We study stochastic dynamic games with a large number of players, where players are coupled via their cost functions. A standard solution concept for stochastic games is Markov perfect equilibrium (MPE). In MPE, each player's strategy is a function of its own state as well as the state of the other players. This makes MPE computationally prohibitive as the number of players becomes large. An approximate solution concept called oblivious equilibrium (OE) was introduced in [1], where each player's decision depends only on its own state and the "long-run average" state of other players. This makes OE computationally more tractable than MPE. It was shown in [1] that, under a set of assumptions, as the number of players become large, OE closely approximates MPE. In this paper we relax those assumptions and generalize that result to cases where the cost functions are unbounded. Furthermore, we show that under these relaxed set of assumptions, the OE approximation result can be applied to large population linear quadratic Gaussian (LQG) games [2].

In this paper we study stochastic dynamic games with many players; these are a fundamental model for a wide range of economic 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. We instead consider the notion of stationary equilibrium (SE), where players optimize assuming the empirical distribution of others' states remains constant at its long run average. We make two main contributions. First, we provide a rigorous justification for using SE. In particular, we provide a parsimonious collection of exogenous conditions over model primitives that guarantee existence of SE, and ensure that an appropriate approximation property to MPE holds, in a general model with possibly unbounded state spaces. Second, we draw a significant connection between the validity of SE, and market structure: under the same conditions that imply SE exist and approximates MPE well, the market becomes fragmented in the limit of many firms. To illustrate this connection, we study in detail a series of dynamic oligopoly examples. These examples show that our conditions enforce a form of "decreasing returns to larger states"; this yields fragmented industries in the limit. By contrast, violation of these conditions suggests "increasing returns to larger states" and potential market concentration. In that sense, our work uses a fully dynamic framework to also contribute to a longstanding issue in industrial organization: understanding the determinants of market structure in different industries. * The authors are grateful for helpful conversations with

We study stochastic games with a large number of players, where players are coupled via their payoff functions. A standard solution concept for stochastic games is Markov perfect equilibrium (MPE). In MPE, each player's strategy is a function of its own state as well as the state of other players. This makes MPE computationally prohibitive as the number of players becomes large. An approximate solution concept called oblivious equilibrium (OE) was introduced by Weintraub et al., where each player's decision depends only on its own state and the "long-run average" state of other players. This makes OE computationally more tractable than MPE.It was shown that under a set of assumptions, as the number of players becomes large, OE closely approximates MPE. However, these assumptions require the computation of OE and verifying that the resulting stationary distribution satisfies a certain light-tail condition. In this paper, we derive exogenous conditions on the state dynamics and the payoff function under which the light-tail condition holds. A key condition is that the agents' payoffs are concave in their own state and actions. These exogenous conditions enable us to characterize a family of stochastic games in which OE is a good approximation for MPE.