Numerical Simulations of Asymmetric First-Price Auctions - discussion paper

41 Pages Posted: 16 Apr 2010 Last revised: 5 Jan 2011

See all articles by Gadi Fibich

Gadi Fibich

Tel Aviv University - School of Mathematical Sciences

Nir Gavish

Technion-Israel Institute of Technology - Faculty of Mathematics

Date Written: November 1, 2009

Abstract

The standard method for computing the equilibrium strategies of asymmetric first-price auctions is the backward-shooting method. In this study we show that the backward-shooting method is inherently unstable, and that this instability cannot be eliminated by changing the numerical methodology of the backward solver. Moreover, this instability becomes more severe as the number of players increases. We then present a novel boundary-value method for computing the equilibrium strategies of asymmetric first-price auctions. We demonstrate the robustness and stability of this method for auctions with any number of players, and for players with mixed types of distributions, including both common distributions and distributions with more than one crossings. Finally, we use the boundary-value method to study large auctions with hundreds of players, to compute the rate at which large auctions first-price and second-price auctions become revenue equivalent, and to study auctions in which the distributions cannot be ordered according to first-order stochastic dominance.

JEL Classification: C63, D44, C72, D82

Suggested Citation

Fibich, Gadi and Gavish, Nir, Numerical Simulations of Asymmetric First-Price Auctions - discussion paper (November 1, 2009). Available at SSRN: https://ssrn.com/abstract=1589722 or http://dx.doi.org/10.2139/ssrn.1589722

Gadi Fibich (Contact Author)

Tel Aviv University - School of Mathematical Sciences ( email )

Tel Aviv 69978
Israel

Nir Gavish

Technion-Israel Institute of Technology - Faculty of Mathematics ( email )

Haifa 32000
Israel
97248294181 (Phone)

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