Incentive compatible core and competitive equilibria in differential information economies

Summary. If the allocations of a differential information economy are defined as incentive compatible state-contingent lotteries over consumption goods, competitive equilibrium allocations exist and belong to the (ex ante incentive) core. Furthermore, any competitive equilibrium allocation can be viewed as an element of the core of the n-fold replicated economy, for every n. The converse holds under the further assumption of independent private values but not in general, as shown by a counter-example. Received: August 9, 1999; revised version: September 12, 1999     

On Intersectoral allocations,factors substitutability and multiple long-run growth paths

Summary. This article considers a two-sector model of economic growth with “labour-augmenting” intersectoral external effects stemming from the aggregate capital stock. It is shown that equilibrium balanced growth paths with a non-trivial labour allocation scheme become available. A set of sufficient conditions for the existence of multiple equilibrium growth rays is provided and their determinacy properties are then characterised. Finally, examination of a parameterised C.E.S. economy illustrates the central role of non-unitary values for the elasticity of substitution in the multiplicity issue. Received: October 31, 2000; revised version: September 25, 2001     

Incentive compatible contractible information

Summary. The paper seeks to characterize what information is always available for contracting, independent of the form of the contract and the probabilities of different states of nature. The paper denotes such information as contractible. It is established that it is possible to speak uniquely of maximal contractible information. Several characterizations are exhibited. In particular, it is shown that if either (a) punishments are bounded everywhere, or (b) deviations from truth-telling are either always or never detected, then maximum contractible information coincides with where is the information partition of agent j. An argument is given for why (b) may be expected to hold. Received: August 7, 2000; revised version: December 21, 2001 RID="*" ID="*" I thank Michael Chwe, Douglas Diamond, Lars Stole, Robert Townsend, Nicholas Yannelis and an anonymous referee for helpful comments.     

Risk aversion and incentive compatibility with ex post information asymmetry

Summary. The paper extends Diamond's (1984) analysis of financial contracting with information asymmetry ex post and endogenous “bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literature, in which debt contracts are optimal for risk averse as well as risk neutral borrowers. Received: December 7, 1998; revised version: June 9, 1999     

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules. Received: August 20, 1998; revised version: November 3, 1999     

Candidate stability and nonbinary social choice

Summary. The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of their impossibility theorems. Received: August 15, 2001; revised version: March 11, 2002 RID="*" ID="*" Parts of this article were previously circulated in somewhat different form in a working paper with the same title by the second author. We are grateful to Michel Le Breton and an anonymous referee for their comments. Correspondence to:J.A. Weymark     

A note on Bossert,Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”

Summary. Recent work by Bossert, Pattanaik and Xu provides axiomatic characterizations of some decision rules for individual decision making under complete uncertainty. This note shows that, in the case of two of these rules, they do not satisfy one of the axioms used for their characterization. A counterexample illustrating this fact is provided, as well as an alternative way to characterize the two rules under consideration, mantaining as far as possible the original axioms proposed by Bossert, Pattanaik and Xu. Received: November 3, 2000; revised version: March 1, 2002 RID="*" ID="*" I am grateful for the encouragement and support of Professor Prasanta Pattanaik. I thank also the suggestions of two anonymous referees. This work was made during an academic visit to the Department of Economics of the University of California in Riverside (UCR). The visit was possible thanks to an invitation by the UCR and the financial support of the Public University of Navarra, the Government of Navarra, and the CICYT (SEC96-0858).     

Optimal design of pension funds: a mission impossible?

Summary. Nowadays many employers offer their employees the possibility of an insurance against too large losses in income when retiring or becoming disabled. This paper models the optimization problem of the employer when setting up such a so-called pension fund. Not surprisingly, it turns out that the optimal solution depends on the premium the employees are willing to pay at most for such an insurance. Since this is private information for an employee and hence not known to the employer, he needs to collect information regarding these maximum premiums. It is shown that if employees' characteristics only differ in the maximum premium they are willing to pay, the employer is unable to perfectly inform himself on these maximum premiums, i.e. he cannot create the right incentives for his employees to reveal their maximum premiums truthfully. Received: March 20, 2000; revised version: March 11, 2002 RID="*" ID="*" The authors acknowledge the helpful comments and suggestions of an anonymous referee. The research of J. Suijs is made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences (KNAW). Correspondence to: J. Suijs     

Rationalizable variable-population choice functions

Summary. We analyze the rationalizability of variable-population social-choice functions in a welfarist framework. It is shown that fixed-population rationalizability and a weakening of congruence together are necessary and sufficient for rational choice, given a plausible dominance property that prevents the choice of alternatives involving low utility levels. In addition, a class of critical-level separable choice functions is characterized. This result, which extends an earlier axiomatization of a related class of bargaining solutions to a variable-population setting, is the first axiomatization of critical-level principles in a general choice-theoretic model. Received: November 30, 1999; revised version: September 11, 2000     

