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131
A Smooth Model of Decision Making Under Ambiguity
 Econometrica
, 2005
"... for helpful discussions and suggestions. We also thank three referees and A. Postlewaite, the coeditor, for offering very useful comments and advice. We also thank a number of seminar and conference audiences. We thank MEDS at Northwestern University, ICER at the University of Torino, and Eurequa a ..."
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Cited by 157 (19 self)
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for helpful discussions and suggestions. We also thank three referees and A. Postlewaite, the coeditor, for offering very useful comments and advice. We also thank a number of seminar and conference audiences. We thank MEDS at Northwestern University, ICER at the University of Torino, and Eurequa at the University of Paris 1 for their hospitality during the visits when part of the research was completed. Mukerji gratefully acknowledges financial support from the
2002): “Envelope Theorems for Arbitrary Choice Sets
 Econometrica
"... The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the tradi ..."
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Cited by 107 (9 self)
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The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left and rightdifferentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddlepoint problems, problems with parameterized constraints, and optimal stopping problems.
Representing Preferences with a Unique Subjective State Space
 Econometrica
, 2001
"... for helpful comments. ..."
Topographic Maps and Local Contrast Changes in Natural Images
 Int. J. Comp. Vision
, 1999
"... . We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Ka ..."
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Cited by 51 (8 self)
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. We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusiontransparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. Keywords: topographic map, mathematical morphology, level set, junctions, contrast changes, digitization 1.
Expected Utility Theory without the Completeness Axiom,”Journal of Economic Theory, Volume 115, Issue 1
, 2004
"... We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a mul ..."
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Cited by 28 (5 self)
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We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteriesby meansof a set of von Neumann–Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multiutility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a welldefined sense.
Networks in Labor Markets: Wage and Employment Dynamics and Inequality
 CALVÓARMENGOL, ANTONI AND YANNIS IOANNIDES (2005) “SOCIAL NETWORKS IN LABOR MARKETS,” IN THE NEW PALGRAVE, L. BLUME AND S. DURLAUF (EDS), LONDON: MACMILLAN PRESS (IN PRESS) GRANOVETTER, MARK
, 2003
"... We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wage ..."
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Cited by 28 (2 self)
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We present a model of labor markets that accounts for the social network through which agents hear about jobs. We show that an improvement in the wage or employment status of either an agent's direct or indirect contacts leads to an increase in the agent's employment probability and expected wages, in the sense of first order stochastic dominance. A similar effect results from an increase in the network contacts of an agent. In terms of dynamics and patterns, we show that both wages and employment are positively associated (a strong form of correlation) across time and agents. We also analyze the decisions of agents regarding staying in the labor market or dropping out. If there are costs to staying in the labor market, and we compare two networks of agents that are identical except that one group starts with a worse wage status, then that group's dropout rate will be higher than the other's and there will be a persistent di#erence in wages between the groups.
An Axiomatic Model of NonBayesian Updating
 Rev. Econ. Stud
, 2003
"... This paper models an agent in a threeperiod setting who does not update according to Bayes' Rule, and who is selfaware and anticipates her updating behavior when formulating plans. The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on ..."
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Cited by 21 (5 self)
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This paper models an agent in a threeperiod setting who does not update according to Bayes' Rule, and who is selfaware and anticipates her updating behavior when formulating plans. The agent is rational in the sense that her dynamic behavior is derived from a single stable preference order on a domain of statecontingent menus of acts. A representation theorem generalizes the (dynamic version of) AnscombeAumann's theorem so that both the prior and the way in which it is updated are subjective.
Comparative Statics by Adaptive Dynamics and The Correspondence Principle
 Econometrica
, 2000
"... This paper formalizes the relation between comparative statics and the outofequilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o# learning dynamics that involve larger values of the endoge ..."
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Cited by 21 (6 self)
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This paper formalizes the relation between comparative statics and the outofequilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o# learning dynamics that involve larger values of the endogenous variables. Second, equilibrium selections that are not monotone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent. JEL Classification: C61, C62, C72, C73 Keywords: Monotone comparative statics, supermodularity, strategic complements, learning, correspondence principle. # Discussions with Ilya Segal and Chris Shannon were very important for this work, I am very grateful for all their help. For comments and advice, I also thank Robert Anderson, Juan Dubra, Nestor Gandelman, Ernesto Lopez Cordova, Marcelo Moreira, Charles Pugh, Matthew Rabin, Tarun Sabarwal and Miguel Villa...
Vector Expected Utility and Attitudes toward Variation
, 2007
"... This paper analyzes a model of decision under ambiguity, deemed vector expected utility or VEU. According to the proposed model, an act f: Ω → X is evaluated via the functional V (f) = ..."
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Cited by 19 (3 self)
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This paper analyzes a model of decision under ambiguity, deemed vector expected utility or VEU. According to the proposed model, an act f: Ω → X is evaluated via the functional V (f) =
Ambiguity without a State Space
, 2003
"... Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyzes a third domain of preference: sets of consequential lotte ..."
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Cited by 18 (1 self)
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Many decisions involve both imprecise probabilities and intractable states of the world. Objective expected utility assumes unambiguous probabilities; subjective expected utility assumes a completely specified state space. This paper analyzes a third domain of preference: sets of consequential lotteries. Using this domain, we develop a theory of Knightian ambiguity without explicitly invoking any state space. We characterize a representation that integrates a monotone transformation of first order expected utility with respect to a second order measure. The concavity of the transformation and the weighting of the measure capture ambiguity aversion. We propose a definition for comparative ambiguity aversion and uniquely characterize absolute ambiguity neutrality. Finally, we discuss applications of the theory: reinsurance, games, and a mean–variance–ambiguity portfolio frontier.