Multi-Market Cournot Equilibria with Heterogeneous Resource-Constrained Firms

Abstract

We study Cournot competition among firms in a multi-market framework where each of the firms face different budget / capacity constraints. We assume independent linear inverse demand functions for each market, and completely characterize the resulting unique equilibrium. Specifically, we introduce the notions of augmented and cutoff budgets for firms and markets, respectively. We show, for example, that firm i operates in market j if and only if firm i’s augmented budget is greater than market j’s cutoff budget. We also study the properties of the equilibrium as a function of the number of firms N while keeping the aggregate budget fixed. In a numerical study, we show that increasing N increases the total output across all markets although this monotonicity can fail to hold at the individual market level. Similarly, we show that that while the firms’ cumulative payoff decreases in N, the consumer surplus and social surplus increase in N.

Keywords: Cournot competition, non-cooperative games, heterogeneous products, heterogeneous firms, capacity constraints