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Mixed strategies in discriminatory divisible-good auctions

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  • Edward J. Anderson
  • Pär Holmberg
  • Andrew B. Philpott

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.
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Suggested Citation

  • Edward J. Anderson & Pär Holmberg & Andrew B. Philpott, 2013. "Mixed strategies in discriminatory divisible-good auctions," RAND Journal of Economics, RAND Corporation, vol. 44(1), pages 1-32, March.
    • Handle: RePEc:bla:randje:v:44:y:2013:i:1:p:1-32
    DOI: 1756-2171.12008
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    Cited by:

    1. Peyman Khezr & Anne Cumpston, 2022. "A review of multiunit auctions with homogeneous goods," Journal of Economic Surveys, Wiley Blackwell, vol. 36(4), pages 1225-1247, September.
    2. 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.
    3. 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.
    4. Edward Anderson & Pär Holmberg, 2023. "Multi-unit auctions with uncertain supply and single-unit demand," Working Papers EPRG2310, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    5. Holmberg, Pär & Tangerås, Thomas & Ahlqvist, Victor, 2018. "Central- versus Self-Dispatch in Electricity Markets," Working Paper Series 1257, Research Institute of Industrial Economics, revised 27 Mar 2019.
    6. Pär Holmberg, 2017. "Pro‐competitive Rationing in Multi‐unit Auctions," Economic Journal, Royal Economic Society, vol. 127(605), pages 372-395, October.
    7. Pycia, Marek & Woodward, Kyle, 2021. "Auctions of Homogeneous Goods: A Case for Pay-as-Bid," CEPR Discussion Papers 15656, C.E.P.R. Discussion Papers.
    8. Holmberg, Pär & Lazarczyk, Ewa, 2012. "Congestion Management in Electricity Networks: Nodal, Zonal and Discriminatory Pricing," Working Paper Series 915, Research Institute of Industrial Economics.
    9. Pär Holmberg & Thomas Tangerås, 2021. "Strategic Reserves versus Market-wide Capacity Mechanisms," Working Papers EPRG2109, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    10. Samuel Häfner, 2023. "Risk aversion in share auctions: Estimating import rents from TRQs in Switzerland," Quantitative Economics, Econometric Society, vol. 14(2), pages 419-470, May.
    11. 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.
    12. Benjamin Heymann & Alejandro Jofr'e, 2019. "Optimal auctions for networked markets with externalities," Papers 1907.10080, arXiv.org.
    13. Cumpston, Anne & Khezr, Peyman, 2020. "Multi-Unit Auctions: A Survey of Theoretical Literature," MPRA Paper 101336, University Library of Munich, Germany.
    14. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Working Papers EPRG 1401, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    15. Benjamin Heymann & Alejandro Jofré, 2024. "Reverse auctions with transportation and convex costs," Computational Management Science, Springer, vol. 21(1), pages 1-18, June.
    16. 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).
    17. Shiying Chen & Zhenhuan Dong & Chunming Cao & Changjun Zheng, 2022. "Strategy and design of multi‐unit auction in grouped asymmetric setting," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3435-3453, December.
    18. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.
    19. 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.
    20. Burkett, Justin & Woodward, Kyle, 2020. "Uniform price auctions with a last accepted bid pricing rule," Journal of Economic Theory, Elsevier, vol. 185(C).

    More about this item

    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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