A new solution to the problem of adjudicating conflicting claims

Summary. For the problem of adjudicating conflicting claims, we consider the requirement that each agent should receive at least 1/n his claim truncated at the amount to divide, where n is the number of claimants (Moreno-Ternero and Villar, 2004a). We identify two families of rules satisfying this bound. We then formulate the requirement that for each problem, the awards vector should be obtainable in two equivalent ways, (i) directly or (ii) in two steps, first assigning to each claimant his lower bound and then applying the rule to the appropriately revised problem. We show that there is only one rule satisfying this requirement. We name it the “ rule”, as it is obtained by a recursion. We then undertake a systematic investigation of the properties of the rule.Received: 7 September 2004, Revised: 21 April 2005, JEL Classification Numbers: C79, D63, D74.William Thomson: Correspondence toWe thank Christopher Chambers, Youngsub Chun, Tarík Kara, Çağatay Kayí, Juan Moreno-Ternero, Toyotaka Sakai, and Michel Truchon for their comments. We also thank a referee for useful comments. This paper was presented at Columbia University, CORE, Bilkent University, Sabancí University, Université Laval, and Caltech, and at the Mallorca Review of Economic Design meeting. Thomson acknowledges support from the NSF under grant SES-0214691.     

Learning in asymmetric duopoly markets: competition in information and market correlation

This paper explores experimentation and learning in asymmetric duopoly markets with product differentiation and demand uncertainty. We define the concepts of strategic substitutability and strategic complementarity in information and we show how both the mode of information competition and the transmission of information across markets affect duopoly experimentation. We relate information competition with market competition and we find that, when goods are substitutes and the correlation between market shocks is negative, firms will have a higher incentive to experiment in asymmetric markets than in symmetric ones. The opposite result follows when such correlation is positive. Also, when goods are complements the above findings are reversed.JEL Classification: D83, C72The authors thank partial financial support from the Spanish Ministry of Science and Technology under project B2000-1429, from the Spanish Ministry of Education and Science under project SEJ2004-07554 and from the “Generalitat Valénciana” under project GRUPOS04/13.     

Imperfect common knowledge and the information value of prices

Summary. When economic agents have diverse private information on the fundamentals of the economy, prices may serve as a poor aggregator of this private information. We examine the information value of prices in a monopolistic competition setting that has become standard in the New Keynesian macroeconomics literature. We show that public information has a disproportionate effect on agents’ decisions, crowds out private information, and thereby has the potential to degrade the information value of prices. This effect is strongest in an economy with keen price competition. Monetary policy must rely on less informative signals of the underlying cost conditions.Received: 6 November 2003, Revised: 19 November 2004 JEL Classification Numbers: E31, E32, E58.This paper supersedes the discussion in the first half of our longer paper that circulated under the title “Public and Private Information in Monetary Policy Models”. We thank Andy Filardo, Marvin Goodfriend, Nobu Kiyotaki, John Moore, Stephen Morris and Lars Svensson for advice and comments at various stages of the project, and to Herakles Polemarchakis, Roko Aliprantis and an anonymous referee for their helpful comments and guidance. The views are those of the authors and do not necessarily represent those of the BIS. The second author acknowledges support from the U.K. ESRC under grant RES 000220450. Correspondence to: H.S. Shin     

Portfolio delegation under short-selling constraints

Summary. In this paper we study delegated portfolio management when the manager’s ability to short-sell is restricted. Contrary to previous results, we show that under moral hazard, linear performance-adjusted contracts do provide portfolio managers with incentives to gather information. We find that the risk-averse manager’s effort is an increasing function of her share in the portfolio’s return. This result affects the risk-averse investor’s choice of contracts. Unlike previous results, the purely risk-sharing contract is now shown to be suboptimal. Using numerical methods we show that under the optimal linear contract, the manager’s share in the portfolio return is higher than what it is under a purely risk sharing contract. Additionally, this deviation is shown to be: (i) increasing in the manager’s risk aversion and (ii) larger for tighter short-selling restrictions. As the constraint is relaxed the deviation converges to zero.Received: 25 July 2002, Revised: 12 December 2004, JEL Classification Numbers: D81, D82, J33.Juan-Pedro Gómez: Correspondence toAn earlier version of the paper was circulated under the title “Providing Managerial Incentives: Do Benchmarks Matter?” We are grateful to an anonymous referee whose comments helped to improve the paper. We also thank comments by Viral Acharya, Alexei Goriaev, Ernst Maug, Kristian Rydqvist, Neil Stoughton, Rangarajan Sundaram, Fernando Zapatero and seminar participants at the 1999 SED meetings in Sardinia, the 1999 Workshop in Mutual Fund Performance at EIASM, Brussels, the 2000 EFA meetings in London, the Bank of Norway, the Stockholm Schools of Economics, the Norwegian School of Management and the 2001 WFA meetings in Tucson. Sharma gratefully acknowledges financial support from the Asociacion Mexicana de Cultura.     

