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 every pair of payoff functions of that class, the associated game in strategic form has a Nash equilibrium. A finite game form is N-solvable (for 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 done by an appropriate definition of tightness relative to the underlying structure (topology, Boolean algebra, sigma-algebra). We apply the current results along with well-known results on the determinacy of games with perfect information to infinitely repeated game forms. We prove that a repeated tight game form is light on Borel sets.