Asymmetric first-price auctions-A dynamical-systems approach

Gadi Fibich*, Nir Gavish

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We introduce a new approach for analysis and numerical simulations of asymmetric first-price auctions, which is based on dynamical systems. We apply this approach to asymmetric auctions in which players' valuations are power-law distributed. We utilize a dynamical-systems formulation to provide a proof of the existence and uniqueness of the equilibrium strategies in the cases of two coalitions and of two types of players. In the case of n different players, the singular point of the original system at b=0 corresponds to a saddle point of the dynamical system with n-1 admissible directions. This insight enables us to use forward solutions in the analysis and in the numerical simulations, in contrast with previous analytic and numerical studies that used backward solutions. The dynamical-systems approach provides an intuitive explanation for why the standard backward-shooting method for computing the equilibrium strategies is inherently unstable, and enables us to devise a stable forward-shooting method. In particular, in the case of two types of players, this method is extremely simple, as it does not require any shooting.

Original languageEnglish
Pages (from-to)219-243
Number of pages25
JournalMathematics of Operations Research
Volume37
Issue number2
DOIs
StatePublished - May 2012

Keywords

  • Asymmetric auctions
  • Dynamical systems
  • First-price auctions
  • Numerical methods

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