The structure of strategy-proof random social choice functions over product domains and lexicographically separable preferences

We characterize the class of dominant-strategy incentive-compatible (or strategy-proof) random social choice functions in the standard multi-dimensional voting model where voter preferences over the various dimensions (or components) are lexicographically separable. We show that these social choice functions (which we call generalized random dictatorships) are induced by probability distributions on voter sequences of length equal to the number of components. They induce a fixed probability distribution on the product set of voter peaks. The marginal probability distribution over every component is a random dictatorship. Our results generalize the classic random dictatorship result in Gibbard (1977) and the decomposability results for strategy-proof deterministic social choice functions for multi-dimensional models with separable preferences obtained in LeBreton and Sen (1999).     

Groves mechanisms and communication externalities

We put forward a model of private goods with externalities. Agents derive benefit from communicating with each other. In order to communicate they need to operate on a common platform. Adopting new platforms is costly. We first provide an algorithm that determines the efficient outcome. Then we prove that no individually rational and feasible Groves mechanism exists. We provide sufficient conditions that determine when an individually rational Groves mechanism runs a deficit and we characterize the individually rational Groves mechanism that minimizes such deficit whenever it occurs. Moreover, for 2-agent economies, we single out the only feasible and symmetrical Groves mechanism that is not Pareto dominated by another strategy-proof, feasible and symmetrical mechanism.     

Strategy-proof fuzzy aggregation rules

We investigate the structure of fuzzy aggregation rules which, for every permissible profile of fuzzy individual preferences, specify a fuzzy social preference. We show that all fuzzy aggregation rules which are strategy-proof and satisfy a minimal range condition are dictatorial. In other words, there is an individual whose fuzzy preferences determine the entire fuzzy social ranking at every profile in the domain of the aggregation rule. To prove this theorem, we show that all fuzzy aggregation rules which are strategy-proof and satisfy the minimal range condition must also satisfy counterparts of independence of irrelevant alternatives and the Pareto criterion. There has been hardly any treatment of the manipulability problem in the literature on social choice with fuzzy preferences.     

Differentiable strategy-proof mechanisms for private and public goods in domains that are not necessarily large or quasi-linear

In this paper, we develop a differentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no mechanism which is efficient, strategy-proof and where consumption of both goods is positive for all agents. For the case of two or more agents the same result occurs when nondictatorship is replaced by Individual Rationality. We are very grateful to Atila Abdulkadiroglu, Carmen Beviá, Xavier Calsamiglia, Marco Celentani, Bernardo Moreno, Antonio Romero-Medina, William Thomson, Walter Trockel, an associate editor, three anonymous referees and participants at seminars at Universities of Alicante, Autónoma de Barcelona and Rochester and the Spanish Economic Association meeting in Sevilla for very helpful comments and suggestions.     

Efficient allocations and equilibria with short-selling and incomplete preferences

This paper reconsiders the theory of existence of efficient allocations and equilibria when consumption sets are unbounded below under the assumption that agents have incomplete preferences. Our model is motivated by an example in the theory of assets with short-selling where there is risk and ambiguity. Agents have Bewley’s incomplete preferences. As an inertia principle is assumed in markets, equilibria are individually rational. It is shown that a necessary and sufficient condition for the existence of an individually rational efficient allocation or of an equilibrium is that the relative interiors of the risk adjusted sets of probabilities intersect. The more risk averse, the more ambiguity averse the agents, the more likely is an equilibrium to exist. The paper then turns to incomplete preferences represented by a family of concave utility functions. Several definitions of efficiency and of equilibrium with inertia are considered. Sufficient conditions and necessary and sufficient conditions are given for the existence of efficient allocations and equilibria with inertia.     

Strategyproof multiple assignment using quotas

The allocation of heterogeneous and indivisible objects is considered where there is no medium of exchange. We characterize the set of strategyproof, nonbossy, Pareto-optimal, and neutral social choice functions when preferences are monotonic and quantity-monotonic. The characterized sets of social choice functions are sequential; agents are assigned their favorite objects among the objects not given to others before them, subject to a quota. Received: 5 January 1999 / Accepted: 14 June 1999     

Researching with whom? Stability and manipulation

This paper explores the existence of stable research teams, when the preferences of each agent depend on the set of researchers who are collaborating. We introduce a property over researchers’ preferences, called top responsiveness, guaranteeing the existence of stable research teams configurations. We also provide a stable mechanism, induced by the so-called top covering algorithm, which is strategy-proof when researchers preferences satisfy top responsiveness. Furthermore, we find that, in this framework, the top covering mechanism is the only strategy-proof mechanism that always selects stable allocations.     

