Connections between Finite-and Infinite-player Games : Normal-and Extended-form Analyses

We establish two links between finite-player games and their corresponding nonatomic games (NGs). In a normal-form game setting, we show that an NG’s equilibrium can generate near equilibrium payoffs for large finite games whose player types are sampled from the NG’s signature distribution. In an extended-form game setting involving individual player states that bridge players’ past actions with their future gains, we show that large finite games can use an equilibrium of the NG counterpart to reap close to best payoffs. The action plan recommended by the NG equilibrium is prominent in that it is blind to the current player’s observation of its immediate surrounding. These links especially the latter one have potential to help simplify the analysis of competitive situations with many players.