to the underlyi ng structure (topology, Boolean algebra, sigma-algebra). We apply the current results along with well-known results on the determinacy of ga mes with perfect information to infinitely repeated game forms. We pro ve that a repeated tight game form is light on Borel sets.