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

Sachin Adlakha, Ramesh Johari and Gabriel Y. Weintraub

Journal of Economic Theory, 2015, vol. 156, issue C, 269-316

Abstract: 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.

Keywords: Stochastic dynamic games; Approximation; Stationary equilibrium; Industrial organization (search for similar items in EconPapers)
JEL-codes: C62 C73 L11 L13 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (34)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:156:y:2015:i:c:p:269-316

DOI: 10.1016/j.jet.2013.07.002

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