## Gabriel Weintraub

*Oblivious Equilibrium for Concentrated Industries*

Coauthor(s): Przemyslaw Jeziorski.

**Abstract:**

In a recent paper, Weintraub, Benkard, and Van Roy (2008) propose a method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition with many firms. In that paper, we defined a notion of equilibrium, *oblivious equilibrium* (henceforth, OE), in which each firm is assumed to make decisions based only on its own state and knowledge of the long run industry state, but where firms ignore current information about competitors' states.
The great advantage of OE is that computation of OE is independent of the number of firms in the industry, and thus they are much easier to compute than are Markov perfect equilibria (henceforth, MPE). Moreover, we showed that OE provide meaningful approximations of *long-run* Markov perfect dynamics of an industry with many firms if, alongside some technical requirements, the equilibrium distribution of firm states obeys a *light-tail condition*.

In Weintraub, Benkard, and Van Roy (2009) we showed that OE also often yields good approximations of MPE behavior for industries with characteristics of those studied by empirical researchers. However, for some industries it seems likely that oblivious strategies would be too simple to describe actual behavior. In very concentrated markets in particular, one might expect that the leading firms' strategies might depend on the state variables of the other leading
firms.

In this paper we introduce an important extension to OE designed to address such cases. We develop an extended notion of oblivious equilibrium that we call *partially oblivious equilibrium* (POE) that allows for there to be a set of "dominant firms," whose firm states are always monitored by every other firm in the market. Thus, for example, if there are two "dominant firms," then in POE each firm's strategy will be a function of its own state and also the states of both dominant firms. Such strategies allow for more rich strategic interactions than do oblivious strategies, and our hope is that POE will provide a better model of more concentrated industries.

**Source:** *Working Paper*

**Exact Citation:**

Weintraub, Gabriel, and Przemyslaw Jeziorski. "Oblivious Equilibrium for Concentrated Industries." Working Paper, Columbia Business School, February 2011.

**Date:**
2
2011