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<p>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>i.e.</i>, 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月2日

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  • Iwan Bos,
  • Dries Vermeulen,
  • Niloufar Yousefimanesh

摘要

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.