An alternative direct proof of Gibbard’s random dictatorship theorem

We present an alternative proof of the Gibbards random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbards approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbards proof.Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification: D71, D72Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.     

Walrasian social orderings in exchange economies

We study social ordering functions in exchange economies. We show that if a social ordering function satisfies certain Pareto, individual rationality, and local independence conditions, then (i) the set of top allocations of the chosen social ordering is contained in the set of Walrasian allocations and is typically non-empty, and (ii) all individually rational but non-Walrasian allocations are typically ranked indifferently. Thus, such a social ordering function is quite similar to the Walrasian correspondence, which can be regarded as the social ordering function whose associated indifference classes are the set of Walrasian allocations and the set of other allocations.     

Virtual Nash implementation with admissible support

A social choice correspondence (SCC) is virtually implementable if it is ?$?$-close (in the probability simplex) to some (exactly) implementable correspondence [Abreu, D., Sen, A., 1991. Virtual Implementation in Nash Equilibrium. Econometrica 59, 997–1021] proved that, without restriction on the set of alternatives receiving strictly positive probability at equilibrium, every SCC is virtually implementable in Nash Equilibrium. We study virtual implementation when the supports of equilibrium lotteries are restricted. We provide a necessary and sufficient condition, imposing joint restrictions on SCCs and admissible supports. Next, we discuss how to construct supports, and we underline an important difficulty. Finally, we study virtual implementation when the support is restricted to the efficient or individually rational alternatives.     

Circular domains

I introduce the notion of circular domains and prove that on any circular domain there is no strategy-proof and nondictatorial social choice function. Moreover, I show that on any proper subset of a minimal circular domain, there exists a group strategy-proof and essential social choice function. These results together detect the minimal size of the domains over which the incompatibility arises with respect to pairs of democratic-incentive requirements (nondictatorial, strategy-proof) and (essential, group strategy-proof).     

The Blocking Lemma for a many-to-one matching model

The Blocking Lemma identifies a particular blocking pair for each non-stable and individually rational matching that is preferred by some agents of one side of the market to their optimal stable matching. Its interest lies in the fact that it has been an instrumental result to prove key results on matching. For instance, the fact that in the college admissions problem the workers-optimal stable mechanism is group strategy-proof for the workers and the strong stability theorem in the marriage model follow directly from the Blocking Lemma. However, it is known that the Blocking Lemma and its consequences do not hold in the general many-to-one matching model in which firms have substitutable preference relations. We show that the Blocking Lemma holds for the many-to-one matching model in which firms’ preference relations are, in addition to substitutable, quota q-separable. We also show that the Blocking Lemma holds on a subset of substitutable preference profiles if and only if the workers-optimal stable mechanism is group strategy-proof for the workers on this subset of profiles.     

Strategy-proofness on restricted separable domains

We study a problem in which a group of voters must decide which candidates are elected from a set of alternatives. The voters’ preferences on the combinations of elected candidates are represented by linear orderings. We propose a family of restrictions of the domain of separable preferences. These subdomains are generated from a partition that identifies the friends, enemies and unbiased candidates for each voter. We characterize the family of social choice functions that satisfy strategy-proofness and tops-onlyness properties on each of the subdomains. We find that these domain restrictions are not accompanied by an increase in the family of social choice functions satisfying the two properties.     

Optimality conditions¶and bubbles in sequential economies¶and bounded relative risk-aversion

We provide specific qualifications in order that Kuhn–Tucker type Euler equations and transversality conditions at infinity hold in stochastic equilibrium models with heterogeneous agents and where assets are traded in sequential markets. It is not assumed that uncertainty is modeled as an event-tree structure or that preferences are necessarily bounded. We also describe an important class of preferences based on bounded relative risk aversion which yields relevant simplifications. Our results are used to establish conditions that rule out asset pricing bubbles. Specific examples of economies with bubbles are also discussed. Received: 28 January 2002 / Accepted: 19 July 2002 We are grateful to the editor and an anonymous referee for their valuable comments. This research was partially supported by MURST (Italy), National Group on “Nonlinear Dynamics and Stochastic Models in Economics and Finance”.     

