Thursday, May 30, 2013
Posted by D. Daniel Sokol
Vivek Farias (MIT), Bar Ifrach (Columbia Business School) and Gabriel Weintraub (Columbia University) provide A Framework for Dynamic Oligopoly in Concentrated Industries.
ABSTRACT: We consider dynamic oligopoly models in the spirit of Ericson and Pakes (1995). We introduce a new computationally tractable model for industries with a few dominant firms and many fringe firms. This is a prevalent market structure in consumer and industrial goods. In our model, firms keep track of the detailed state of dominant firms and of few moments of the distribution that describes the states of fringe firms. Based on this idea we introduce a new equilibrium concept that we call moment-based Markov equilibrium (MME). MME is behaviorally appealing and computationally tractable. However, MME can suffer from an important pitfall. Because moments may not summarize all payoff relevant information, MME strategies may not be optimal. We propose different approaches to overcome this difficulty with varying degrees of restrictions on the model primitives and strategies. Our first approach introduces models for which moments! summarize all payoff relevant history and therefore for which MME strategies are optimal. The second approach restrict fringe firm strategies so that again moments become sufficient statistics. The third approach does not impose such restrictions, but introduces a computational error bound to asses the degree of sub-optimality of MME strategies. 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 important classes of models. We also show that, cumulatively, fringe firms discipline dominant firms to behave more competitively, and that ignoring fringe firms in counterfactual analysis may lead to incorrect conclusions. Our model significantly extends the class of dynamic oligopoly models that can be studied computationally. In addition, our methods can also be used to improve approximations in other contexts s! uch as dynamic industry models with an infinite number of heterogeneou s firms and an aggregate shock; stochastic growth models in the spirit of Krusell and Smith (1998); and dynamic models with forward-looking consumers.