Multimarket oligopolies with restricted market access

T. Harks*, M. Klimm

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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Abstract

We study the existence of Cournot equilibria in multimarket oligopolies under the additional restriction that every firm may sell its product only to a limited number of markets simultaneously. This situation naturally arises if market entry is subject to a valid license and each firm holds a fixed number of licenses only, or, equivalently, if the firms’ short-term assets only suffice to serve up to a certain number of markets. We allow for firm-specific market reaction functions modeling heterogeneity among products. As our main result, we show the existence of a Cournot equilibrium under the following assumptions stated informally below: (i) cost functions are convex; (ii) the marginal return functions strictly decrease for strictly increased own quantities and non-decreased aggregated quantities; (iii) for every firm, the firm-specific price functions across markets are identical up to market-specific shifts. While assumptions (i) and (ii) are frequently imposed in the literature on single market oligopolies, only assumption (iii) seems limiting. We show, however, that if it is violated, there are games without a Cournot equilibrium.
Original languageEnglish
Title of host publicationAlgorithmic Game Theory
EditorsR. Lavi
PublisherSpringer
Pages182-193
ISBN (Print)978-3-662-44802-1
DOIs
Publication statusPublished - 1 Jan 2014

Publication series

SeriesLecture Notes in Computer Science
Number8768

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