Cumulative prospect theory and the St. Petersburg paradox

Summary. We find that in cumulative prospect theory (CPT) with a concave value function in gains, a lottery with finite expected value may have infinite subjective value. This problem does not occur in expected utility theory. The paradox occurs in particular in the setting and the parameter regime studied by Tversky and Kahneman [15] and in subsequent works. We characterize situations in CPT where the problem can be resolved. In particular, we define a class of admissible probability distributions and admissible parameter regimes for the weighting- and value functions for which finiteness of the subjective value can be proved. Alternatively, we suggest a new weighting function for CPT which guarantees finite subjective value for all lotteries with finite expected value, independent of the choice of the value function. Some of these results have already been found independently by Blavatskyy [4] in the context of discrete lotteries.Received: 14 October 2004, Revised: 6 May 2005, JEL Classification Numbers: C91, D81.We thank Pavlo Blavatskyy and Thorsten Hens for their helpful remarks regarding our paper. Moreover, we thank the referee for his constructive suggestions. This research was supported by the University Research Priority Program “Finance and Financial Markets” a research instrument of the University of Zürich.     

Ascending auctions for multiple objects: the case for the Japanese design

Summary. We consider two ascending auctions for multiple objects, namely, an English and a Japanese auction, and derive a perfect Bayesian equilibrium of the Japanese auction by exploiting its strategic equivalence with the survival auction, which consists of a finite sequence of sealed-bid auctions. Thus an equilibrium of a continuous time game is derived by means of backward induction in finitely many steps. We then show that all equilibria of the Japanese auction induce equilibria of the English auction, but that many collusive or signaling equilibria of the English auction do not have a counterpart in the Japanese auction.Received: 2 September 2004, Revised: 20 April 2005, JEL Classification Numbers: C72, D44.Fabrizio Germano: Correspondence toWe are indebted to Philippe Jehiel for useful discussions and to Nicolas Vieille for suggestions in the proof of Proposition 2; we also thank seminar audiences in Athens, Basel, Beer-Sheva, Berlin, Brussels, Cambridge, Edinburgh, Exeter, Lausanne, Lisbon, London, Louvain-la-Neuve, Namur and Tel Aviv. Germano acknowledges financial support from Euopean Commission, TMR Network Grant ERBFMRXCT0055, “Cooperation and Information” as well from the Spanish Ministry of Science and Technology, Grants SEC2001-0792, SEJ2004-06319, and in form of a Ramon y Cajal Fellowship. Lovo is member of GREGHEC, unité CNRS, FRE-2810. The support of the Economic and Social Research Council (ESRC) is also gratefully acknowledged. The work was part of the programme of the ESRC Research for Economic Learning and Social Evolution.     

Interest rate rules, inflation and the Taylor principle: an analytical exploration

Summary. The purpose of this article is to characterize optimal interest rate rules in the framework of a dynamic stochastic general equilibrium model, and notably to scrutinize the “Taylor principle”, according to which the nominal interest rate should respond more than one for one to inflation. This model yields explicit solutions for the optimal rule. We find that the elasticity of response depends on numerous factors, such as the degree of price rigidity, the autocorrelation of the underlying shocks, or which measure of inflation is used. In general the optimal elasticity of the interest rate with respect to inflation needs not be greater than one.Received: 6 November 2003, Revised: 17 August 2004 JEL Classification Numbers: E5, E52, E58.J.-P. Bénassy: I wish to thank Daniel Laskar and an anonymous referee for their perceptive comments on earlier drafts of this paper. Of course all remaining deficiencies are mine.     

