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1.
We introduce and analyze three definitions of equilibrium for finite extensive games with imperfect information and ambiguity averse players. In a setting where players’ preferences are represented by maxmin expected utility, as characterized in Gilboa and Schmeidler (J Math Econ 18(2):141–153, 1989), our definitions capture the intuition that players may consider the possibility of slight arbitrary mistakes. This generalizes the idea leading to trembling-hand perfect equilibrium as introduced in Selten (Int J Game Theory 4(1):25–55, 1975), by allowing for ambiguous trembles characterized by sets of distributions. We prove existence for two of our equilibrium notions and relate our definitions to standard equilibrium concepts with expected utility maximizing players. Our analysis shows that ambiguity aversion can lead to behavioral implications that are distinct from those attained under expected utility maximization, even if ambiguous beliefs only arise from the possibility of slight mistakes in the implementation of unambiguous strategies.  相似文献   

2.
We modify the epistemic conditions for Nash equilibrium only to accommodate Gilboa and Schmeidler's [I. Gilboa, D. Schmeidler, Maxmin expected utility with nonunique prior, J. Math. Econ. 18 (1989) 141-153] maxmin expected utility preferences, and identify the equilibrium concept in n-player strategic games that characterizes the modified epistemic conditions. The epistemic characterization supports the equilibrium concept as a minimal generalization of Nash equilibrium, in the sense that it deviates from Nash equilibrium only in terms of players' attitude towards ambiguity. Consequently, comparing it with Nash equilibrium constitutes a ceteris paribus study of the effects of ambiguity on how a game is played. For example, with ambiguity, (beliefs about) action choices are in general correlated.  相似文献   

3.
Summary This paper examines the effects of extrinsic uncertainty or sunspots on competitive equilibrium when financial markets are incomplete. For the canonical two-period, pure-exchange model with bonds (or so-called nominal assets, yielding fixed overall returns specified in units of account, and including pure inside money), the following result is established: Generically in endowments, if there areS sunspot states in the second period, but only 0<I<S distinct types of bonds, then — corresponding to the inherent deficiency in the financial markets — sunspots will generateD=SI dimensions of consumption allocation or real (as well as spot price or nominal) indeterminacy.  相似文献   

4.
Extensive Form Games with Uncertainty Averse Players   总被引:1,自引:0,他引:1  
Nash equilibrium presumes that the beliefs of a player are represented by a probability measure. Motivated by the Ellsberg Paradox and relevant experimental findings demonstrating that this representation of beliefs may be unrealistic, this paper generalizes Nash equilibrium in finite extensive form games to allow for preferences conforming to the multiple priors model developed by Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153]. The implications of this generalization for strategy choices and welfare are studied. Journal of Economic Literature Classification Numbers: C72, D81.  相似文献   

5.
The paper applies the rule for adaptation of the aspiration level suggested by Gilboa and Schmeidler to a situation in which the similarity between acts is represented by an arbitrary similarity function [Gilboa, I., Schmeidler, D., 1996. Case-based optimization. Games Econ. Behav. 15, 1–26]. I show that the optimality result derived by Gilboa and Schmeidler in general fails. With a concave similarity function, only corner acts are chosen in the limit. The optimality result can be reestablished by introducing convex regions into the similarity function and modifying the aspiration adaptation rule. A similarity function which is “sufficiently convex” allows approximating optimal behavior with an arbitrary degree of precision.  相似文献   

6.
Attitude toward imprecise information   总被引:3,自引:0,他引:3  
This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.  相似文献   

7.
Summary. In a multiple priors model á la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and non-atomicity of all priors.Received: 25 November 2002, Revised: 24 June 2004, JEL Classification Numbers: D81.We thank Roko Aliprantis, Maristella Botticini, Erio Castagnoli, Larry Epstein, Paolo Ghirardato, Itzhak Gilboa, Luigi Montrucchio, David Schmeidler, Marciano Siniscalchi, an Associate Editor, and an anonymous referee for helpful discussions. Fabio Maccheroni and Massimo Marinacci gratefully acknowledge the financial support of MIUR and NOMOS Sistema (Milano).  相似文献   

