## Abstract

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller's revenue in any k-price auction (k = 1,2,...). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n^{2}) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n^{2}) revenue equivalent. The generalization, that all large auctions are O(1/n^{2}) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n → ∞ with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n → ∞.

Original language | English |
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Pages (from-to) | 359-390 |

Number of pages | 32 |

Journal | International Journal of Game Theory |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jul 2010 |

## Keywords

- Asymptotic analysis
- Equilibrium strategy
- Large auctions
- Revenue equivalence
- Risk aversion

## ASJC Scopus subject areas

- Statistics and Probability
- Mathematics (miscellaneous)
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty