The nonatomic supermodular game

We introduce the nonatomic supermodular game, where no playerʼs action has any discernible impact on other playersʼ payoffs and yet strategic complementarities prevail among all playersʼ types and actions. For both semi-anonymous and anonymous games, we show that monotone equilibria form nonempty complete lattices and among these equilibria, the largest and smallest members vary in monotone fashions with respect to certain game-changing parameters. Results here complement existing nonatomic-game works, which focused more on pure equilibria of anonymous games where opponentsʼ types are not influential. They are also applicable to price competition involving diverse cost/quality parameters, as well as a slew of other situations.