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Computational Economics

, Volume 42, Issue 2, pp 241–266 | Cite as

Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions

  • Timothy P. HubbardEmail author
  • René Kirkegaard
  • Harry J. Paarsch
Article

Abstract

In models of first-price auctions, when bidders are ex ante heterogeneous, deriving explicit equilibrium bid functions is typically impossible, so numerical methods are often employed to find approximate solutions. Recent theoretical research concerning asymmetric auctions has determined some properties these bid functions must satisfy when certain conditions are met. Plotting the relative expected pay-offs of bidders is a quick, informative way to decide whether the approximate solutions are consistent with theory. We approximate the (inverse-)bid functions by polynomials and employ theoretical results in two ways: to help solve for the polynomial coefficients and to evaluate qualitatively the appropriateness of a given approximation. We simulate auctions from the approximated solutions and find that, for the examples considered, low-degree polynomial approximations perform poorly and can lead to incorrect policy recommendations concerning auction design, suggesting researchers need to take care to obtain quality solutions.

Keywords

First-price auctions Asymmetric auctions Numerical methods 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Timothy P. Hubbard
    • 1
    Email author
  • René Kirkegaard
    • 2
  • Harry J. Paarsch
    • 3
  1. 1.Department of EconomicsColby CollegeWatervilleUSA
  2. 2.University of GuelphGuelphCanada
  3. 3.University of MelbourneMelbourneAustralia

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