Bargaining and inequity aversion: On the efficiency of the double auction

In a bargaining setting with asymmetrically informed, inequity-averse parties, a fully efficient mechanism (i.e., the double auction) exists if and only if compassion is strong. Less compassionate parties do not trade in the double auction in the limit of strong envy.     

On the optimality of optimal income taxation

The Mirrleesian model of income taxation restricts attention to simple allocation mechanism with no strategic interdependence, i.e., the optimal labor supply of any one individual does not depend on the labor supply of others. It has been argued by Piketty (2009) [12] that this restriction is substantial because more sophisticated mechanisms can reach first-best allocations that are out of reach with simple mechanisms. In this paper, we assess the validity of Piketty?s critique in an independent private values model. As a main result, we show that the optimal sophisticated mechanism is a simple mechanism, or, equivalently, a Mirrleesian income tax system.     

On the genericity of full surplus extraction in mechanism design

Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233], using convex combinations of models, showed that full surplus extraction (FSE) in mechanism design is generically impossible, contrary to the seminal work of Cremer and McLean [J. Cremer, R. McLean, Full extraction of the surplus in Bayesian and dominant strategy auctions, Econometrica 53 (1988) 345-361]. Since Cremer and McLean did not allow convex combinations of models, the two results are not comparable. We show that FSE is generically impossible when convex combinations of models are not allowed, provided that we do not hold fixed the cardinality of models.     

Revenue ranking of first-price auctions with resale

When the price setter in post-auction resale is chosen according to exogenous probabilities, Hafalir and Krishna (2008) [2] showed that the first-price auction brings more expected revenues than the second-price auction with truth-bidding bidders. We complete their revenue ranking by proving that the first-price auction produces higher expected revenues the higher the probability the auction winner sets the resale price.     

Asymmetric English auctions

This paper studies equilibria of the n-bidder single-object English, or open ascending price, auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universität Kiel, Kiel, 1992, pp. 115-136.) showed that if the values satisfy a “single crossing” condition, then the two-bidder English auction has an efficient equilibrium. In this paper, two extensions of the single crossing condition, the “average crossing” condition and the “cyclical crossing” condition, are introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium.     

On optimal head starts in all-pay auctions

We consider a two-player all-pay auction with symmetric independent private values that are uniformly distributed. The designer chooses the size of a head start that is given to one of the players. The designer’s objective is to maximize a convex combination of the expected highest effort and the expected aggregate effort. Unless the weight on the highest effort is one, small head starts are always worse than no head start. Moreover, the optimal head start is strictly positive if and only if the weight on the highest effort is large enough.     

Information acquisition and full surplus extraction

It is well known that when agents' types are correlated, the mechanism designer can extract the entire surplus. This creates an incentive for agents to acquire information about other agents' types. Robust lotteries (are payment schemes that) support full extraction and partially robust lotteries support efficient implementation in the presence of information acquisition opportunities. Necessary and sufficient conditions for existence of robust and partially robust lotteries are derived. If an agent's information signal spans other agents' types then robust lotteries do not exist. However, if all agents report their signal realizations then robust lotteries exist in an extended type space.     

Best-of-three all-pay auctions

We study a best-of-three all-pay auction. It is shown that with values of winning and without values of losing, this auction is less productive (the players’ total expected effort is smaller) than the one-stage all-pay auction. However, with different values of losing over the contest’s stages it may be more productive than the one-stage all-pay auction.     

Competition among auctioneers in large markets

We analyse a multistage game of competition among auctioneers. First, the auctioneers commit to some reserve prices; second, the bidders enter one auction, if any; and finally, the auctions take place. We show that for any finite set of feasible reserve prices, each auctioneer announces a reserve price equal to his production cost if the numbers of auctioneers and bidders are sufficiently large, though finite. Our result supports the idea that optimal auctions may be quite simple. Our model also confirms previous results for some “limit” versions of the model by McAfee (Econometrica 61 (1993) 1281-1312), Peters (Rev. Econ. Stud. 64 (1997) 97-123), and Peters and Severinov (J. Econ. Theory 75 (1997) 141-179).     

Bidding for the unemployed: An application of mechanism design to welfare-to-work programs

This paper applies the theory of mechanism design to welfare-to-work programs. When procuring welfare-to-work projects to employment service providers, governments face the problems of adverse selection (the winning provider is not the most efficient one) and moral hazard (the winning provider shirks in its responsibility to reintegrate unemployed people). We compare the constant-reward second-price auction with the socially optimal mechanism and show that the auction generates social welfare that is close to the optimal mechanism, while requiring less information and weaker commitment.     

A note on the incompatibility of strategy-proofness and Pareto-optimality in quasi-linear settings with public budgets

We show that any deterministic mechanism, for allocating identical items that are complements to budget-constrained bidders, cannot simultaneously satisfy individual-rationality, strategy-proofness, Pareto-efficiency, and no-positive-transfers. This holds even for two bidders, two items, and commonly-known budgets, and generalizes to richer settings.     

Corrigendum to “Reserve price signaling” [J. Econ. Theory 135 (1) (2007) 253-268]

We find an error in [H. Cai, J. Riley, L. Ye, Reserve price signaling, J. Econ. Theory 135 (1) (2007) 253-268]. The existence of the separating signaling equilibrium is not challenged, but the related comparative statics, while valid in the case without informational externalities between bidders, do not generalize to the case with informational externalities as claimed by the authors. General results on the influence of the number of bidders are obtained in a linear specification of the informational externalities.     

Mixed bundling auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling.     

Optimal search auctions

We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller's problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry.     

Maxmin mechanism in a simple common value auction

This paper models the data generating process of common value auctions in a parameter-estimation way, known as the classical approach in statistical inference. Viewing the true value of the object as a parameter that nobody ever knows, we let our value function be the average of the individual estimations (signals) of all agents, a robust estimation of the parameter. Under this simple value function, we select almost uniquely the mechanism that gives the seller the largest portion of the true value in the worst situation among all the direct mechanisms that are feasible, ex-post implementable and individual rational. Our Maxmin mechanism, which randomly assigns the object to one agent, provides the seller (n−1)/n$(n-1)/n$ of the true value when expected revenue is concerned, where n$n$ is the number of the agents.