Markov Perfect Industry Dynamics With Many Firms

Abstract

We propose an approximation method for analyzing Ericson and Pakes (1995)-style dynamic models of imperfect competition. We develop a simple algorithm for computing an ``oblivious equilibrium,'' in which each firm is assumed to make decisions based only on its own state and knowledge of the long run average industry state, but where firms ignore current information about competitors' states. We prove that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain ``light-tail'' condition, then oblivious equilibria closely approximate Markov perfect equilibria. We develop bounds that can be computed to assess the accuracy of the approximation for any given applied problem. Through computational experiments, we find that the method often generates useful approximations for industries with hundreds of firms and in some cases even tens of firms.

Equilibria of dynamic games with many players: Existence, approximation, and market structure

“…An important condition that is required for this approximation result to hold is that the distribution of players' states in the SE under consideration must possess a light-tail, as originally observed in Weintraub et al (2008) for a sequence of finite games, and in Weintraub et al (2011) for a limiting infinite model like the one studied in this paper. In a light-tailed equilibrium, no single agent is "dominant;" without such a condition it is not possible for agents' to rationally ignore the state fluctuations of their dominant competitors.…”

“…Crucially, the light-tail assumption as used in Weintraub et al (2008) and Weintraub et al (2011) is an endogenous condition on the equilibrium outcome. A central contribution of this work is to develop exogenous conditions over model primitives that ensure the existence of light-tailed SE.…”

“…We call such players oblivious, and refer to their strategies as oblivious strategies. (This terminology is due to Weintraub et al 2008.) Formally, we let M O denote the set of (stationary, nonrandomized) oblivious strategies, defined as follows.…”

A nonatomic‐game model for timing clearance sales under competition

“…To further cope with situations involving nonignorable market shares of leading firms, Weintraub et al [26] proposed the concept of oblivious equilibrium. In that approach, firms are only aware of the long-run average state of the industry instead of the latter's exact present state.…”

“…By iteratively checking on initial conditions, we can match the problem (12) about the environment f = (f k n (t)|k ∈ {0, 1}, n = 1, 2, ..., N , t ∈ [0, T ]) of a particular seller type with the problem described by (26) …”