In the setting of non-cooperative game theory strategic negligibility of individual agents or diffuseness of information has been modelled as a non-atomic measure space typically the unit interval endowed with Lebesgue measure However recent work has shown that with uncountable action sets as for example the unit interval there do not exist pure-strategy Nash equilibria in such non-atomic games In this brief announcement we show that there is a perfectly satisfactory existence theory for non-atomic games provided this non-atomicity 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
