Auctions with Almost Homogeneous Bidders

We deviate from the symmetric case of the independent private value model by allowing the bidders’ value distributions, which depend on parameters, to be slightly different. We show that previous results about the equality to the first-order in the parameters between revenues from the second-price auction and other auction mechanisms follow from the joint differentiability of the equilibria with respect to the parameters. We prove this differentiability for the first-price auction and obtain general formulas for the different first-order effects. From our results about the first-price auction, we analytically generate examples with continuous distributions where a stochastic improvement to a bidder’s value distribution reduces his equilibrium payoff. In another application, we show that, starting from competition among cartels of equal sizes, allowing in a small number of members from other cartels can be profitable only if the members or the synergies between them are strong enough.Independent private value model; auctions; asymmetry; first-price auction, second-price auction; differentiability; revenue equivalence theorem

Incomplete Information and Rent Dissipation in Deterministic Contests

In a deterministic contest or all-pay auction, all rents are dissipated when information is complete and contestants are identical. As one contestant becomes "stronger", that is, values the prize more, total expenditures are known to decrease monotonically. Thus, asymmetry among contestants reduces competition and rent dissipation. Recently, this result has been shown to hold for other, non-deterministic, contest success functions as well, thereby suggesting a certain robustness. In this paper, however, the complete information assumption is shown to be crucial. With incomplete information -- regardless of how little -- total expenditures in a deterministic two-player contest increase when one contestant becomes marginally stronger, starting from a symmetric contest. In fact, both contestants expend resources more aggressively; with complete information, neither of them do so.All-pay auctions, Asymmetric auctions, Rent seeking.

Mechanism design by an informed principal: the quasi-linear private-values case

We show that, in environments with independent private values and transferable utility, a privately informed principal can solve her mechanism selection problem by implementing an allocation that is ex-ante optimal for her. No type of the principal can gain from proposing an alternative mechanism that is incentivefeasible with any belief that puts probability 0 on types that would strictly lose from proposing the alternative. We show that the solution exists in essentially any environment with finite type spaces, and in any linear-utility environment with continuous type spaces, allowing for arbitrary disagreement outcomes. As an application, we consider a bilateral exchange environment (Myerson and Satterthwaite, 1983) in which the principal is one of the traders. If the property rights over the good are dispersed among the traders, then the principal will implement an allocation in which she is almost surely better off than if her type is commonly known. The optimal mechanism is a combination of a participation fee, a buyout option for the principal, and a resale stage with posted prices and, hence, is a generalization of the posted price that would optimal if the principal's valuation were commonly known

Auctions with almost homogeneous bidders

We prove that, around the symmetric case, where the values are identically distributed, the equilibrium of the first price auction is jointly differentiable with respect to general bidder-specific parameters of the value distributions. We show that the revenue equivalence between the first-price and the second-price auctions to the first-order in the size of the parameters is an immediate consequence of this differentiability and the Revenue Equivalence Theorem; thereby formally establishing the first-order equivalence Fibich et al. [G. Fibich, A. Gavious, A. Sela, Revenue equivalence in asymmetric auctions, J. Econ. Theory 115 (2004) 309-321] noticed for their particular perturbation.Independent private value model Auctions Asymmetry First-price auction Second-price auction Differentiability Revenue Equivalence Theorem