Updating ambiguity averse preferences

Eran Hanany; Peter Klibanoff

doi:10.2202/1935-1704.1547

Updating ambiguity averse preferences

Eran Hanany^*, Peter Klibanoff

^*Corresponding author for this work

Managerial Economics, Decision Sciences and Operations

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.

Original language	English (US)
Article number	37
Journal	B.E. Journal of Theoretical Economics
Volume	9
Issue number	1
DOIs	https://doi.org/10.2202/1935-1704.1547
State	Published - 2009

Funding

KEYWORDS: updating, dynamic consistency, ambiguity, regret, Ellsberg, Bayesian, consequentialism, smooth ambiguity ∗We thank Nabil Al-Najjar, Sandeep Baliga, Eddie Dekel, Jurgen Eichberger, Larry Epstein, Raphaël Giraud, Simon Grant, Ian Jewitt, Massimo Marinacci, Sujoy Mukerji, Bob Nau, Ben Polak, Chris Shannon, Marciano Siniscalchi, Tomasz Strzalecki, Kane Sweeney, Tim Van Zandt and especially Fabio Maccheroni for helpful comments and discussion. We also thank the coeditor, Federico Echenique, and two anonymous referees for their comments. Additional thanks to seminar audiences at INSEAD, HEC, Johns Hopkins, Northwestern and Technion and at FUR XII, RUD ‘07, Fall ’07 Midwest Economic Theory, ESNASM ’08, the 3rd Israeli Game Theory Conference and the 3rd World Congress of the Game Theory Society. This research was partially supported by Grant No. 2006264 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

Keywords

Ambiguity
Bayesian
Consequentialism
Dynamic consistency
Ellsberg
Regret
Smooth ambiguity
Updating

ASJC Scopus subject areas

General Economics, Econometrics and Finance

Access to Document

10.2202/1935-1704.1547

Cite this

@article{ab312ec29b6d4a2c8fde7183f186ef8d,

title = "Updating ambiguity averse preferences",

abstract = "Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.",

keywords = "Ambiguity, Bayesian, Consequentialism, Dynamic consistency, Ellsberg, Regret, Smooth ambiguity, Updating",

author = "Eran Hanany and Peter Klibanoff",

note = "Funding Information: KEYWORDS: updating, dynamic consistency, ambiguity, regret, Ellsberg, Bayesian, consequentialism, smooth ambiguity ∗We thank Nabil Al-Najjar, Sandeep Baliga, Eddie Dekel, Jurgen Eichberger, Larry Epstein, Rapha{\"e}l Giraud, Simon Grant, Ian Jewitt, Massimo Marinacci, Sujoy Mukerji, Bob Nau, Ben Polak, Chris Shannon, Marciano Siniscalchi, Tomasz Strzalecki, Kane Sweeney, Tim Van Zandt and especially Fabio Maccheroni for helpful comments and discussion. We also thank the coeditor, Federico Echenique, and two anonymous referees for their comments. Additional thanks to seminar audiences at INSEAD, HEC, Johns Hopkins, Northwestern and Technion and at FUR XII, RUD {\textquoteleft}07, Fall {\textquoteright}07 Midwest Economic Theory, ESNASM {\textquoteright}08, the 3rd Israeli Game Theory Conference and the 3rd World Congress of the Game Theory Society. This research was partially supported by Grant No. 2006264 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.",

year = "2009",

doi = "10.2202/1935-1704.1547",

language = "English (US)",

volume = "9",

journal = "B.E. Journal of Theoretical Economics",

issn = "1935-1704",

publisher = "Berkeley Electronic Press",

number = "1",

}

TY - JOUR

T1 - Updating ambiguity averse preferences

AU - Hanany, Eran

AU - Klibanoff, Peter

N1 - Funding Information: KEYWORDS: updating, dynamic consistency, ambiguity, regret, Ellsberg, Bayesian, consequentialism, smooth ambiguity ∗We thank Nabil Al-Najjar, Sandeep Baliga, Eddie Dekel, Jurgen Eichberger, Larry Epstein, Raphaël Giraud, Simon Grant, Ian Jewitt, Massimo Marinacci, Sujoy Mukerji, Bob Nau, Ben Polak, Chris Shannon, Marciano Siniscalchi, Tomasz Strzalecki, Kane Sweeney, Tim Van Zandt and especially Fabio Maccheroni for helpful comments and discussion. We also thank the coeditor, Federico Echenique, and two anonymous referees for their comments. Additional thanks to seminar audiences at INSEAD, HEC, Johns Hopkins, Northwestern and Technion and at FUR XII, RUD ‘07, Fall ’07 Midwest Economic Theory, ESNASM ’08, the 3rd Israeli Game Theory Conference and the 3rd World Congress of the Game Theory Society. This research was partially supported by Grant No. 2006264 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.

PY - 2009

Y1 - 2009

N2 - Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.

AB - Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we characterize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As applications of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth ambiguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of the Bayes' rule.

KW - Ambiguity

KW - Bayesian

KW - Consequentialism

KW - Dynamic consistency

KW - Ellsberg

KW - Regret

KW - Smooth ambiguity

KW - Updating

UR - http://www.scopus.com/inward/record.url?scp=73149100133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73149100133&partnerID=8YFLogxK

U2 - 10.2202/1935-1704.1547

DO - 10.2202/1935-1704.1547

M3 - Article

AN - SCOPUS:73149100133

SN - 1935-1704

VL - 9

JO - B.E. Journal of Theoretical Economics

JF - B.E. Journal of Theoretical Economics

IS - 1

M1 - 37

ER -

Updating ambiguity averse preferences

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this