Nonatomic Game with General Preferencees on Returns

Abstract

We study nonatomic games in which players' choices are guided by general preferences. Rather than ones over actions while also under influences of player-action profiles, we let the preferences be over returns received by individual players and let the returns be then linked to all players' actions. Our modeling choice has rendered otherwise standard analysis quite fruitful. Not only can we establish equilibrium existence results, but we can also simultaneously derive the upper hemi-continuity of equilibrium sets with respect to the return function and players' preference profile. Advances concerning pure equilibria can also be made on a setting involving a rich set of players, cruder traits, and an externality between semi-anonymity and anonymity.