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Contest vs. Competition in Cournot Duopoly: Schaffer's Paradox

Author

Listed:
  • Rabah Amir
  • Igor V. Evstigneev
  • Mikhail V. Zhitlukhin

Abstract

The paper compares two types of industrial organization in the Cournot duopoly: (a) the classical one, where the market players maximize profits and the outcome of the game is a Cournot-Nash equilibrium; (b) a contest in which players strive to win a fixed prize/bonus employing unbeatable strategies. Passing from (a) to (b) leads to a perfect competition with zero profits of the players (Schaffer's paradox). Transition from (b) to (a) results in a substantial decline in the production output, which also seems paradoxical, as it is commonly accepted that competition increases efficiency. We examine these phenomena in two versions of the Cournot model: with a homogeneous good and with differentiated goods.

Suggested Citation

  • Rabah Amir & Igor V. Evstigneev & Mikhail V. Zhitlukhin, 2025. "Contest vs. Competition in Cournot Duopoly: Schaffer's Paradox," Papers 2509.00960, arXiv.org.
    • Handle: RePEc:arx:papers:2509.00960
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    References listed on IDEAS

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    1. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2024. "Unbeatable strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 891-920, June.
    2. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    3. Fuhito Kojima, 2006. "Stability and instability of the unbeatable strategy in dynamic processes," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 41-53, March.
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