When and how to dismantle nuclear weapons

This paper first derives revenue-maximizing auctions with identity-specific externalities among all players (seller and buyers). Our main findings are as follows. Firstly, a modified second-price sealed-bid auction with appropriate entry fees and reserve price is revenue-maximizing. Secondly, seller may physically destroy the auctioned item if the item is unsold or use destroying the item as nonparticipation threat. Thirdly, the revenue-maximizing auction induces full participation of buyers. Fourthly, each losing buyer's payment includes an externality-correcting component that equals the allocative externality to him. These components eliminate the impact of externalities on strategic bidding behavior. The paper further studies revenue-maximizing auctions with financial externalities. One-to-one correspondences between revenue-maximizing auctions for settings with and without financial externalities are established through incorporating externality-correcting payments. This result provides a general method for designing revenue-maximizing auctions in different settings of financial externalities, since revenue-maximizing auctions can be obtained through transforming the revenue-maximizing auctions for the regular settings without externalities.Auctions design; Endogenous participation; Externality

Endogenous entry and auctions design with private participation costs

This paper studies endogenous entry and ex ante revenue-maximizing auctions in an independent private value setting where potential bidders have private-information entry costs. The contribution of this paper is four-fold. First, we show that any equilibrium entry can be characterized through a set of continuous and monotonic shutdown curves that separate the bidders' types into participating and nonparticipating categories. Second, the expected winning probability of a participant does not depend on his private entry cost. Furthermore, the expected winning probabilities of the participating types are given by the slopes of the shutdown curves. Third, symmetric entry equilibria (shutdown curves) implemented by the classes of ex post efficient or ex post revenue-maximizing mechanisms are completely characterized. Fourth, within these two classes of mechanisms, a modified Vickrey auction with uniform reserve price and entry subsidy is ex ante revenue-maximizing. The desired entry subsidy and reserve price are determined by the lower end of the corresponding shutdown curve.Auctions Design; Ex Post Efficiency; Endogenous Participation; Multidimensional Screening; Vickrey Auction

Estimating risk aversion from ascending and sealed-bid auctions: the case of timber auction data

Estimating bidders’ risk aversion in auctions is a challeging problem because of identification issues. This paper takes advantage of bidding data from two auction designs to identify nonparametrically the bidders’ utility function within a private value framework. In particular, ascending auction data allow us to recover the latent distribution of private values, while first-price sealed-bid auction data allow us to recover the bidders’ utility function. This leads to a nonparametric estimator. An application to the US Forest Service timber auctions is proposed. Estimated utility functions display concavity, which can be partly captured by constant relative risk aversion.Risk Aversion; Nonparametric Identi.cation; Nonparametric and Semipara-metric Estimation; Timber Auctions

Contest design and optimal endogenous entry

This paper derives the effort-maximizing contest rule and the optimal endogenous entry in a context where potential participants bear fixed entry costs. The organizer is allowed to design the contest under a fixed budget with two strategic instruments: he sets the value of the prize purse, and arranges a monetary transfer (entry subsidy or fee) for each participating contestant. In other words, the budget can either be used to subsidize participation or an entry fee can be charged to fund the prize purse. The results show that the optimally designed contest attracts exactly two participating contestants in its unique subgame perfect equilibrium (when there is a positive fixed entry cost) and extracts all the surplus from participating contestants. The study also shows that the direction and amount of the monetary transfer depend on the magnitude of the entry cost: the contest organizer subsidizes entry when contestants bear substantial entry costs, but charges an entry fee to fund the prize purse whenever the entry cost is sufficiently low.Contest; Endogenous Entry; Entry Cost; Subsidy; Entry Fee

Unifying Contests: from Noisy Ranking to Ratio-Form Contest Success Functions

This paper proposes a multi-winner noisy-ranking contest model. Contestants are ranked in a descending order by their perceived outputs, and rewarded by their ranks. A contestant's perceivable output increases with his/her autonomous effort, but is subject to random perturbation. We establish, under plausible conditions, the equivalence between our model and the family of (winner-take-all and multi-winner) lottery contests built upon ratio-form contest success functions. Our model thus provides a micro foundation for this family of often studied contests. In addition, our approach reveals a common thread that connects a broad class of seeming disparate competitive activities and unifies them in the nutshell of ratio-form success functions.Multi-Winner Contest; Contest Success Function; Noisy Ranking

The beauty of "bigness" in contest design: merging or splitting?

