Contest architecture

A contest architecture specifies how the contestants are split among several sub-contests whose winners compete against each other (while other players are eliminated). We compare the performance of such dynamic schemes to that of static winner-take-all contests from the point of view of a designer who maximizes either the expected total effort or the expected highest effort. For the case of a linear cost of effort, our main results are: (1) If the designer maximizes expected total effort, the optimal architecture is a single grand static contest. (2) If the designer maximizes the expected highest effort, and if there are sufficiently many competitors, it is optimal to split the competitors in two divisions, and to have a final among the two divisional winners. Finally, if the effort cost functions are convex, the designer may benefit by splitting the contestants into several sub-contests, or by awarding prizes to all finalists.     

Partnerships, lemons, and efficient trade

We analyze the possibility of efficient trade with informationally interdependent valuations and with a dispersed ownership. A main role is played by the effects of adverse selection on incentive payments and budget constraints. Variations in the degree of interdependence directly influence the incentive payments and ultimately lead to a tightening or relaxation of the budget constraint, thus affecting the ability to achieve efficient trade. We derive precise possibility conditions for efficient trade, and we offer a framework in which the interplay of insights previously obtained by Akerlof (Quart. J. Econom. 89 (1970) 488), Myerson and Satterthwaite (J. Econom. Theory 28 (1983) 265), and Cramton et al. (Econometrica 55 (1987) 615) can be analyzed. In addition, we discuss to what extent possibility results previously obtained for private values environments can be generalized.     

Coarse matching with incomplete information

We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), an intermediary’s revenue, and the agents’ welfare (defined as the total surplus minus payments to the intermediary). Following Chao and Wilson (Am Econ Rev 77: 899–916, 1987) and McAfee (Econometrica 70:2025–2034, 2002), our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than random matching, while still requiring only a minimal amount of information.     

The production and cost-sharing of an excludable public good

Summary We study a model of negotiation and coalition formation concerning a public expenditure and its financing. The agents must determine which coalition will jointly produce a public good, how much will be produced, and how the cost is to be shared. Agents that do not belong to the final coalition are excluded from consumption of the public good. Subgame-perfect Nash equilibria in stationary strategies lead to the formation of the grand coalition with an agreed alternative in the core of the economy. Conversely, for each alternative in the core, there exists a subgame-perfect Nash equilibrium in (pure) stationary strategies that leads to the formation of the grand coalition with that alternative.I wish to thank Dieter Balkenborg, Georg Noldeke, Shlomo Weber and Eyal Winter for helpful discussions. The comments of an anonymous referee greatly improved the quality of the exposition. Financial support from Deutsche Forschungsgemeinschaft, SFB 303, is gratefully acknowledged.     

Ex-post implementation and preference aggregation via potentials

We introduce several notions of potentials for mechanism design problems with interdependent values, and relate them to implementation in ex-post equilibrium. Whereas ex-post implementation is closely linked to the ordinal concept of best-alternative potentials, the celebrated Vickrey–Clarke–Groves mechanism corresponds to the stronger notion of a cardinal potential: agents agree not only on the best alternative, but also on the quantitative differences between all alternatives. We characterize all valuations that allow for cardinal potentials, and use this characterization for: (1) Identifying valuations for which ex-post implementation is possible; (2) Identifying classes of valuations for which all ex-post implementable choice rules correspond to cardinal potentials. The latter allows us to extend to interdependent valuations a result for dominant strategy implementation in private values settings, due to Roberts (The Characterization of Implementable Choice Rules, North-Holland, Amsterdam, 1979). We wish to thank an associate editor, two anonymous referees, Paul Milgrom and Burkhard Schipper for helpful comments and stimulating remarks.     

Optimal seedings in elimination tournaments

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

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].     

License Auctions and Market Structure

We analyze the interplay between license auctions and market structure in a model with several incumbents and several potential entrants. The focus is on the competitiveness induced by the number of auctioned licenses. Under plausible conditions, we show that auctioning more licenses need not result in a more competitive final outcome, contrary to what common sense suggests. This is due to the nature of competition among incumbents, which sometimes exhibits free-riding. We illustrate some results with examples drawn from the recent European license-auctions for third generation (3G) mobile telephony.