Computing Markov Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model

62 Pages Posted: 24 Jan 2007 Last revised: 26 Sep 2010

See all articles by Ariel Pakes

Ariel Pakes

National Bureau of Economic Research (NBER); Harvard University - Department of Economics

Paul McGuire

Yale University

Date Written: January 1992

Abstract

This paper provides an algorithm for computing Markov Perfect Nash Equilibria (Maskin and Tirole, 1988a and b) for dynamic models that allow for heterogeneity among firms and idiosyncratic (or firm specific) sources of uncertainty. It has two purposes. To illustrate the ability of such models to reproduce important aspects of reality, and to provide a tool which can be used for both descriptive and policy analysis in a framework rich enough to capture many of the features of firm level data sets (thereby enabling it to be integrated with the empirical detail in those data sets). We illustrate by computing the policy functions, and simulating the industry structures, generated by a class of dynamic differentiated product models in which the idiosyncratic uncertainty is due to the random outcomes of each firm's research process (we also allow for an autonomous aggregate demand process). The illustration focuses on comparing the effects of different regulatory and institutional arrangements on market structure and on welfare for one particular set of parameter values. The simulation results are of independent interest and can be read without delving into the technical detail of the computational algorithm The last part of the paper begins with an explicit consideration of the computational burden of the algorithm, and then introduces approximation techniques designed to make computation easier. This section provides some analytic results which dramatically reduce the computational burden of computing equilibria for industries in which a large number of firms are typically active.

Suggested Citation

Pakes, Ariel and McGuire, Paul, Computing Markov Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model (January 1992). NBER Working Paper No. t0119. Available at SSRN: https://ssrn.com/abstract=573114

Ariel Pakes (Contact Author)

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Harvard University - Department of Economics ( email )

Littauer Center
Room 117
Cambridge, MA 02138
United States
617-495-5320 (Phone)
617-495-8570 (Fax)

Paul McGuire

Yale University

New Haven, CT 06520
United States

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