NONATOMIC GAMES ON LOEB SPACES

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountabl e action sets, for example the unit interval, there do not exist pure- strategy Nash equilibria in such nonatomic games, In this brief announ cement, we show that there is a perfectly satisfactory existence theor y for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces . We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.