Columbia Business School
Industrial Organization/Macroeconomics/International Seminar
Dynamic Oligopoly Models For Concentrated Industries
We consider dynamic oligopoly models in the spirit of Ericson and Pakes (1995) that are not amenable to exact solution due to the curse of dimensionality. We introduce new computationally tractable models and methods to study industries with a few dominant firms and many fringe firms. This is a prevalent market structure in consumer and industrial goods. First, we discuss an extension of oblivious equilibrium (Weintraub, Benkard, Van Roy 2008) that accommodates this market structure (joint work with C.L. Benkard and P. Jeziorski). Second, we discuss an approach based on approximate dynamic programming in which the value function is approximated by a linear combination of basis functions and an approximation to an equilibrium is found by iterating an approximate best response operator (joint work with V. Farias and D. Saure).
Finally, the main part of the talk is devoted to describing a new behavioral model in which firms keep track of the detailed state of dominant firms and of few moments of the distribution that describes the states of fringe firms (joint work with B. Ifrach and V. Farias). The latter state aggregation technique, which is similar to Krusell and Smith (1998), makes the model computationally tractable. However, it introduces significant challenges, because moments may not form a Markov process even if the underlying process is Markov. Hence, standard dynamic programming results do not apply and moments do not summarize all payoff relevant information. We propose different approaches to overcome these difficulties with varying degrees of restrictions on the model primitives and strategies. Notably, we introduce a novel computational error bound to asses the accuracy of the approximation when firms' incorrectly assume that moments are Markov. This bound allows to evaluate whether a finer state aggregation is necessary, for example by adding more moments. We provide computational experiments to show that our algorithms and error bound work well in practice for an important class of models. We also show that, cumulatively, fringe firms discipline dominant firms to behave more competitively; hence, ignoring fringe firms in counterfactual analysis may lead to incorrect conclusions.
Our models and methods significantly extend the class of dynamic oligopoly models that can be studied computationally and open up the door to study novel issues in industry dynamics. In addition, we envision that our methods can help researchers in other areas of economics to find better approximations in models with heterogeneous agents and aggregate shocks, such as stochastic growth models in the spirit of Krusell and Smith (1998).