Equilibria of Dynamic Games with Many Players: Existence, Approximation, and Market Structure

61 Pages Posted: 13 Apr 2011 Last revised: 19 Dec 2011

See all articles by Sachin Adlakha

Sachin Adlakha

California Institute of Technology

Ramesh Johari

Stanford University

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University; Columbia University - Columbia Business School - Decision Risk and Operations

Date Written: November 2011

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 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 Games, Market Structure, Stationary Equilibrium

Suggested Citation

Adlakha, Sachin and Johari, Ramesh and Weintraub, Gabriel Y., Equilibria of Dynamic Games with Many Players: Existence, Approximation, and Market Structure (November 2011). Available at SSRN: https://ssrn.com/abstract=1807460 or http://dx.doi.org/10.2139/ssrn.1807460

Sachin Adlakha (Contact Author)

California Institute of Technology ( email )

Pasadena, CA 91125
United States

Ramesh Johari

Stanford University ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

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