8.
Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.  相似文献   

9.
Summary. This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumers preferences: dependence upon prices and dependence upon other agents consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].Received: 25 May 2004, Revised: 19 October 2004, JEL Classification Numbers: D62, D51, H23. Correspondence to: Bernard CornetThis paper has benefited from comments and valuable discussions with Erik Balder, Stefan Balint, Jean-Marc Bonnisseau, Alessandro Citanna, Gael Giraud, Filipe Martins-da-Rocha, Jean-Philippe Médecin, Jean-François Mertens, Nicholas Yannelis and an anonymous referee.  相似文献   

10.
Summary. Economists have long argued that loan contracts should be indexed to remove the risks arising from fluctuations in the purchasing power of money: indexation however while eliminating one risk, substitutes another, arising from fluctuations in relative prices of goods. We present a theoretical framework which permits the relative merits of a nominal versus an indexed bond to be assessed in a general equilibrium setting. Received: July 31, 1995; revised version August 7, 1996  相似文献   

11.
Summary. We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al. , 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and endstate fairness.Received: 9 September 2003, Revised: 12 December 2004, JEL Classification Numbers: C78, D63. Correspondence to: Flip KlijnWe thank two referees and a co-editor for helpful comments and suggestions. B. Klauss and F. Klijns research has been supported by Ramón y Cajal contracts of the Spanish Ministerio de Ciencia y Tecnología. The work of the authors has also been partially supported by Research Grant BEC2002-02130 from the Spanish Ministerio de Ciencia y Tecnología and by the Barcelona Economics Program of CREA. This paper is part of the Polarization and Conflict Project CIT-2-CT-2004-506084 funded by the European Commission-DG Research Sixth Framework Programme. This article reflects only the authors views and the Community is not liable for any use that may be made of the information contained therein.  相似文献   

12.
Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997  相似文献   

13.
14.
15.
Summary This paper examines the efficiency properties of competitive equilibrium in an economy with adverse selection. The agents (firms and households) in this economy exchange contracts, which specify all the relevant aspects of their interaction. Markets are assumed to be complete, in the sense that all possible contracts can, in principle, be traded. Since prices are specified as part of the contract, they cannot be used as free parameters to equate supply and demand in the market for the contract. Instead, equilibrium is achieved by adjusting the probability of trade. If the contract space is sufficiently rich, it can be shown that rationing will not be observed in equilibrium. A further refinement of equilibrium is proposed, restricting agents' beliefs about contracts that are not traded in equilibrium. Incentive-efficient and constrained incentive-efficient allocations are defined to be solutions to appropriately specified mechanism design problems. Constrained incentive efficiency is an artificial construction, obtained by adding the constraint that all contracts yield the same rate of return to firms. Using this notion, analogues of the fundamental theorems of welfare economics can be proved: all refined equilibria are constrained incentive-efficient and all constrained incentive-efficient allocations satisfying some additional conditions can be decentralized as refined equilibria. A constrained incentive-efficient equilibrium is typically not incentive-efficient, however. The source of the inefficiency is the equilibrium condition that forces all firms to earn the same rate of return on each contract.Notation ={ 1,..., k } set of outcomes - : + generic contract or lottery - A = () ; - Ao A{, where denotes the null contract or no trade - S={1,...,¦S¦} set of seller types - L(s) number of type-s sellers - M number of buyers - u: × S seller's utility function, which can be extended toA× S by puttingu(, s) ; - v. × S buyer's utility function, which can be extended toA × S by puttingv(, s) ; - f:A 0 ×S + allocation of sellers - g:A 0 ×S + allocation of buyers - A + sellers' trading function - :A ×S + buyers' trading function This paper has had a long gestation period, during which I have been influenced by helpful conversations with many persons, by their work, or both. Among those who deserve special mention are Martin Hellwig, Roger Myerson, Edward Prescott, Robert Townsend and Yves Younés. Earlier versions were presented to the NBER/CEME Conference on Decentralization at the University of Toronto and the NBER Conference on General Equilibrium at Brown University. I would like to thank John Geanakoplos, Walter Heller, Andreu Mas Colell, Michael Peters, Michel Poitevin, Lloyd Shapley, John Wooders, Nicholas Yannelis and an anonymous referee for their helpful comments and especially Robert Rosenthal for his careful reading of two drafts. The financial support of the National Science Foundation under Grant No. 912202 is gratefully acknowledged.  相似文献   

