Analysis of Markovian Competitive Situations using Nonatomic Games—the Shock-driven Case

We show that equilibria derived for certain multi-period nonatomic games (NGs) can be used by their large finite counterparts to achieve near-equilibrium performances. In these games, the evolution of a player’s state is influenced by his own action as well as other players’ states and actions. Also, both random state transitions and players’ random actions are driven by independently generated shocks. Therefore, we consider NG equilibria in the form of maps from state-shock pairs to actions. Their suitability in large finite games constitute our main transient results. These in turn form the basis for a link between NGs’ stationary equilibria (SEs) and stationary versions of large finite games. Our results can be applied to situations like dynamic price competition.