Groupe d’études et de recherche en analyse des décisions

Approximations for Markov perfect industry dynamics

Gabriel Y. Weintraub

Dynamic oligopoly models are used in industrial organization to analyze diverse dynamic phenomena such as investments in R&D, advertising, or capacity, the entry and exit of firms, learning-by-doing, and network effects. The applicability of these models has been severely limited, however, by the curse of dimensionality involved in the Markov perfect equilibrium (MPE) computation. In previous work, we introduced oblivious equilibrium (OE); a new solution concept for approximating MPE that alleviates the curse of dimensionality. In this work we introduce several important extensions to OE.

First, in order to capture short-run transitional dynamics that may result, for example, from shocks or policy changes, we develop a nonstationary version of OE. A great advantage of nonstationary OE (NOE) is that they are much easier to compute than MPE. We present an asymptotic result that provides a theoretical justification for the use of NOE as an approximation. We also present algorithms for bounding approximation error for each problem instance. We report results from computational case studies that serve to assess the accuracy of our approximation and to illustrate economic applications. Our results suggest that our method greatly increase the set of dynamic oligopoly models that can be analyzed computationally.

Second, we extend the definition of OE, originally proposed for models with only firm-specific idiosyncratic random shocks, to accommodate models with aggregate random shocks. This extension is important when analyzing the dynamic effects of industry-wide business cycles. We also discuss extensions of our methods to concentrated industries. Finally, we discuss extensions to general dynamic stochastic games.

(This is joint work with C. Lanier Benkard, Przemyslaw Jeziorski, and Benjamin Van Roy)