Jaap Abbring (Tilburg University)

“Simple Markov-Perfect Industry Dynamics”

Abstract

This paper develops a tractable model for the computational and empirical analysis of infinite-horizon oligopoly dynamics. It features aggregate demand uncertainty, sunk entry costs, stochastic idiosyncratic technological progress, and irreversible exit. We develop an algorithm for computing a symmetric Markov-perfect equilibrium quickly by finding the fixed points to a finite sequence of low-dimensional contraction mappings. If at most two heterogenous firms serve the industry, the result is the unique “natural” equilibrium in which a high profitability firm never exits leaving behind a low profitability competitor. With more than two firms, the algorithm always finds a natural equilibrium. We present a simple rule for checking ex post whether the calculated equilibrium is unique, and we illustrate the model’s application by assessing the robustness of Fershtman and Pakes’ (2000) finding that collusive pricing can increase consumer surplus by stimulating product development. The hundreds of equilibrium calculations this requires take only a few minutes on an off-the-shelf laptop computer. We also present a feasible algorithm for the model’s estimation using nonlinear least squares.