Technical Note: Multimarket Cournot Equilibria with Heterogeneous Resource-Constrained Firms

Charactering Cournot equilibria in settings with asymmetric firms is a challenging problem. In their technical note “Multimarket Cournot Equilibria with Heterogeneous Resource-Constrained Firms,” R. Caldentey and M. Haugh consider competition in a multimarket setting where firms are subject to varying budget or capacity constraints. They explicitly characterize the unique equilibrium in this environment by introducing the concepts of augmented and cutoff budgets for firms and markets. In particular, they show that a firm operates in a particular market if only if its augmented budget surpasses the market’s cutoff budget. They also investigate how the equilibrium properties change as the number of firms N varies while maintaining a fixed aggregate budget. They show via a numerical study that increasing N leads to a higher total output across all markets but that this monotonicity need not hold individual at the level of an individual market level. They also show that, although the firms’ cumulative payoff decreases in N, the consumer surplus and social surplus increase in N.