Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

A mechanism implementing the proportional solution

We consider the problem of a commonly owned technology which transforms a single input into a single output. We are interested in implementing a social choice rule called theproportional solution. We introduce a mechanism which implements the proportional solution in Nash, strong (Nash) and undominated Nash equilibria. In the mechanism each agent announces only two numbers which can be interpreted as the total output and her share of the total input-output combination. This paper was originally titled "Doubly implementing the proportional solution." I would like to thank my advisor William Thomson for his detailed comments and suggestions. I would also like to thank Jeffrey Banks and Sung-Whee Shin for their comments. Two anonymous referees and an editor’s comments improved this paper substantially.     

Equilibrium allocations of endowment-pretension games in public good economies

In a public good economy where agents' preferences are known but endowments are private information, instituting an allocation rule and asking the agents their initial endowments induces an endowment-pretension game. We analyse the Nash equilibrium allocations of this game and discuss its welfare properties with reference to voluntary contributions allocations. Received: 30 May 2001, Accepted: 23 September 2005 JEL Classification: H41 I am grateful to Murat Sertel for his continuous support and encouragement; to G?ksel Asan and Arunava Sen for their invaluable help. I would also like to thank Fikret Adaman, Ahmet Alkan, Salvador Barberá, Semih Koray, Andrei Ratiu, Muhamet Yíldíz, ünal Zenginobuz, an Associate Editor and two referees of the Review of Economic Design for their enlightening comments on previous drafts. Earlier versions of this paper were written during my stay at Universitat Autónoma de Barcelona and at the Indian Statistical Institute. Both visits have been possible by the kindness of the host institutions and the financial support of the Turkish Academy of Sciences and Serem Ltd. It is a pleasure for me to express my gratitude to all these institutions. Of course, all possible errors are mine.     

Implementation of Pareto efficient allocations

This paper considers Nash implementation and double implementation of Pareto efficient allocations for production economies. We allow production sets and preferences are unknown to the planner. We present a well-behaved mechanism that fully implements Pareto efficient allocations in Nash equilibrium. The mechanism then is modified to fully doubly implement Pareto efficient allocations in Nash and strong Nash equilibria. The mechanisms constructed in the paper have many nice properties such as feasibility and continuity. In addition, they use finite-dimensional message spaces. Furthermore, the mechanism works not only for three or more agents, but also for two-agent economies.     

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.     

Implementation of marginal cost pricing equilibrium allocations with transfers in economies with increasing returns to scale

This paper considers implementation of marginal cost pricing equilibrium allocations with transfers for production economies with increasing returns to scale. We present a mechanism whose Nash equilibrium allocations coincide with the set of marginal cost pricing equilibrium allocations with transfers that characterizes Pareto efficient allocations for economies with non-convex production technologies. We allow production sets and preferences to be unknown to the planner. The mechanism has some nice properties such as feasibility, continuity, and finite-dimension of message space. Furthermore, it works not only for three or more agents, but also for two-agent economies.     

The Pazner-Schmeidler social ordering: A defense

It is shown that the Pazner-Schmeidler social ordering appears as a very natural solution to the problem of defining social preferences over distributions of divisible goods. The paper analyses various ways of deriving this social ordering from minimally egalitarian conditions and informational parsimony requirements.Received: 10 October 2003, Accepted: 4 April 2005, JEL Classification: D63, D71This paper was written while I was a research fellow at the ZiF (Bielefeld), for the project “Procedural Approaches to Conflict Resolution”, and the last version was prepared during my sabbatical year at Nuffield College, Oxford. I thank my hosts for their hospitality. D. Dimitrov and F. Maniquet have provided valuable comments on an earlier draft. I also thank the audience of a seminar at the U. of Montreal. Finally, the comments of three anonymous referees and the Associate Editor have been very helpful.     

Characterizing neutrality in the voluntary contribution mechanism

When public goods are provided by voluntary contributions, redistribution of initial holdings among an unchanged set of contributors will not alter the Nash equilibrium allocation.Constraint invariance, where a participant faces the same class of constraints even after her endowment is changed, impliesglobal neutrality under a generalized Nash equilibrium concept. Geometrically,path invariance, where the best response path does not move even after the endowment change, is equivalent to global neutrality assuming a sufficiently rich class of economies. We thank Shinji Ohseto, Hiroaki Osana and Stephen Turnbull for their comments. We are also grateful to an anonymous referee and an associate editor for their comments and suggestion. Research was partially supported by the Nomura Foundation for the Social Sciences and the Grant in Aid for General Research 03803008 of the Ministry of Education, Science and Culture of Japan.     

