Numerical Solution of Asymmetric Auctions

Timothy C. Au (), David Banks () and Yi Guo ()
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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

Decision Analysis, 2021, vol. 18, issue 4, 321-334

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.

Keywords: asymmetric auctions; first-price auctions; numerical solutions; simulation (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ordeca:v:18:y:2021:i:4:p:321-334

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