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- Title
Technical Note—Multimarket Cournot Equilibria with Heterogeneous Resource-Constrained Firms.
- Authors
Caldentey, René; Haugh, Martin B.
- Abstract
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. We study Cournot competition among firms in a multimarket 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, although the firms' cumulative payoff decreases in N, the consumer surplus and social surplus increase in N. Funding: R. Caldentey thanks the University of Chicago Booth School of Business for financial support.
- Subjects
UNIVERSITY of Chicago. Booth School of Business; NASH equilibrium; BUDGET; BUSINESS schools; DEMAND function; CONSUMERS' surplus; BUDGET surpluses
- Publication
Operations Research, 2024, Vol 72, Issue 3, p940
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.2022.0664