## Abstract

One of the most important results in auction theory is that when bidders are symmetric (homogeneous), then under quite general conditions, the seller's expected revenue is independent of the auction mechanism (Revenue Equivalence Theorem). More often than not, however, bidders are asymmetric, and so revenue equivalence is lost. Previously, it was shown that asymmetric auctions become revenue equivalent as n→∞ , where n is the number of bidders. In this paper, we go beyond the limiting behavior and explicitly calculate the revenue to O(1/n^{3}) accuracy, essentially with no information on the auction payment rules or bidders' equilibrium strategies, for a large class of asymmetric auctions that includes first-price, second-price, and optimal auctions. These calculations show that the revenue differences among asymmetric auctions scale as "epsilon 2/n^{3}, where "epsilon is the level of asymmetry (heterogeneity) among the bidders. Therefore, bidders' asymmetry has a negligible effect on revenue ranking of auctions with as few as n = 6 bidders.

Original language | English |
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Pages (from-to) | 1489-1510 |

Number of pages | 22 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 78 |

Issue number | 3 |

DOIs | |

State | Published - 2018 |

## Keywords

- Asymmetric auction
- Asymptotic methods
- Auction theory
- Averaging
- First-price auction
- Game theory
- Homogenization
- Laplace method for integrals
- Optimal auction
- Revenue equivalence
- Revenue ranking
- Second-price auction