Equilibria of dynamic games with many players: Existence, approximation, and market structure
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 SE 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.
© 2013 Elsevier Inc. Received 2 December 2011, Revised 29 January 2013, Accepted 27 June 2013, Available online 25 July 2013. The authors are grateful for helpful conversations with Vineet Abhishek, Lanier Benkard, Peter Glynn, Andrea Goldsmith, Ben Van Roy, and Assaf Zeevi, and seminar participants at the INFORMS Annual Meeting and the Behavioral and Quantitative Game Theory Workshop. We thank the editors of the special issue, and in particular Larry Blume, as well as an anonymous referee for helpful comments that help improved the paper. This work was supported by DARPA under the ITMANET program, and by the National Science Foundation.
Submitted - 1011.5537v5.pdf