Nonatomic Game with General Preferencees on Returns

Abstract

We study non-atomic games in which players' choices are guided by general preferences. Rather than ones over actions while under direct influences of player-action profiles, we let the preferences be over returns received by individual players while the returns are linked to all players' actions. In the more general semi-anonymous case, a player's return depends on his own action as well as the joint player-action distribution formed by other players. In the more special anonymous setting, others influence the current player only through the action distribution they form. 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.