Balázs Szentes

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare. We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium. We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.

Beyond chopsticks: Symmetric equilibria in majority auction games

Majority auction games are simultaneous sealed-bid auctions of identical objects among identical bidders who each want to win a specified fraction (more than a half) of the objects. Each bidder receives no benefit from winning less than the specified fraction and no additional benefit from winning more than it. Symmetric equilibria having simple, intuitive forms are shown to exist in first-price, second-price and all-pay versions of such games when the number of bidders is sufficiently large. This contrasts with earlier results for the two-bidder “pure chopstick” majority auction games where the only known equilibria are more complicated.

Definable and Contractible Contracts

This paper analyzes Bayesian normal form games in which players write contracts that condition their actions on the contracts of the other players. These contracts are required to be representable in a formal language. This is accomplished by constructing contracts which are definable functions of the Godel code of every other players contract. We provide a complete characterization of the set of allocations supportable as pure strategy Bayesian equilibrium of this contracting game. When information is complete, this characterization provides a folk theorem. In general, the set of supportable allocations is smaller than the set supportable by a centralized mechanism designer.

On the Market for Venture Capital

We propose a theory of the market for venture capital that links the excess return to venture equity to the scarcity of venture capitalists (VCs). High returns make the VCs more selective and eager to terminate nonperforming ventures because they can move on to new ones. The scarcity of VCs enables them to internalize their social value, and the competitive equilibrium is socially optimal. Moreover, the bilaterally efficient contract is a simple equity contract. We estimate the model for the period 1989–2001 and compute the excess return to venture capital, which turns out to be 8.6 percent. Finally, we back out the return of solo entrepreneurs, which is increasing in their wealth and ranges between zero and 3.5 percent.

Two-Object Two-Bidder Simultaneous Auctions

Symmetric equilibria are constructed for a class of symmetric auction games. The games all have two identical bidders bidding in two simultaneous sealed-bid auctions for identical objects. Information is complete and the objects are either complements or substitutes. In both cases a continuum of mixed-strategy equilibria are identified. All these equilibria have a surprising structure: The supports of all the mixtures that generate equilibria are two one-dimensional curves, and they surround a two-dimensional set of pure best responses.

Equilibrium transformations and the Revenue Equivalence Theorem

I develop a method that transforms an equilibrium strategy profile from one auction to another. The method is constructive and does not require complicated computation. This provides a new approach to revenue equivalence and extends the theorem to domains where it had not previously been known, in particular to simultaneous multiple object auctions with complete information and to auction environments having correlated private values and common values.

On the biological foundation of risk preferences

This paper considers a continuous-time biological model in which the growth rate of a population is determined by the risk attitude of its individuals. We consider choices over lotteries which determine the number of offspring and involve both idiosyncratic and aggregate risks. We distinguish between two types of aggregate risk: environmental variations and natural disasters. Environmental variations influence the death and birth rates, while natural disasters result in instantaneous drops in population size.

An Evolutionary Theory of Suicide

We analyze a model in which individuals have hereditary reproductive types. The reproductive value of an individual is determined by her reproductive type and the amount of resources she can access. We introduce the possibility of suicide and assume it is also a genetic trait that interacts with the reproductive type of an individual. The main result of the paper is that populations where suicide is possible grow faster than other populations.