Pre-Auction Offers in Asymmetric First-Price and Second-Price Auctions

We consider “must-sell” auctions with asymmetric buyers. First, we study auctions with two asymmetric buyers, where the distribution of valuations of the strong buyer is “stretched” relative to that of the weak buyer. Then, it is known that inefficient first-price auctions are more profitable for the seller than efficient second-price auctions. This is because the former favor the weak buyer. However, we show that the seller can do one better by augmenting the first-price auction by a pre-auction offer made exclusively to the strong buyer. Should the strong buyer reject the offer, the object is simply sold in an ordinary first-price auction. The result is driven by the fact that the unmodified first-price auction is too favorable to the weak buyer, and that the pre-auction offer allows some correction of this to the benefit of the seller. Secondly, we show quite generally that pre-auction offers never increase the profitability of second-price auctions, since they introduce the wrong kind of favoritism from the perspective of seller profits.first-price and second-price auctions; asymmetric bidders; pre-auction offers

Charitable asymmetric bidders

Recent papers show that all-pay auctions are better at raising money for charity than first-price auctions with symmetric bidders and under incomplete information. Yet, this result is lost with sufficiently asymmetric bidders and under complete information. In this paper, we consider a framework on charity auctions with asymmetric bidders under some incomplete information. We find that all-pay auctions still earn more money than first-price auction. Thus, all-pay auctions should be seriously considered when one wants to organize a charity auction.All-pay auctions, Charity, Externalities

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. We prove that in this context the second price auction yields a higher expected revenue than the first price auction for a broad set of parameter values, although the opposite result is common in the literature on asymmetric auctions. For instance, the second price auction is superior both when a bidder’s valuation is more uncertain that the valuation of the other bidder, and in case of a not too large distribution shift or rescaling. In addition, we show that in some cases the revenue in the first price auction decreases when all the valuations increase [in doing so, we correct a claim in Maskin and Riley (1985), and we derive the bidders’ preferences between the two auctions.Asymmetric auctions, First price auctions, Second price auctions.

Investment Incentives in Auctions: An Experiment

We experimentally analyze first and second price auctions where one bidder can achieve a comparative advantage by investment prior to the auction. We find that, as predicted by theory, bidders invest more often prior to second price auctions than prior to first price auctions. In both auction formats bidding is more aggressive than the equilibrium prediction. However, bidding is closer to equilibrium than in control treatments where the comparative advantage is exogenous.Auctions, Investment Incentives, Asymmetric Auctions, Experimental Economics

Charity Auctions for the Happy Few

Recent literature has shown that all-pay auctions raise more money for charity than winner-pay auctions. We demonstrate that the first-price and second-price winner-pay auctions outperform the first-price and second-price all-pay auction when bidders are sufficiently asymmetric. To prove it, we consider a framework with complete information. Complete information is realistic and corresponds to events that occur, for instance, in a local service club (such as a voluntary organization) or in a show business dinner.All-pay auctions, charity, complete information, externalities

Multiple equilibria in asymmetric first-price auctions

Maskin and Riley (2003) and Lebrun (2006) prove that the Bayes-Nash equilibrium of �rst-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric �rst-price auctions (with or without a minimum bid), the relaxation of this assumption results in additional equilibria that are "substantial." Although in each of these additional equilibria no buyer wins with a bids above his value, the allocation of the object and the selling price may vary among the equilibria. Furthermore, we show that such phenomena can only occur under asymmetry in the distributions of values.Asymmetric auctions, �first-price auctions, multiple equilibria

Numerical Analysis of Asymmetric First Price Auctions

We develop a powerful and user-friendly program for numerically solving first price auction problems where an arbitrary number of bidders draw independent valuations from heterogenous distributions and the auctioneer imposes a reserve price for the object. The heterogeneity in this model arises both from the specification of ex-ante heterogenous, non-uniform distributions of private values for bidders, as well as the possibility of subsets of these bidders colluding. The technique extends the work of Marshall, Meurer, Richard, and Stromquist (1994), where they applied backward recursive Taylor series expansion techniques to solve two-player asymmetric first price auctions under uniform distributions. The algorithm is also used to numerically investigate whether revenue equivalence between first price and second price auctions in symmetric models extend to the asymmetric case. In particular, we simulate the model under various environments and find evidence that under the assumption of first order stochastic dominance, the first price auction generates higher expected revenue to the seller, while the second price auction is more susceptible to collusive activities. However, when the assumption of first order stochastic dominance is relaxed, and the distributions of private values cross once, the evidence suggests that the second price auction may in some cases generate higher expected revenue to the sellerAsymetric, Optimal Reserve, Ex-ante Heterogeneity

Ranking Asymmetric Auctions using the Dispersive Order

The revenue ranking of asymmetric auctions with two heterogenous bidders is examined. The main theorem identifies a general environment in which the first-price auction is more profitable than the second-price auction. By using mechanism design techniques, the problem is simplified and several extensions are made possible. Roughly speaking, the first-price auction is more profitable when the strong bidder's distribution is flatter and more disperse than the weak bidder's distribution. These sufficient conditions turn out to have appealing geometric and economic interpretations. The theorem applies to certain environments with multi-dimensional types. It is also possible, for the first time, to extend the ranking to auctions with reserve prices and to auctions with more bidders. Implications for contests architecture and other auction formats are also pursued.Asymmetric Auctions, Convex Transform Order, Dispersive Order, Multi-dimensional types, Revenue Ranking, Star order.

On Rationalizable Outcomes in Private-Value First-Price Discrete Auctions

In this paper, we extend the result of Dekel and Wollinsky ("Rationalizable Outcomes of Large Private-Value First-Price Discrete Auctions" Games and Economic Behavior, 2003) on rationalizable outcomes in first-price auctions. Dekel and Wollinsky show that under certain conditions, each player chooses a unique bid conditional on her valuation. Their result however depends on the assumption that the number of players is sufficiently large (relative to the number of available bids). We first provide a different set of sufficient conditions for the uniqueness result. We then show that for the independent (possibly asymmetric) private value case, (i) the result holds if the distributions are such that the inverse hazard rate is sufficiently high for each valuation, implying that auctions need not necessarily be large, and (ii) if the distributions satisfy the conditions of Dekel and Wollinsky, they always satisfy oursFirst-Price Auctions, Rationalizability, Dominance

Asymmetric First-Price Menu Auctions under Intricate Uncertainty

This paper studies asymmetric first-price menu auctions in the procurement environment where the buyer does not commit to a decision rule and asymmetric sellers have interdependent costs and statistically affiliated signals. Sellers compete in bidding a menu of contracts, where a contract specifies a vector of characteristics and a payment required from the buyer for delivering these characteristics. The buyer does not commit ex-ante to a decision rule but rather upon observing all the menus offered by sellers chooses the best contract. This paper establishes the existence of a continuum of separating monotone equilibria in this game bounded above by the jointly ex-post efficient outcome and below by the jointly interim efficient outcome. It shows that the jointly ex-post efficient equilibrium outcome is the only ex-post renegotiation proof outcome and it is also ex-ante robust to all continuation equilibriafirst-price menu auction, interdependent values, monotone equilibria, joint ex-post renegotiation-proofness, ex-ante robustness