Hervé Crès

Scheduling with Opting Out: Improving upon Random Priority

In a scheduling problem where agents can opt out, we show that the familiar random priority RP mechanism can be improved upon by another mechanism dubbed probabilistic serial PS. Both mechanisms are nonmanipulable in a strong sense, but the latter is Pareto superior to the former and serves a larger expected number of agents. The PS equilibrium outcome is easier to compute than the RP outcome; on the other hand, RP is easier to implement than PS. We show that the improvement of PS over RP is significant but small: at most a couple of percentage points in the relative welfare gain and the relative difference in quantity served. Both gains vanish when the number of agents is large; hence both mechanisms can be used as a proxy of each other.

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision makerʼs utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision makerʼs set of priors is precisely all the weighted-averages of priors, where an expertʼs prior is taken from her set and the weight vector is taken from Λ; (ii) the decision makerʼs valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the expertsʼ valuations.

Externalities, Internalization and Fluctuations

In this paper, the authors introduce consumption externalities as developed by K. Arrow in overlapping-generations economies. They show how the internalization of externalities--through exchanges at markets for externalities--may give rise to new phenomena such as altered stability properties and fluctuations, even though it restores optimality. Copyright 1997 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Production in incomplete markets: Expectations matter for political stability

In the present paper we study voting-based corporate control in a general equilibrium model with incomplete financial markets. Since voting takes place in a multi-dimensional setting, super-majority rules are needed to ensure existence of equilibrium. In a linear-quadratic setup we show that the endogenization of voting weights (given by portfolio holdings) can give rise to - through self-fulfilling expectations - dramatical political instability, i.e. Condorcet cycles of length two even for very high majority rules.

A Geometric Study of Shareholders’ Voting in Incomplete Markets: Multivariate Median and Mean Shareholder Theorems

AbstractA simple parametric general equilibrium model with S states of nature and K < S firms is considered. Since markets are incomplete, at a (financial) equilibrium shareholders typically disagree on whether to keep or not the status quo production plans. Hence each firm faces a genuine problem of social choice. The setup proposed in the present paper allows to study these problems within a classical (Downsian) spatial voting model. Given the multidimensional nature of the latter, super majority rules with rate

Symmetry breakings in Malinvaud's model with individual risks

\rho \in [1/2, 1]

Free Access to the Commons: Random Priority versus Average Cost

are needed to guarantee existence of politically stable production plans. A simple geometric argument is proposed showing why a 50%-majority stable production equilibrium exists when K=S−1. When the degree of incompleteness is more severe, under more restrictive assumptions on agents’ preferences and the distribution of agents’ types, equilibria are shown to exist for rates ρ smaller than Caplin and Nalebuff (Econometrica 59: 1–23, 1991) bound of 0.64: they obtain for production plans whose span contains the ‘ideal securities’ of all K mean shareholders.

Voting in Assemblies of Shareholders and Incomplete Markets

A commodity is shared between some individuals; some selection procedure is used to choose allocations. In order to reflect that laws and rules rather than allocations are implemented and that they involve an element of randomness because of incomplete information, selection procedures are taken to be probability measures over the set of allocations. Illustrations and interpretations of the selection procedures are given.