Optimal Voting Rules

Abstract:

We study dominant strategy incentive compatible (DIC) and deterministic mechanisms in a social choice setting with several alternatives. The agents are privately informed about their preferences, and have single-crossing utility functions. Monetary transfers are not feasible. We use an equivalence between deterministic, DIC mechanisms and generalized median voter schemes to construct the constrained-efficient, optimal mechanism for an utilitarian planner. Optimal schemes for other welfare criteria such as, say, a Rawlsian maximin can be analogously obtained.

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417.pdf

The optimal prize structure of symmetric Tullock contests

Abstract:

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts.

Keywords: Tournaments, Incentive structures, Rent seeking
JEL Classification: C7, D72, J31

November 2008

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250.pdf

Collective Production and Incentives

Abstract:

We analyse incentive problems in collective production environments where contributors are compensated according to their observed and ranked efforts. This provides incentives to the contributors to choose first best efforts.

December 2006

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186.pdf

Tournaments with Midterm Reviews

Abstract:

In many tournaments investments are made over time and conducting a review only once at the end, or also at points midway through, is a strategic decision of the tournament designer. If the latter is chosen, then a rule according to which the results of the different reviews are aggregated into a ranking must also be determined. This paper takes a first step in the direction of answering how such rules are optimally designed. A characterization of the optimal aggregation rule is provided for a two-agent two-stage tournament. In particular, we show that treating the two reviews symmetrically may result in an equilibrium effort level that is inferior to the one in which only a final review is conducted. However, treating the two reviews lexicographically by first looking at the final review, and then using the midterm review only as a tie-breaking rule, strictly dominates the option of conducting a final review only. The optimal mechanism falls somewhere in between these two extreme mechanisms. It is shown that the more effective the first-stage effort is in determining the final review’s outcome, the smaller is the weight that should be assigned to the midterm review in determining the agents’ ranking.

May 2006

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145.pdf

When queueing is better than push and shove

Abstract:

We address the scheduling problem of reordering an existing queue into its efficient order through trade. To that end, we consider individually rational and balanced budget direct and indirect mechanisms. We show that this class of mechanisms allows us to form efficient queues provided that existing property rights for the service are small enough to enable trade between the agents. In particular, we show on the one hand that no queue under a fully deterministic service schedule such as first-come, first-serve can be dissolved efficiently and meet our requirements. If, on the other hand, the alternative is service anarchy (ie. a random queue), every existing queue can be transformed into an efficient order.

Keywords: Scheduling, Queueing, Mechanism design
JEL Classification: C72, D44, D82
June 2006

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144.pdf

On Seller Estimates and Buyer Returns

Abstract:

This paper revisits recent empirical research on buyer credulity in arts auctions and auctions for assets in general. We show that elementary results in auction theory can fully account for some stylized facts on asset returns that have been held to suggest that sellers of assets can exploit buyers by providing biased estimates of asset values. We argue that, rather than showing that buyers are credulous, the existing evidence can serve as an indirect test of the rationality assumptions underlying auction theory.

Keywords: Auctions, information disclosure, seller manipulation, buyer credulity
JEL Classification: D44, D82, G12, G14
February 2006

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143.pdf

Allocative and Informational Externalities in Auctions and Related Mechanisms

Abstract:

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study.

October 2005

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142.pdf

Mixed Bundling Auctions

Abstract:

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.

February 2006

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141.pdf

Optimal Seedings in Elimination Tournaments

Abstract:

We study an elimination tournament with heterogenous contestants whose ability is common-knowledge. Each pair-wise match is modeled as an all-pay auction where the winner gets the right to compete at the next round. Equilibrium efforts are in mixed strategies, yielding rather complex play dynamics: the endogenous win probabilities in each match depend on the outcome of other matches through the identity of the expected opponent in the next round. The designer can seed the competitors according to their ranks. For tournaments with four players we find optimal seedings with respect to three different criteria: 1) maximization of total effort in the tournament; 2) maximization of the probability of a final among the two top ranked teams; 3) maximization of the win probability for the top player. In addition, we find the seedings ensuring that higher ranked players have a higher probability to win the tournament. Finally, we compare the theoretical predictions with data from NCAA basketball tournaments.

Keywords: Elimination tournaments, Seedings, All-Pay Auctions
JEL Classification: D72, D82, D44
July 2003

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140.pdf

Abstract:

We study the optimal design of organizations under the assumption that agents in a contest care about their relative position. A judicious definition of status categories can be used by a principal in order to influence the agents’ performance. We first consider a pure status case where there are no tangible prizes. Our main results connect the optimal partition in status categories to various properties of the distribution of ability among contestants. The top status category always contains an unique element. For distributions of abilities that have an increasing failure rate, a proliferation of status classes is optimal, while in other cases the optimal partition involves some coarseness. Finally, we modify the model to allow for status categories that are endogenously determined by monetary prizes of different sizes. If status is solely derived from monetary rewards, we show that the optimal partition in status classes contains only two categories.

July 2005

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139.pdf

Labour market screening with intermediaries

Abstract:

We consider a Rothschild-Stiglitz-Spence labour market screening model and employ a centralised mechanism to coordinate the efficient matching of workers to firms. This mechanism can be thought of as operated by a recruitment agency, an employment office or head hunter. In a centralised descending-bid, multi-item procurement auction, workers submitwage-bids for each job and are assigned stable jobs as equilibrium outcome. We compare this outcome to independent, sequential hiring by firms and conclude that, in general, a stable assignment can only be implemented if firms coordinate to some extent.

Keywords: Matching, Multi-item auctions, Sequential auctions, Screening
JEL Classification: C78, D44, E24, J41
June 2006

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138.pdf

Sequential bargaining with pure common values

Abstract:

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players in return for some payment among players. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium of this game which is essentially unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and nondeterministically. The better informed player obtains a rent.

Keywords: Sequential bargaining, Common values, Incomplete information, Repeated games
JEL Classification: C73, C78, D44, D82, J12
June 2006

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137.pdf

Sequential bargaining with pure common values and incomplete information on both sides

Abstract:

We study the alternating-offer bargaining problem of sharing a common value pie under incomplete information on both sides and no depreciation between two identical players. We characterise the essentially unique perfect Bayesian equilibrium of this game which turns out to be in gradually increasing offers.

Keywords: Gradual bargaining, Common values, Incomplete information, Repeated games
JEL Classification: C73, C78, D44, D82, J12
June 2006

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136.pdf

All Nash Equilibria of the Multi-Unit Vickrey Auction

Abstract:

This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.

Keywords: Vickrey auction, Multi-unit auction, ex-post equilibrium, reserve price, uniqueness
JEL Classification: C72, D44
June 2006

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116.pdf

The Theory of Assortative Matching Based on Costly Signals

Abstract:

We study two-sided markets with a finite numbers of agents on each side, and with two-sided incomplete information. Agents are matched assortatively on the basis of costly signals. A main goal is to identify conditions under which the potential increase in expected output due to assortative matching (relative to random matching) is completely offset by the costs of signalling. We also study how the signalling activity and welfare on each side of the market change when we vary the number of agents and the distribution of their attributes, thereby displaying effects that are particular to small markets. Finally, we look at the continuous version of our two-sided market model and establish the connections to the finite version. Technically, the paper is based on the very elegant theory about stochastic ordering of (normalized) spacings and other linear combinations of order statistics from distributions with monotone failure rates, pioneered by R. Barlow and F. Proschan (1966, 1975) in the framework of reliability theory.

December 2005

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85.pdf

Priority Auctions and Queue Disciplines that Depend on Processing Time

Abstract:

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004

We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium.

May 2004

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5.pdf