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Mixed Strategies in Discriminatory Divisible-good Auctions


  • Anderson, Edward J.

    (Faculty of Economics and Business)

  • Holmberg, Pär

    () (Research Institute of Industrial Economics (IFN))

  • Philpott, Andrew B.

    (Department of Engineering Science)


Author: Edward J. Anderson, Pär Holmberg and Andrew B. Philpott Keywords: Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets Pages: 71 Published: November 24, 2009 JEL-codes: D43; D44; C72 Download Wp814.pdf (756 kB) Abstract Using the concept of market-distribution functions, we derive general optimality conditions for discriminatory divisible-good auctions, which are also applicable to Bertrand games and non-linear pricing. We introduce the concept of offer distribution function to analyze randomized offer curves, and characterize mixed-strategy Nash equilibria for pay-as-bid auctions where demand is uncertain and costs are common knowledge; a setting for which pure-strategy supply function equilibria typically do not exist. We generalize previous results on mixtures over horizontal offers as in Bertrand-Edgeworth games, but more importantly we characterize novel mixtures over partly increasing supply functions.

Suggested Citation

  • Anderson, Edward J. & Holmberg, Pär & Philpott, Andrew B., 2009. "Mixed Strategies in Discriminatory Divisible-good Auctions," Working Paper Series 814, Research Institute of Industrial Economics.
  • Handle: RePEc:hhs:iuiwop:0814

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    Cited by:

    1. Holmberg, Pär & Philpott, Andrew, 2012. "Supply Function Equilibria in Networks with Transport Constraints," Working Paper Series 945, Research Institute of Industrial Economics, revised 10 Aug 2015.
    2. Pär Holmberg, 2014. "Pro-competitive rationing in multi-unit auctions," Cambridge Working Papers in Economics 1435, Faculty of Economics, University of Cambridge.
    3. Holmberg, Pär & Lazarczyk, Ewa, 2012. "Congestion Management in Electricity Networks: Nodal, Zonal and Discriminatory Pricing," Working Paper Series 915, Research Institute of Industrial Economics.
    4. Pär Holmberg and Ewa Lazarczyk, 2015. "Comparison of congestion management techniques: Nodal, zonal and discriminatory pricing," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    5. 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.
    6. Benjamin Heymann & Alejandro Jofré, 2016. "Mechanism design and allocation algorithms for network markets with piece-wise linear costs and externalities," Working Papers hal-01416411, HAL.
    7. Bunn, Derek & Koc, Veli & Sapio, Alessandro, 2015. "Resource externalities and the persistence of heterogeneous pricing behavior in an energy commodity market," Energy Economics, Elsevier, vol. 48(C), pages 265-275.
    8. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Cambridge Working Papers in Economics 1421, Faculty of Economics, University of Cambridge.

    More about this item


    Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets;

    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
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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