On evolutionarily stable behavior in contests

It is argued in this paper that the solution concept of an evolutionary stable strategy (ESS) is an adequate analysis tool for contest theory. Moreover, it is shown that in a contest ESS always differs from Nash equilibrium, the hitherto dominant solution concept in contest theory. Finally, an interpretation of finite population ESS contest behavior in terms of Nash behavior is supplied.Received: 10 February 2002, Accepted: 8 July 2002, JEL Classification: C79, D72, D 74Wolfgang Leininger: I have benefited from the comments and suggestions of Burkhard Hehenkamp and two anonymous referees.     

The Aubin private core of differential information economies

Abstract We establish characterizations of Radner equilibrium allocations via private core notions in the framework of differential information economies with a finite number of states of nature and a measure space of agents that may have atoms. The commodity space is an ordered separable Banach space whose positive cone admits an interior point. We introduce the notion of Aubin private core and prove that it provides a characterization of Radner equilibrium allocations. We show that the Aubin private core is equivalent to Edgeworth private equilibria and to privately non-dominated allocations of suitable associated economies. Mathematics Subject Classification (2000): 91B50, 91B44 Journal of Economic Literature Classification: D51, D82, D11     

Efficient provision of public goods with endogenous redistribution

We study a balanced mechanism that is capable of implementing in Nash equilibrium all the Pareto-efficient individually rational allocations for an economy with public goods. The Government chooses a set of weights directly related to the Lindahl prices corresponding to the Pareto-efficient allocation to be implemented. The mechanism then guarantees that initial endowments are re-allocated so that the chosen vector of Lindahl prices is indeed a Lindahl equilibrium, and implements the corresponding Lindahl allocation. Finally, besides being balanced, our mechanism is simple. Each agent has to declare a desired increase in the amount of public good, and a vector of redistributive transfers of initial endowments (across other agents).Received: 9 May 2003, Accepted: 22 October 2003, JEL Classification: C79, H21, H30, H41We wish to thank Jeremy Edwards, Andrew Postlewaite and Emanuela Sciubba for helpful comments. Of course, any remaining errors are our own.     

Implementation of the Walrasian correspondence by market games

Abstract. In this paper we present a set of axioms guaranteeing that, in exchange economies with or without indivisible goods, the set of Nash, Strong and active Walrasian Equilibria all coincide in the framework of market games. Received: 25 December 1998 / Accepted: 8 April 2002 We are very grateful to William Thomson for many suggestions. Also we would like to thank comments from J. Alcalde, R. Bhattacharya, C. Herrero, P. Marhuenda, D. Pérez-Castrillo, A. Romero-Medina, T. Shinotsuka, T. Sj?str?m, and A. Villar, an associated editor and an anonymous referee. The first author thanks financial support from DGCYT and Direcció General de Reserca under projects PB98-0870, and SGR2000-00054. The second author wishes to acknowledge financial help from DGCYT under project PB98-0940.     

Non-Walrasian decentralization of the core

We show that in large finite economies, core allocations can be approximately decentralized as Nash (rather than Walras) equilibrium. We argue that this exercise is an essential complement to asymptotic core equivalence results, because it implies that in some approximate sense individual attempts to manipulate the decentralizing prices cannot be beneficial, which fits precisely the interpretation of asymptotic core convergence, namely the emergence of price taking.     

Equilibria and core of large economies

In this paper we apply results on regular economies to study equilibria and core in a non-differentiable framework. We show that the distributions of agents' characteristics of regular economies form a dense subset of all distributions of agents' characteristics. Therefore ‘most’ economies have equilibria which are contained in finitely many ?-balls. And the core of ‘most’ sufficiently large economies is contained in finitely many ?-balls centered at equilibrium allocations of these economies.     

Switching from complete to incomplete information

We construct an elementary mechanism [Dutta, B., Sen, A., Vohra, R., 1995. Nash implementation through elementary mechanisms in economic environments. Review of Economic Design 1, 173–203] that Nash implements the constrained Walrasian correspondence. We extend it to incomplete and non-exclusive information economies by enlarging the message space of agents. In addition, measurability restrictions on allocations with respect to prices proper to constrained rational expectations equilibria are imposed in the outcome function. We show that by imposing such restrictions, the mechanism Bayesian implements the constrained rational expectations equilibrium correspondence. This result shows game-theoretic connections between these two market equilibrium concepts. However, these connections are obtained at the price of strong restrictions on the behavior of agents.     