Strategy-proofness, core, and sequential trade

We extend the Shapley-Scarf (1974) model - where a finite number of indivisible objects is to be allocated among a finite number of individuals - to the case where the primary endowment set of an individual may contain none, one, or several objects and where property rights may be transferred (objects inherited) as the allocation process unfolds, under the retained assumption that an individual consumes at most one object. In this environment we analyze the core of the economy and characterize the set of strategy-proof and Pareto efficient mechanisms. As an alternative approach, we consider property rights implicitly defined by a strategy-proof and Pareto efficient mechanism and show a core property for the mechanism-induced endowment rule.Received: 19 February 2004, Accepted: 14 April 2005, JEL Classification: C71, C78, D71, D78We would like to thank two anonymous referees for valuable comments. Financial support from The Swedish Council for Research in the Humanities and Social Sciences is gratefully acknowledged by Lars-Gunnar Svensson. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged by Bo Larsson.     

Implementation with partial verification

This paper examines the implementability of social choice functions when only partial verification of private information is possible. Green and Laffont (1986) used this framework to derive a necessary and sufficient condition for the revelation principle to continue to hold with partial verification. We provide economically interesting characterizations of this condition, which suggest that it may be too restrictive. This leads us to consider implementation (not necessarily truthful) in general, when there is partial verification. We consider the case where compensatory transfers are allowed, giving the mechanism designer further leeway. We show how partial verification may allow efficient implementation of bilateral trade, where it would otherwise not be possible. Received: 1 August 1998 / Accepted: 5 September 2000     

Sprumont's characterization of the uniform rule when all single-peaked preferences are admissible

Sprumont (1991) has established that the only allocation rule for the division problem that is strategy-proof, efficient, and anonymous is the uniform rule when the domain is the set of all possible profiles of continuous single-peaked preferences. Sprumont's characterization of the uniform rule is shown to hold on any larger domain of single-peaked preferences. Received: 15 December 1998 / Accepted: 12 April 1999     

Nash implementation with an infinite-dimensional trade space

This paper deals with the problem of implementing the Walras correspondence via Nash equilibria, in exchange economies with infinitely many commodities and finitely many households with possibly non-ordered preferences. We explicitly construct a feasible mechanism enjoying some features, which have natural economic meanings. Under a fairly weak boundary condition, this game fully implements the Walras equilibria. If this condition is not fulfilled, our mechanism nevertheless implements the constrained Walras equilibria. Received: 11 December 2003, Accepted: 29 July 2005 JEL Classification: D41, D43, D51 We thank (without implicating) Prof. Jean-Marc Bonnisseau and Cuong Le Van for helpful comments. The views expressed in this paper reflect those of the authors and not necessarily those of Calyon.     

A note on the equilibrium theory of economies with asymmetric information

In this note, we give an equilibrium existence theorem for exchange economies with asymmetric information and with an infinite dimensional commodity space. In our model, we assume that preferences are represented by well behaved utility functions, the positive cone has a non empty interior and the individual rational utility set is compact. Our result complements the corresponding one in Podczeck and Yannelis (2008), in the sense that is applicable to commodity spaces in which the order intervals are (possibly) not compact with respect to any Hausdorff linear topology.     

ANALYTICAL MARXISM

Abstract This paper provides a comprehensive survey of the literature on Analytical Marxism (AM) and analyses its relevance for social theory. AM is precisely defined and distinguished from Rational Choice Marxism (RCM). The different substantive implications of the two approaches are discussed: according to RCM, the role of Marxism in the social sciences is exhausted, whereas AM has reconstructed a set of propositions that aim to provide the foundations of a distinctive approach in social theory. The methodological debate around and within AM is analysed and the shortcomings of methodological individualism and rational choice theory are stressed, raising doubts on the claim that RCM is the only scientific approach to Marx's theory. Yet, wholesale rejections on a priori methodological or exegetical grounds are questioned. A focused, immanent critique of RCM is developed, which emphasizes the lack of an adequate analysis of structural constraints and endogenous preferences in RCM models. It is argued that the analysis of endogenous preferences and structural constraints is consistent with an anti‐reductionist AM approach and it may provide the outline of a fertile, distinctive research programme in explanatory social theory that builds on the core of Marxism identified by AM.