Indeterminacy with almost constant returns to scale: capital-labor substitution matters

Summary. This paper shows, in the benchmark one-sector Ramsey model, that indeterminacy and sunspots may occur when externalities are small, provided that capital and labor are more substitutable than in the usual Cobb-Douglas specification. Key to the results are the general formulations of both preferences and technology that we consider. In particular, indeterminacy is shown to occur under almost constant returns to scale provided that both concavity of utility for consumption is small enough and labor supply is close to indivisible. An important implication of the results is that, when labor supply is positively sloped, indeterminacy does not necessarily require the equilibrium wage-hours locus to be upward sloping.Received: 16 June 2004, Revised: 8 March 2005, JEL Classification Numbers: C62, D58, D91, E32.This is a companion paper of “Sunspots in real business-cycle models: completing calibration”, with new results that have emerged from extending the analysis contained in the latter article. The author would like to thank, without implicating, Bruno Decreuse, Andrew Postlewaite, Alain Venditti, Yi Wen, participants at the 2003 Society for Economic Dynamics Meeting, as well as C.D. Aliprantis, the Editor, and an anonymous referee for useful comments and suggestions.     

Benefit and Distance Functions

We explore the relationship between R. W. Shephard's input distance function (“Cost and Production Functions,” Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ.21(1992a), 461–481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in both price and input space. D. McFadden's (Cost, revenue, and profit functions,in“Production Economics: A Dual Approach to Theory and Applications, “North-Holland/Elsevier, New York, 1978) composition rules for input sets and input distance functions are then extended to the directional input distance function.Journal of Economic LiteratureClassification Numbers : D21, D24, D29.     

Quasi-weightings, Trading, and Desirability Relations in Simple Games

We investigate the problem of simultaneously characterizing various classes of simple games in three different ways: (i) the existence of “quasi-weightings” in which smaller numerical values are assigned to losing coalitions than are assigned to winning ones, (ii) the robustness of “winningness” with respect to trades involving groups of players, and (iii) the acyclicity of certain strict “orderings” that intuitively correspond to the idea of one player being more desirable than another.Journal of Economic LiteratureClassification Number: C71.     

Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Eliciting Preferences to Assign Positions and Compensation

We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent–position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness, the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley–Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness. The results extend to models (without externalities) in which agents share positions. Journal of Economic Literature Classification Numbers: C72, D70.     

Learning to Learn, Pattern Recognition, and Nash Equilibrium

The paper studies a large class of bounded-rationality, probabilistic learning models on strategic-form games. The main assumption is that players “recognize” cyclic patterns in the observed history of play. The main result is convergence with probability one to a fixed pattern of pure strategy Nash equilibria, in a large class of “simple games” in which the pure equilibria are nicely spread along the lattice of the game. We also prove that a necessary condition for convergence of behavior to a mixed strategy Nash equilibrium is that the players consider arbitrarily long histories when forming their predictions.Journal of Economic LiteratureClassification Numbers: C72, D83.     

Institutions and economic development: How strong is the relation?

This paper investigates the relationship between institutions and economic development (output per worker). As in Hall and Jones (1999), we find that a 1% improvement in institutions (as we measure them) generates on average a 5% increase in output per worker. However, this relationship is not linear and the data have important heterogeneity. Countries with the same value of institutions have different levels of income per worker. We ask whether the “returns to institutions” are the same across countries conditional on the level of institutions. Using quantile regression methods, we show that for countries at the top of the conditional distribution of international incomes, the “returns to institutions” are lower (around 3.8%,) than for countries at the bottom of this distribution (around 6.2%). We show that this result is robust for different model specifications and definitions of institutions. We also provide evidence that, conditional on the level of institutional development, the distribution of output per worker tends to become less disperse as countries improve their institutional framework. In other words, having better institutions is essential in order to close the output-per-worker gap across countries. Finally, we provide the rationale behind the results through a modified version of a Neoclassical Growth Model with time varying wedges, representing policy distortions and institutions.We thank Lee Alston, Roger Koenker, and Stephen L. Parente for helpful discussion, Werner Baer for useful comments, and Chad Jones for facilitating access to the data set. We are also indebted to an anonymous referee and an associate editor for important suggestions that improved the final paper. The analysis, opinions and findings expressed herein represent the views of the authors, they are not necessarily those of the Banco de Portugal. Any remaining errors are our responsibility.First version received: May 2001/Final version received: August 2003     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

Abreu–Matsushima Mechanisms: Experimental Evidence

Abreu–Matsushima mechanisms can be applied to a broad class of games to induce any desired outcome as the unique rationalizable outcome. We conduct experiments investigating the performance of such mechanisms in two simple coordination games. In these games one pure-strategy equilibrium is “focal”; we assess the efficacy of Abreu–Matsushima mechanisms for implementing the other pure-strategy equilibrium outcome. Abreu–Matsushima mechanisms induce some choices consistent with the desired outcome, but more choices reflect the focal outcome. Moreover, “strengthening” the mechanism has a perverse effect when the desired outcome is a Pareto-dominated risk-dominated equilibrium.Journal of Economic LiteratureClassification Number: C7.     