16.
Due to lag structure, currency devaluation is said to worsen the trade balance first and improve it later resulting in a pattern that resemble the letter J, hence the J-Curve phenomenon. Since its introduction by Magee in 1973 Magee, SP. 1973. Currency contracts, pass through and devaluation. Brooking Papers on Economic Activity, 1: 30325.   (Brooking Papers on Economic Activity, 1, pp. 303–25), a large number of studies have attempted to test the phenomenon using different techniques and different model specifications. The results are at best ambiguous and deserve to be collected together for the future generation of researchers and graduate students. This paper fills such a vacuum in the literature by reviewing the J-Curve related empirical papers.  相似文献   

17.
This paper examines how price setting plays a key role in explaining the steady-state effects of inflation in a monopolistic competition economy with transactions-facilitating money. Three pricing variants (optimal prices, indexed prices, and unchanged prices) are introduced through a generalization of the Calvo-type setting that allows price indexation. We found that in an economy with less indexed prices, the steady-state negative impact of inflation on output is higher. Regarding welfare analysis, our results support a long-run monetary policy aimed at price stability with a close-to-zero inflation target. This finding is robust to any price setting scenario.JEL Classification: E13, E31, E50The writing of this paper commenced during the time I spent on the Research Visitors Programme 2001 of the European Central Bank and an earlier version of the paper became ECB Working Paper No. 140. I would like to thank Bennett T. McCallum, Frank Smets, and Oscar Bajo-Rubio for their valuable comments and suggestions, and the Ministerio de Ciencia y Tecnología of Spain for its financial support (Research Project 2002/00954).  相似文献   

18.
Uncertainty is an obstacle for commitments under cap and trade schemes for emission permits. We assess how well intensity targets, where each country’s permit allocation is indexed to its future realized GDP, can cope with uncertainties in international greenhouse emissions trading. We present some empirical foundations for intensity targets and derive a simple rule for the optimal degree of indexation to GDP. Using an 18-region simulation model of a cooperative, global cap-and-trade treaty in 2020 under multiple uncertainties and endogenous commitments, we show that optimal intensity targets could reduce the cost of uncertainty and achieve significant increases in global abatement. The optimal degree of indexation to GDP would vary greatly between countries, including super-indexation in some advanced countries, and partial indexation for most developing countries. Standard intensity targets (with one-to-one indexation) would also improve the overall outcome, but to a lesser degree and not in all individual cases. Although target indexation is no magic wand for a future global climate treaty, gains from reduced cost uncertainty and the potential for more stringent environmental commitments could justify the increased complexity and other potential downsides of intensity targets.   相似文献   

19.
Summary A semiorder can be thought of as a binary relationP for which there is a utilityu representing it in the following sense:xPy iffu(x) –u(y) > 1. We argue that weak orders (for which indifference is transitive) can not be considered a successful approximation of semiorders; for instance, a utility function representing a semiorder in the manner mentioned above is almost unique, i.e. cardinal and not only ordinal. In this paper we deal with semiorders on a product space and their relation to given semiorders on the original spaces. Following the intuition of Rubinstein we find surprising results: with the appropriate framework, it turns out that a Savage-type expected utility requires significantly weaker axioms than it does in the context of weak orders.We wish to thank Tatsuro Ichiishi, Jorge Nieto, Ariel Rubinstein, Efraim Sadka and especially David Schmeidler and anonymous referees for stimulating discussions and comments. I. Gilboa received partial financial support from NSF grants nos. IRI-8814672 and SES-9113108, as well as from the Alfred P. Sloan Foundation.  相似文献   

20.
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