Distributions for the first-order approach to principal-agent problems

Summary. The first-order approach is a technical shortcut widely used in agency problems. The best known set of sufficient conditions for its validity are due to Mirrlees and Rogerson and require that the distribution function is convex in effort and has a likelihood ratio increasing in output. Only one nontrivial example was so far known to satisfy both properties. This note provides two rich families of examples displaying both properties. Received: December 4, 2000; revised version: December 10, 2001     

Tilting the supply schedule to enhance competition in uniform-price auctions

Uniform-price auctions of a divisible good in fixed supply admit underpricing equilibria, where bidders submit high inframarginal bids to prevent competition on prices. The seller can obstruct this behavior by tilting her supply schedule and making the amount of divisible good on offer change endogenously with its (uniform) price. Precommitting to an increasing supply curve is a strategic instrument to reward aggressive bidding and enhance expected revenue. A fixed supply may not be optimal even when accounting for the cost to the seller of issuing a quantity different from her target supply.     

Decision analysis using targets instead of utility functions

A common precept of decision analysis under uncertainty is the choice of an action which maximizes the expected value of a utility function. Savage's (1954) axioms for subjective expected utility provide a normative foundation for this principle of choice. This paper shows that the same set of axioms implies that one should select an action which maximizes the probability of meeting an uncertain target. This suggests a new perspective and an alternate target-based language for decision analysis. We explore the implications and the advantages of this target-based approach for both individual and group decision-making.     

Upper and lower bounds for expected utility

Summary.   The decision-theoretic literature has developed very few techniques to bound the expected utility of a random variable when only simple statistics like its median or mode or mean are known. One reason for this lack of results is that we are missing a convenient way to link probability theory and expected utility. This paper is written to demonstrate a general (and genuinely probabilistic) technique to obtain upper and lower bounds for the expected utility of a lottery. Received: December 14, 1999; revised version: March 8, 2000     

Efficient egalitarian equivalent allocations over a single good

This paper studies efficient and egalitarian allocations over a single heterogeneous and infinitely divisible good. We prove the existence of such allocations using only measure-theoretic arguments. Under the additional assumption of complete information, we identify a sufficient condition on agents’ preferences that makes it possible to apply the Pazner–Schmeidler rule for uniquely selecting an efficient egalitarian equivalent allocation. Finally, we exhibit a simple procedure that implements the Pazner–Schmeidler selection in a subgame-perfect equilibrium. We thank Gabrielle Demange, William Thomson, two referees and seminar audiences at Boston, Palermo and Rochester University for their comments. Financial support from MIUR is acknowledged.     

Convergence of outcomes and evolution of strategic behavior in double auctions

We study the emergence of strategic behavior in double auctions with an equal number of buyers and sellers, under the distinct assumptions that orders are cleared simultaneously or asynchronously. The evolution of strategic behavior is modeled as a learning process driven by a genetic algorithm. We find that, as the size of the market grows, allocative inefficiency tends to zero and performance converges to the competitive outcome, regardless of the order-clearing rule. The main result concerns the evolution of strategic behavior as the size of the market gets larger. Under simultaneous order-clearing, only marginal traders learn to be price takers and make offers equal to their valuations/costs. Under asynchronous order-clearing, all intramarginal traders learn to be price makers and make offers equal to the competitive equilibrium price. The nature of the order-clearing rule affects in a fundamental way what kind of strategic behavior we should expect to emerge.     

Benchmarking real-valued acts

A benchmarking procedure ranks real-valued acts by the probability that they outperform a benchmark β which may itself be a random variable; that is, an act f is evaluated by means of the functional V(f)=P(fβ). Expected utility is a special case of benchmarking procedure, where the acts and the benchmark are stochastically independent. This paper provides axiomatic characterizations of preference relations that are representable as benchmarking procedures. The key axiom is the sure-thing principle. When the state space is infinite, different continuity assumptions translate into different properties of the probability P.     

Introduction to the Milestones series

Decisions in Economics and Finance - This piece in the Milestones series is dedicated to the paper coauthored by David Gale and Lloyd Shapley and published in 1962 under the title “College...     

Feature-weighted categorized play across symmetric games

Experimental Economics - Experimental game theory studies the behavior of agents who face a stream of one-shot games as a form of learning. Most literature focuses on a single recurring identical...