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BY PAOLO GHIRARDATO AND MARCIANO SINISCALCHI APPENDIX S.A: LOCALLY LIPSCHITZ PREFERENCES
"... WE CONSIDER A PREFERENCE � that admits a monotonic, continuous, normalized, Bernoullian representation (I � u), and introduce a novel axiom that is equivalent to the assertion that I is locally Lipschitz. 1 Recall that xh ∈ X denotes the certainty equivalent of act h ∈ F. AXIOM 1—Locally Bounded Imp ..."
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WE CONSIDER A PREFERENCE � that admits a monotonic, continuous, normalized, Bernoullian representation (I � u), and introduce a novel axiom that is equivalent to the assertion that I is locally Lipschitz. 1 Recall that xh ∈ X denotes the certainty equivalent of act h ∈ F. AXIOM 1—Locally Bounded Improvements: For every h ∈ F int, there are y ∈ X and g ∈ F with g(s) ≻ h(s) for all s such that, for all (h n) ⊂ F and (λ n) ⊂ [0 � 1] with h n → h and λ n ↓ 0, λ n g + ( 1 − λ n) h n ≺ λ n y + ( 1 − λ n) xh n eventually. To gain intuition, focus on the constant sequence with h n = h. Since preferences are Bernoullian, the individual’s evaluation of λy + (1 − λ)xh changes linearly with λ. On the other hand, her evaluation of λg + (1 − λ)h may improve in arbitrary nonlinear (though continuous) ways as λ increases from 0 to 1 (recall that g is pointwise preferred to h). The axiom states that when λ is close to 0, this improvement is comparable to the linear change in preference that applies to λy + (1 − λ)xh (which may still be very rapid, if y is much preferred to xh). Hence, it imposes a bound on the instantaneous rate of change in preferences as a function of λ. Furthermore, this bound is required to be uniform in a neighborhood of h. PROPOSITION S1: Let � be a preference that admits a monotonic, continuous, Bernoullian, normalized representation (I � u). Then � satisfies Axiom 1 if and only if I is locally Lipschitz in the interior of its domain. PROOF: If. Functionally, the displayed equation in Axiom 1 is equivalent to
Massimo MarinacciRevealed Ambiguity and Its Consequences: Updating 1
, 2007
"... 2002). We are grateful to Marciano Siniscalchi for many conversations on the topic of this paper. ..."
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2002). We are grateful to Marciano Siniscalchi for many conversations on the topic of this paper.
Risk Sharing in the Small and in the Large
, 2015
"... www.carloalberto.org/research/workingpapers © 2014 by Paolo Ghirardato and Marciano Siniscalchi. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto. ..."
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www.carloalberto.org/research/workingpapers © 2014 by Paolo Ghirardato and Marciano Siniscalchi. Any opinions expressed here are those of the authors and not those of the Collegio Carlo Alberto.
Axiomatic foundations of multiplier preferences
, 2007
"... This paper axiomatizes the robust control criterion of multiplier preferences introduced by Hansen and Sargent (2001). The axiomatization relates multiplier preferences to other classes of preferences studied in decision theory. Some properties of multiplier preferences are generalized to the broade ..."
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Cited by 31 (3 self)
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of observable choice data and provides a useful tool for applications. I am indebted to my advisor Eddie Dekel for his continuous guidance, support, and encouragement. I am grateful to Peter Klibanoff and Marciano Siniscalchi for many discussions which resulted in significant improvements of the paper. I would
A Subjective Spin on Roulette Wheels
, 2001
"... We provide a behavioral foundation to the notion of `mixture' of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann [1]. Our construction allows one to formulate mixturespace axioms even in a fully subjective setting, without assuming the existence ..."
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Utility, Incomplete Preferences A Subjective Spin on Roulette Wheels # Paolo Ghirardato Fabio Maccheroni Massimo Marinacci Marciano Siniscalchi
Robust Multiplicity with a Grain of Naiveté∗
, 2013
"... In an important paper, Weinstein and Yildiz (2007) show that if players have an infinite depth of reasoning and this is commonly believed, types generically have a unique rationalizable action in games that satisfy a richness condition. We show that this result does not extend to environments where ..."
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that it is common belief that players have an infinite depth, if only slightly. ∗This paper supersedes Heifetz and Kets (2011). We thank Sandeep Baliga, Eddie Dekel, Alessandro Pavan, David Pearce, Marciano Siniscalchi, and Satoru Takahashi for valuable input, and we are grateful to
Parametric Representation of Preferences∗†
, 2010
"... A preference is invariant with respect to a transformation τ if its ranking of acts is unaffected by a reshuffling of the states under τ. We show that any invariant preference must be parametric: there is a unique sufficient set of parameters such that the preference ranks acts according to their ex ..."
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here, including subjective sufficient statistic theorem, parametric representations, and parameterbased acts appeared there, as did the major technical results on ergodic theory. †We thank Paolo Ghirardato, Ben Polak and Marciano Siniscalchi for extensive discussions and thoughtful comments when we
Context E¤ects: A Representation of Choices from Categories
, 2007
"... This paper axiomatizes a utility representation for referencedependent preferences over menus of lotteries. Most papers in the relevant literature use as the reference point some status quo element and characterize the complete set of preferences by using various assumptions on how the conditional ..."
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and the moment of the choice of the most preferred option within the menu. I would like to thank Marciano Siniscalchi for very helpful comments and discussions. I also thank comments
Theoretical Economics 7 (2012), 57–98 15557561/20120057 Forward induction reasoning revisited
"... Battigalli and Siniscalchi (2002) formalize the idea of forward induction reasoning as “rationality and common strong belief of rationality ” (RCSBR). Here we study the behavioral implications of RCSBR across all type structures. Formally, we show that RCSBR is characterized by a solution concept we ..."
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Battigalli and Siniscalchi (2002) formalize the idea of forward induction reasoning as “rationality and common strong belief of rationality ” (RCSBR). Here we study the behavioral implications of RCSBR across all type structures. Formally, we show that RCSBR is characterized by a solution concept
Choice Under Uncertainty with the Best and Worst in Mind: Neoadditive Capacities
 Journal of Economic Theory
, 2007
"... The concept of a nonextremeoutcomeadditive capacity(neoadditive capacity) is introduced. Neoadditive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies. Moreover, neoadditive capacities can be applied easily in economic problems, ..."
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Cited by 71 (15 self)
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The concept of a nonextremeoutcomeadditive capacity(neoadditive capacity) is introduced. Neoadditive capacities model optimistic and pessimistic attitudes towards uncertainty as observed in many experimental studies. Moreover, neoadditive capacities can be applied easily in economic problems, as we demonstrate by examples. This paper provides an axiomatisation of Choquet expected utility with neocapacities in a framework of purely subjective uncertainty. JEL Classification:
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