Equilibrium existence in price-quantity games: a sunk cost paradox

Iwan Bos, Dries Vermeulen and Niloufar Yousefimanesh
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Dries Vermeulen: Maastricht University
Niloufar Yousefimanesh: Maastricht University

International Journal of Game Theory, 2025, vol. 54, issue 2, No 6, 30 pages

Abstract: Abstract Nonexistence of a pure-strategy Nash equilibrium is a notorious problem in price-quantity games. What drives this problem is the presence of spillover demand, i.e., demand coming from competitors’ unserved customers. We argue that such demand spillovers may stem from a strong implicit assumption that costs associated with obtaining a product are sunk and do not affect consumers’ future payoffs. We relax this assumption by considering a more general class of cost functions. This is shown to admit a pure-strategy equilibrium that coincides with the Bertrand price equilibrium.

Keywords: Price-quantity competition; Spillover demand; Sunk cost (search for similar items in EconPapers)
JEL-codes: C72 D43 L13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00182-025-00955-1

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