Truthful mechanism design for multidimensional scheduling via cycle monotonicity

We consider the makespan-minimization problem on unrelated machines in the context of algorithmic mechanism design. No truthful mechanisms with non-trivial approximation guarantees are known for this multidimensional domain. We study a well-motivated special case (also a multidimensional domain), where the processing time of a job on each machine is either “low” or “high.” We give a general technique to convert any c-approximation algorithm (in a black-box fashion) to a 3c-approximation truthful-in-expectation mechanism. Our construction uses fractional truthful mechanisms as a building block, and builds upon a technique of Lavi and Swamy [Lavi, R., Swamy, C., 2005. Truthful and near-optimal mechanism design via linear programming. In: Proc. 46th FOCS, pp. 595–604]. When all jobs have identical low and high values, we devise a deterministic 2-approximation truthful mechanism. The chief novelty of our results is that we do not utilize explicit price definitions to prove truthfulness. Instead we design algorithms that satisfy cycle monotonicity [Rochet, J., 1987. A necessary and sufficient condition for rationalizability in a quasilinear context. J. Math. Econ. 16, 191–200], a necessary and sufficient condition for truthfulness in multidimensional settings; this is the first work that leverages this characterization.     

When does the majority become a majority? Empirical analysis of the time at which main market adopters purchase the bulk of our sales

The idea of a dual-market structure in the early stages of a product's life cycle has become one of the most widely accepted ideas among new product marketing practitioners in the past decade. Concepts such as “Early Market/Main Market” and “Visionaries/Pragmatists” have entered the lexicon of high-tech executives to express the notion that the market for new products is composed of early and main markets with a discontinuity in the diffusion process in between them. Moreover, these concepts have been at least partially tested and verified in the marketing academic literature in the past few years.We extend this branch of research by investigating the timing issues in dual-market cases. We define Change-of-Dominance Time (CD-Time) as the number of years it takes main market adopters to outnumber early market adopters. We empirically investigate this timing issue on a comprehensive data set of new product sales in the consumer electronics industry. We find that regarding explanatory determinants of CD-Time, external influence, such as advertising, to the early market is the most important explanatory variable.We examine the relationship between CD-Time and other early product life cycle phenomena: Takeoff, Saddle, and Rogers' size of adopter categories. We found relatively high correlations between these phenomena and CD-Time.The answer to the question “When does the majority become a majority?” is indeed “at 16%”! In a dual-market setting, the average time at which the main market outnumbers the early market is when 16% of the market has already adopted the product. In terms of time, in 75% of the cases the majority becomes a majority in 5 to 10 years.     

War and peace: Third-party intervention in conflict

This paper develops a simple sequential-move game to characterize the endogeneity of third-party intervention in conflict. We show how a third party's “intervention technology” interacts with the canonical “conflict technologies” of two rival parties in affecting the sub-game perfect Nash equilibrium outcome. From the perspective of deterrence strategy, we find that it is more costly for a third party to support an ally to deter a challenger from attacking (i.e., to maintain peace or acquiescence), as compared to the alternative case when the third party supports the ally to gain a disputed territory by attacking (i.e., to create war), ceteris paribus. However, an optimally intervening third party can be either “peace-making”, “peace-breaking”, or neither depending on the characteristics of the conflict and the stakes the third party holds with each of the rival parties.     

Games with Imperfectly Observable Commitment

[1]claims that, in models of commitment, “the first-mover advantage is eliminated when there is aslightamount of noise associated with the observation of the first-mover's selection.” We show that the validity of this claim depends crucially on the restriction to pure strategy equilibria. The game analyzed by Bagwell always has a mixed equilibrium that is close to the Stackelberg equilibrium when the noise is small. Furthermore, an equilibrium selection theory that combines elements from the theory of[7]with elements from the theory of [6], actually selects this “noisy Stackelberg equilibrium.”Journal of Economic LiteratureClassification Number: C72.