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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. Pär Holmberg, 2017. "Pro‐competitive Rationing in Multi‐unit Auctions," Economic Journal, Royal Economic Society, vol. 127(605), pages 372-395, October.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Pär Holmberg & Andy Philpott, 2014. "Supply function equilibria in transportation networks," Cambridge Working Papers in Economics 1421, Faculty of Economics, University of Cambridge.
    9. 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.
    10. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.
    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. Holmberg, Pär & Lazarczyk, Ewa, 2012. "Congestion Management in Electricity Networks: Nodal, Zonal and Discriminatory Pricing," Working Paper Series 915, Research Institute of Industrial Economics.
    13. Benjamin Heymann & Alejandro Jofr'e, 2019. "Optimal auctions for networked markets with externalities," Papers 1907.10080, arXiv.org.
    14. 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.
    15. 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.
    16. Cumpston, Anne & Khezr, Peyman, 2020. "Multi-Unit Auctions: A Survey of Theoretical Literature," MPRA Paper 101336, University Library of Munich, Germany.
    17. 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.
    18. 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).
    19. 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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