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Competitive versus collusive Nash equilibria in affine supply function competition with quadratic costs

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  • Alexander Zimper

    (Zimper)

Abstract

This paper studies strategic games of supply function competition under the assumptions that (i) the sellers can choose arbitrarily increasing or decreasing affine supply functions, (ii) they have an identical quadratic cost function, and (iii) the deterministic affine demand function is strictly decreasing. Based on the description of all symmetric Nash equilibria---and the ensuing characterization of an extreme-point price function as a Moebius transformation---, I derive an `almost anything goes' result which determines the set of all market-clearing prices that can be generated by the symmetric Nash equilibria. I discuss in detail competitive Nash equilibria---which generate the minimal equilibrium price at zero profits for the sellers---and collusive Nash equilibria---which generate the monopoly price. Both extreme types of Nash equilibria uniquely exist for non-zero quadratic costs and consist of strictly decreasing supply functions.

Suggested Citation

  • Alexander Zimper, 2026. "Competitive versus collusive Nash equilibria in affine supply function competition with quadratic costs," ERSA Working Paper Series 373, Economic Research Southern Africa.
    • Handle: RePEc:rza:ersawp:373
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    References listed on IDEAS

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    1. Susan Athey & Kyle Bagwell & Chris Sanchirico, 2004. "Collusion and Price Rigidity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 317-349.
    2. Holmberg, Pär & Newbery, David, 2010. "The supply function equilibrium and its policy implications for wholesale electricity auctions," Utilities Policy, Elsevier, vol. 18(4), pages 209-226, December.
    3. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    4. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    5. Bolle, Friedel, 1992. "Supply function equilibria and the danger of tacit collusion : The case of spot markets for electricity," Energy Economics, Elsevier, vol. 14(2), pages 94-102, April.
    6. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
    7. Turnbull, Stephen J., 1983. "Choosing duopoly solutions by consistent conjectures and by uncertainty," Economics Letters, Elsevier, vol. 13(2-3), pages 253-258.
    8. Aitor Ciarreta & Carlos Gutiérrez-Hita, 2012. "Collusive behaviour under cost asymmetries when firms compete in supply functions," Journal of Economics, Springer, vol. 106(3), pages 195-219, July.
    9. Flavio M. Menezes & John Quiggin, 2025. "Ex ante and ex post equilibrium supply curves," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 79-98, April.
    10. Green, Richard J & Newbery, David M, 1992. "Competition in the British Electricity Spot Market," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 929-953, October.
    11. Menezes, Flavio M. & Quiggin, John, 2012. "More competitors or more competition? Market concentration and the intensity of competition," Economics Letters, Elsevier, vol. 117(3), pages 712-714.
    12. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    13. Ihsan Celen & Ismail Saglam, 2022. "Collusion in supply functions under technology licensing," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(5), pages 1362-1378, July.
    14. Marc Escrihuela‐Villar & Carlos Gutiérrez‐Hita & José Vicente‐Pérez, 2020. "Supply function competition in a mixed electric power market," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(4), pages 1151-1175, August.
    15. Back, Kerry & Zender, Jaime F, 1993. "Auctions of Divisible Goods: On the Rationale for the Treasury Experiment," The Review of Financial Studies, Society for Financial Studies, vol. 6(4), pages 733-764.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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