Approval voting in subset elections

Summary. Approval voting is designed to be “insensitive to numbers” of voters, and likely to elect a Condorcet candidate. However, the result of an election among one group of candidates gives no information about the results of elections among any other groups, even if every voter follows the recommended utility-maximizing strategy, which places strong restrictions on the individual voter's subset ballots. Thus the addition of a single candidate could completely reverse the outcome of an election, or a Condorcet candidate could finish last. Received: November 5, 1998; revised version: November 30, 1998     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

Approximation by finite horizons of the undiscounted one-sector growth model

Summary. In this paper I give a method for finding long-run-average policies in the undiscounted economic growth problem using approximations by finite horizons. Required hypothesis is the strong interiority of T-horizon solutions. Received: March 25, 1996; revised version: July 29, 1997     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

On the constancy of bribe-proof solutions

Summary. We consider the problem of choosing one point in a set of alternatives when monetary transfers are possible. In this context, Schummer (2000) shows that a social choice function must be a constant function if manipulation through bribes is ruled out. But he requires two kinds of domain-richness conditions. One is either smooth connectedness or the finiteness of the set of alternatives and the other is monotonical closedness. However, dispensing with the former condition, we alternatively prove the same result under a weaker condition than monotonical closedness. Received: April 11, 2000; revised version: February 25, 2002 RID="*" ID="*" This paper received the Osaka University Institute of Social and Economic Research Moriguchi Prize in January 2001. I am grateful to Prof. Ryoichi Nagahisa, Prof. Tatsuyoshi Saijo, Prof. Ken-ichi Shimomura, Prof. Ken Urai, and especially two anonymous referees for their useful and helpful comments and suggestions. I am a Research Fellow of the Japan Society for the Promotion of Science.     

A KKM-result and an application for binary and non-binary choice functions

Summary. By generalizing the classical Knaster-Kuratowski-Mazurkiewicz Theorem, we obtain a result that provides sufficient conditions to ensure the non-emptiness of several kinds of choice functions. This result generalizes well-known results on the existence of maximal elements for binary relations (Bergstrom [4]; Walker [16]; Tian [15]), on the non-emptiness of non-binary choice functions (Nehring [12]; Llinares and Sánchez [9]) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-finite sets. Received: December 29, 1999; revised version: October 18, 2001     

Nash implementation with a private good

Summary. I construct a general model of social planning problems, including mixed production economies and regulatory problems with negative externalities as special cases, and I give simple mechanisms for Nash implementation under three increasingly general sets of assumptions. I first construct a continuous mechanism to implement the (constrained) Lindahl allocations of an economy, and I then extend this to arbitrary social choice rules based on prices. I end with a mechani sm to implement any monotonic social choice rule, assuming only the existence of a private (not necessarily transferable) good. In that general case, each agent simply reports an upper contour set, an outcome, and I need two agents to make binary numerical announcements. I do not require the usual no-veto-power condition. Received: February 19, 1998; revised version: January 30, 2002     

A characterization of efficient, bayesian incentive compatible mechanisms

Summary. A mechanism that is both efficient and incentive compatible in the Bayesian-Nash sense is shown to be payoff-equivalent to a Groves mechanism at the point in time when each agent has just acquired his private information. This equivalence result simplifies the question of whether or not an efficient, Bayesian incentive compatible mechanism can satisfy other desired objectives, for the search for an appropriate mechanism can be restricted to the family of Groves mechanisms. The method is used to extend the result of Myerson and Satterthwaite on the inefficiency of bilateral bargaining to a multilateral setting. Received: June 30, 1997; revised version: May 22, 1998     

A difficulty with the address models of product differentiation

Summary. In models of product differentiation and location models it is implicitly assumed that consumers can afford to buy the differentiated goods in the market. I show that with income heterogeneity there are severe existence problems of a price equilibrium in models of horizontal product differentiation with unit demand because some consumers are income-constrained. The result generalizes to other models of product differentiation, search, and switching costs. I present an alternative specification of variable individual demand in which this kind of existence problem cannot arise. Received: October 17, 1997; revised version: February 20, 1998     

How helpful is a long memory on financial markets?

Summary. How should portfolio decisions depend on the past? In a simple model with boundedly rational agents we show that there is no universal answer to this question. Both, long and short memory, can be optimal in the appropriate environment. In most cases there is an equilibrium where both dispositions are equally successful. We characterize such equilibria for the case of two assets and two states. For dynamics based on average payoff, equilibria are global attractors whereas discrete choice dynamics in general do not converge to the equilibrium. Received: August 31, 1998; revised version: November 15, 1999