This paper studies in a multiple-winner contest setting how the total efforts may vary between a grand contest and a set of subcontests. We first show that the rent-dissipation rate increases when the numbers of contestants and prizes are "scaled up". In other words, the total efforts of a contest exhibit a striking "increasing return to scale" property: when the numbers of contestants and prizes scale up proportionally, the total efforts of the contest increase more than proportionally. Thus, the total efforts must increase when a set of identical subcontests are merged into a grand contest. Equivalently, the total efforts decrease when a grand contest is evenly divided. We further allow the grand contest to be split into uneven subcontests. We show that under a mild and plausible condition (regular contest technology), the grand contest generates more efforts as compared to any split contests.Contests; Multiple-winners; Efforts; Size; Replication

Unifying Contests: from Noisy Ranking to Ratio-Form Contest Success Functions

This paper proposes a multi-winner noisy-ranking contest model. Contestants are ranked in a descending order by their perceived outputs, and rewarded by their ranks. A contestant's perceivable output increases with his/her autonomous effort, but is subject to random perturbation. We establish, under plausible conditions, the equivalence between our model and the family of (winner-take-all and multi-winner) lottery contests built upon ratio-form contest success functions. Our model thus provides a micro foundation for this family of often studied contests. In addition, our approach reveals a common thread that connects a broad class of seeming disparate competitive activities and unifies them in the nutshell of ratio-form success functions.Multi-Winner Contest; Contest Success Function; Noisy Ranking

All Pay Quality-Bids in Score Procurement Auctions

In this paper, we study score procurement auctions with all-pay quality bids. A supplier’s score is the difference between his quality and price bids. The supplier with the highest score wins and gets paid his own price bid. The procurer’s payoff is the difference between the winner’s quality and the procurer’s payments to the suppliers. Equilibrium quality and price bids are solved without first obtaining the corresponding equilibrium scores. We find that quality bids, the suppliers’ payoffs and the procurer’s payoff do not depend on whether price bids are made contingent on quality bids. Compared to a benchmark of winner-pay quality bids, in which the losing suppliers’ quality bidding costs are reimbursed by the procurer, all-pay quality bids tend to reduce quality provision and suppliers\u27 payoffs, but they tend to increase the total surplus and the procurer’s payoff

Perfect bidder collusion through bribe and request

We study collusion in a second-price auction with two bidders in a dynamic environment. One bidder can make a take-it-or-leave-it collusion proposal, which consists of both an offer and a request of bribes, to the opponent. We show that there always exists a robust equilibrium in which the collusion success probability is one. In the equilibrium, for each type of initiator the expected payoff is generally higher than the counterpart in any robust equilibria of the single-option model (Es\"{o} and Schummer (2004)) and any other separating equilibria in our model

Existence of monotone equilibrium in first price auctions with private risk aversion and private initial wealth

In this paper, we study the existence of monotone equilibrium in first price auctions where bidders have a three-dimensional private type, i.e. their private values, degrees of risk aversion and initial wealth. Bidders' utility functions belong to the class of constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The bidders' types are independent across bidders, while a bidder's private value, initial wealth and degree of risk aversion are allowed to be correlated. We show that a monotone equilibrium always exists in a general setting allowing for asymmetric bidders. Moreover, with symmetric bidders, a symmetric monotone equilibrium strategy must exist. A bidder's equilibrium strategy increases with bidders' private values and degrees of risk aversion. When bidders have CRRA utility, equilibrium bids decrease with initial wealth; when bidders have CARA utility, equilibrium bids are invariant to initial wealth