Theory and computation
In part with Nan Yang, we have developed new theoretical results and fast computational methods for canonical dynamic oligopoly models.
This paper extends the static analysis of oligopoly structure into an infinite-horizon setting with sunk costs and demand uncertainty. The observation that exit rates decline with firm age motivates the assumption of last-in first-out dynamics: An entrant expects to produce no longer than any incumbent. This selects an essentially unique Markov-perfect equilibrium. With mild restrictions on the demand shocks, sequences of thresholds describe firms' equilibrium entry and survival decisions. Bresnahan and Reiss' (1993) empirical analysis of oligopolists' entry and exit assumes that such thresholds govern the evolution of the number of competitors. Our analysis provides an infinite-horizon game-theoretic foundation for that structure.
- We maintain a MATLAB package that implements this paper's procedures and replicates its computations, with online documentation.
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 the generalized method of moments.