Equilibria of dynamic games with many players: Existence, approximation, and market structure

In this paper we study stochastic games with many players; such games are relevant for a wide range of social, economic, and engineering applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well known that MPE computation becomes intractable as the number of players increases. Further, MPE demands a perhaps implausible level of rationality on the part of players in large games. In this paper we instead consider stationary equilibrium (SE), where players optimize assuming the empirical distribution of others’ states remains constant at its long run average.We make three main contributions. First, we provide exogenous conditions over model primitives to ensure stationary equilibria exist, in a general model with possibly unbounded state spaces. Second, we show that the same conditions that ensure existence of SE also ensure that SE is a good approximation to MPE in large finite games. Finally, we consider a series of applications, including dynamic oligopoly models, supply chain competition, and consumer learning. These examples highlight that our conditions amount to a dichotomy between “decreasing” and “increasing” returns to larger states; SE approximates MPE well in the former case in which the equilibrium market structure becomes fragmented in the limit. In the latter case, SE may not approximate MPE well.