Estimation of quantity games in the presence of indivisibilities and heterogeneous firms

摘要

This paper presents a theoretical framework that allows estimation of game theoretic models of quantity competition, including a non-trivial class of differentiated product quantity games. The simplest examples of quantity games are entry games, wherethe strategy each firm i makes is discrete, s_i S_i = (0, 1) (do not enter/enter). I consider a general class of games where strategy sets are "chains", which includes the situation where they are a finite set of integers, S_i = {0,1,..., M}. In addition, I assume that profits of each firm can be written as a function of the firm's own strategy s, and a possibly parametric index of market output, Q(s_i,s_(-i)), so that pi_i(s_i,s_(_i); 0) = PSI_i(s_i, Q(s_i,s_(-i); 0_1); 0_2) where 0 = (theta_1,theta_2). The main theoretical result in the paper establishes easily verifiable conditions under which the index of market output is uniquely determined within the set of Nash equilibria of the game. The model's parameters may then be estimated by comparing the predicted index of market output in a cross section of markets. The paper provides both a generalization and an extension of the theoretical results developed by Bresnahan and Reiss (1991. Empirical models of discrete games. Journal of Econometrics 48,57-82.) and Berry (1992. Estimation of a model of entry in the airline industry.