Dynamic Choice Under Ambiguity

This paper analyzes sophisticated dynamic choice for ambiguity-sensitive decision makers. It characterizes Consistent Planning via axioms on preferences over decision trees. Furthermore, it shows how to elicit conditional preferences from prior preferences. The key axiom is a weakening of Dynamic Consistency, deemed Sophistication. The analysis accommodates arbitrary decision models and updating rules. Hence, the results indicate that (i) ambiguity attitudes, (ii) updating rules, and (iii) sophisticated dynamic choice are mutually orthogonal aspects of preferences. As an example, a characterization of prior-by-prior Bayesian updating and Consistent Planning for arbitrary maxmin-expected utility preferences is presented. The resulting sophisticated MEU preferences are then used to analyze the value of information under ambiguity; a basic trade-off between information acquisition and commitment is highlighted.

[1]  Martin Schneider,et al.  Recursive multiple-priors , 2003, J. Econ. Theory.

[2]  Andrew Caplin,et al.  The recursive approach to time inconsistency , 2006, J. Econ. Theory.

[3]  Faruk Gul,et al.  The Case for Mindless Economics , 2005 .

[4]  Simon Grant,et al.  Preference for Information and Dynamic Consistency , 2000 .

[5]  Ted O’Donoghue,et al.  Doing It Now or Later , 1999 .

[6]  E. McClennen.  Rationality and Dynamic Choice: Foundational Explorations , 1996 .

[7]  Ariel Rubinstein,et al.  On the Interpretation of Decision Problems with Imperfect Recall , 1996, TARK.

[8]  P. Hammond.  Consequentialist foundations for expected utility , 1988 .

[9]  Edi Karni,et al.  Atemporal dynamic consistency and expected utility theory , 1991 .

[10]  R. H. Strotz.  Myopia and Inconsistency in Dynamic Utility Maximization , 1955 .

[11]  J. Eichberger,et al.  Updating Choquet Beliefs , 2007 .

[12]  Eddie Dekel.  An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom , 1986 .

[13]  Alvaro Sandroni,et al.  Non-Bayesian Updating: a Theoretical Framework , 2005 .

[14]  C. Starmer.  Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk , 2000 .

[15]  Evan L. Porteus,et al.  Temporal Resolution of Uncertainty and Dynamic Choice Theory , 1978 .

[16]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[17]  M. Machina.  Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty , 1989 .

[18]  Marciano Siniscalchi.  Bayesian Updating for General Maxmin Expected Utility Preferences , 2001 .

[19]  M. Allais.  Le comportement de l'homme rationnel devant le risque : critique des postulats et axiomes de l'ecole americaine , 1953 .

[20]  Tan Wang,et al.  Conditional preferences and updating , 2003, J. Econ. Theory.

[21]  Eran Hanany,et al.  Updating Preferences with Multiple Priors , 2006 .

[22]  Larry G. Epstein.  An Axiomatic Model of Non-Bayesian Updating , 2006 .

[23]  Costis Skiadas,et al.  Recursive utility and preferences for information , 1998 .

[24]  Marciano M. Siniscalchi.  A Behavioral Characterization of Plausible Priors , 2006, J. Econ. Theory.

[25]  Barton L. Lipman,et al.  REPRESENTING PREFERENCES WITH A UNIQUE SUBJECTIVE STATE SPACE , 2001 .

[26]  Jean-Yves Jaffray,et al.  Dynamic Decision Making with Belief Functions , 1992 .

[27]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[28]  Paolo Ghirardato,et al.  Revisiting Savage in a conditional world , 2002 .

[29]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework , 1989 .

[30]  Zvi Safra,et al.  Behaviorally consistent optimal stopping rules , 1990 .

[31]  Kim C. Border,et al.  Infinite dimensional analysis , 1994 .

[32]  C. Harris,et al.  Existence and Characterization of Perfect Equilibrium in Games of Perfect Information , 1985 .

[33]  Larry G. Epstein,et al.  Dynamically Consistent Beliefs Must Be Bayesian , 1993 .

[34]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[35]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[36]  Emre Ozdenoren,et al.  Subjective recursive expected utility , 2004 .

[37]  Massimo Marinacci,et al.  Dynamic variational preferences , 2006, J. Econ. Theory.

[38]  Peter J. Hammond,et al.  Consistent Plans, Consequentialism, and Expected Utility , 1989 .

[39]  J. D. Carrillo,et al.  Strategic Ignorance as a Self-Disciplining Device , 2000 .

[40]  Faruk Gul,et al.  Betweenness satisfying preferences and dynamic choice , 1990 .

[41]  Wolfgang Pesendorfer,et al.  The Revealed Preference Theory of Changing Tastes , 2005 .

[42]  Itzhak Gilboa,et al.  Updating Ambiguous Beliefs , 1992, TARK.

[43]  Uzi Segal,et al.  Two Stage Lotteries Without the Reduction Axiom , 1990 .

[44]  Robin P. Cubitt,et al.  Dynamic Choice and the Common Ratio Effect: An Experimental Investigation , 1998 .

[45]  C. Pires.  A Rule For Updating Ambiguous Beliefs , 2002 .

[46]  David M. Kreps.  Notes On The Theory Of Choice , 1988 .

[47]  P. Wakker,et al.  Dynamic Choice and NonExpected Utility , 1998 .

[48]  Faruk Gul,et al.  Temptation and Self‐Control , 1999 .

[49]  Massimo Marinacci,et al.  APPLIED MATHEMATICS WORKING PAPER SERIES Risk, Ambiguity, and the Separation of Utility and Beliefs † , 2001 .

[50]  B. Peleg,et al.  On the Existence of a Consistent Course of Action when Tastes are Changing , 1973 .

[51]  J. Quiggin.  A theory of anticipated utility , 1982 .

[52]  Robin P. Cubitt.  RATIONAL DYNAMIC CHOICE AND EXPECTED UTILITY THEORY , 1996 .

[53]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[54]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[55]  David M. Kreps.  A REPRESENTATION THEOREM FOR "PREFERENCE FOR FLEXIBILITY" , 1979 .

[56]  Zvi Safra,et al.  Ascending bid auctions with behaviorally consistent bidders , 1989 .

[57]  Roger B. Myerson,et al.  Axiomatic Foundations of Bayesian Decision Theory , 1986 .