Repeated implementation and complexity considerations

A game form is commitment-free if single actions of players do not have physical consequences, i.e., affect the continuation game. Such game can be thought to represent inifinite interaction with complete patience. A choice rule can be Nash implemented via a commitment-free mechanism if and only if it coincides with the feasible set of a normal form game. However, when players are complexity averse (in the lexicographic sense), then any Nash implementable choice rule becomes available. I am very grateful to Matt Jackson and a referee for their comments. I also thank Klaus Kultti and Hannu Salonen for useful conversations.     

Optimal money growth in a limited participation model with heterogeneous agents

This paper studies optimal money growth in a cash-in-advance production economy with heterogeneity in patience levels and know-how. We show that the rate of deflation suggested by the Friedman rule is limited by the subjective discount rate of the most patient agent in the economy. The output distortion due to cash-in-advance constraints on firms can completely be eliminated by means of the Friedman rule if and only if firms are run by the most patient agents.Received: 16 August 2003, Accepted: 22 March 2005, JEL Classification: D52, D90, E21, E41, E52Parts of this paper were completed while the first and second authors were visiting the University of York and Princeton University respectively. We are thankful for the hospitality of these institutions. The second author also acknowledges the hospitality and support of Bilkent University that he is currently visiting, the support from the Turkish Academy of Sciences in the framework of the ‘Distinguished Young Scientist Award Program’ (TUBA-GEBIP/2004), the grant awarded by the Scientific and Technical Research Council of Turkey (TUBITAK) under the NATO Science Fellowship Program as well as the support from the Center for Economic Design of Bogaziçi University. This paper was presented in the ERC/METU Second International Conference on Economics, Ankara, September 1998, and at seminars in Bilkent, Bogaziçi and Ohio State Universities. We thank, in particular, Emre Alper, Sumru Altug, Huw Dixon, Tatsuro Ichiishi, Ivan Pastine, Murat Sertel and Alan Sutherland for useful comments. We also thank two anonymous referees for comments and suggestions. The views expressed in this paper are those of the authors and do not necessarily reflect that of the Central Bank of Republic of Turkey.     

Consulting experts with vested interests: The power of benchmarking

A decisionmaker gets independent advice from two experts, who can be of two different types. Experts are risk-neutral and prefer certain policies irrespective of the state of nature, so to induce information-sharing the decisionmaker must reward truthful experts. I show that, in this environment, a heterogeneous committee has no informational advantage over a single expert: a decision rule that encourages one expert to be honest immediately makes honesty less attractive for the other. With a homogenous committee, the higher is the correlation between the experts’ signals, the more the decisionmaker is willing to pay to secure independent advice.Received: April 2004, Accepted: Accepted: January 2005, JEL Classification: D71, D82Lars Frisell: I thank David Austen-Smith, Tim Feddersen, Johan Lagerlöf, Jan Potters, Ken Shotts, Jonas Vlachos, Jörgen W. Weibull, an anonymous referee, and especially Karl Wärneryd for helpful comments. Financial support from the Jan Wallander and Tom Hedelius Foundation and the Sweden-America Foundation is gratefully acknowledged.     

Rational expectations equilibrium and the strategic choice of costly information

This paper studies costly information acquisition in one-good production economies when agents acquire private information and prices transmit information. Before asset markets open, agents choose the quality of their private information. After this information stage, agents trade assets in sequentially complete markets taking into account their private information and the information revealed by equilibrium prices (rational expectations equilibrium, (Radner, R., 1979. Rational expectations equilibrium: generic existence and the information revealed by prices, Econometrica 47, 655–678.)). An overall equilibrium in asset and information market is defined as a Nash equilibrium of the information game in which agents’ actions are information choices and their utility payoffs are the ex-ante expected utilities of the corresponding rationale expectations equilibrium. This paper shows that for a generic set of economies parameterized by endowments and productivity shocks, an overall equilibrium in information and asset market (a Nash equilibrium of the induced information game) with costly information acquisition and fully-revealing prices exists. In other words, informational efficiency is in general consistent with costly information acquisition.     

Convergence to competitive equilibria and elimination of no-trade (in a strategic market game with limit prices)

The strategic market games literature contains many results that predict Walrasian equilibria in the competitive limit. However, they usually come at the expense of ad hoc assumptions that rule out “pathological” no trade equilibria. This paper studies a strategic market game with limit prices. The set of Nash equilibrium allocations of this game converges to the set containing all competitive equilibria and no-trade, when players are replicated. Moreover, two rounds of iterated deletion of weakly dominated strategies eliminate the no-trade equilibria. Hence, replication paired with two rounds of iterated dominance gives a clean prediction of competitive equilibrium.