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Numerical Solution of Asymmetric Auctions

Author

Listed:
  • Timothy C. Au

    (Google LLC, 1600 Amphitheatre Parkway, Mountain View, California 94043)

  • David Banks

    (Department of Statistical Science, Duke University, Durham, North Carolina 27708)

  • Yi Guo

    (Department of Statistical Science, Duke University, Durham, North Carolina 27708)

Abstract

We propose the backward indifference derivation (BID) algorithm, a new method to numerically approximate the pure strategy Nash equilibrium (PSNE) bidding functions in asymmetric first-price auctions. The BID algorithm constructs a sequence of finite-action PSNE that converges to the continuum-action PSNE by finding where bidders are indifferent between actions. Consequently, our approach differs from prevailing numerical methods that consider a system of poorly behaved differential equations. After proving convergence (conditional on knowing the maximum bid), we evaluate the numerical performance of the BID algorithm on four examples, two of which have not been previously addressed.

Suggested Citation

  • Timothy C. Au & David Banks & Yi Guo, 2021. "Numerical Solution of Asymmetric Auctions," Decision Analysis, INFORMS, vol. 18(4), pages 321-334, December.
    • Handle: RePEc:inm:ordeca:v:18:y:2021:i:4:p:321-334
    DOI: 10.1287/deca.2021.0432
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    References listed on IDEAS

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    Cited by:

    1. David Banks & Yi Guo, 2022. "Uncommon Knowledge in Multiparty Auctions," Decision Analysis, INFORMS, vol. 19(3), pages 220-228, September.

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