Universal Interactive Preferences

We prove that a universal preference type space exists under much more general conditions than those postulated by Epstein and Wang (1996). To wit, it is enough that preferences can be encoded by a countable collection of continuous functionals, while the preferences themselves need not necessarily be continuous or regular, like, e.g., in the case of lexicographic preferences. The proof relies on a far-reaching generalization of a method developed by Heifetz and Samet (1998).

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

[2]  P. Meyer,et al.  Probabilities and potential C , 1978 .

[3]  Byung-Soo Lee,et al.  Admissibility and assumption , 2016, J. Econ. Theory.

[4]  Larry G. Epstein,et al.  "Beliefs about Beliefs" without Probabilities , 1996 .

[5]  S. Zamir,et al.  Formulation of Bayesian analysis for games with incomplete information , 1985 .

[6]  A. Tversky,et al.  An axiomatization of cumulative prospect theory , 1993 .

[7]  Byung Soo Lee,et al.  Conditional Beliefs and Higher-Order Preferences , 2013 .

[8]  Edi Karni,et al.  On State-Dependent Prefer-ences and Subjective Probabilities , 1983 .

[9]  P. Wakker Prospect Theory: For Risk and Ambiguity , 2010 .

[10]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[11]  Marciano M. Siniscalchi,et al.  Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games , 1999 .

[12]  Burkhard C. Schipper,et al.  Unawareness, Beliefs, and Speculative Trade , 2012, Games Econ. Behav..

[13]  David S. Ahn Hierarchies of ambiguous beliefs , 2007, J. Econ. Theory.

[14]  A. Rényi,et al.  On Conditional Probability Spaces Generated by a Dimensionally Ordered Set of Measures , 1956 .

[15]  Martin Meier Universal knowledge-belief structures , 2008, Games Econ. Behav..

[16]  I. Gilboa,et al.  Advances in Economics and Econometrics: Ambiguity and the Bayesian Paradigm , 2011 .

[17]  Miklós Pintér,et al.  Generalized type spaces , 2011 .

[18]  Massimo Marinacci,et al.  Uncertainty averse preferences , 2011, J. Econ. Theory.

[19]  J. Schreiber Foundations Of Statistics , 2016 .

[20]  A. Heifetz,et al.  All Types Naive and Canny , 2012 .

[21]  Eddie Dekel,et al.  Lexicographic Probabilities and Choice Under Uncertainty , 1991 .

[22]  Massimo Marinacci,et al.  Social Decision Theory: Choosing within and between Groups , 2012 .

[23]  Dov Samet,et al.  Knowledge Spaces with Arbitrarily High Rank , 1998 .

[24]  Martin Meier,et al.  Hierarchies of beliefs for compact possibility models , 2005 .

[25]  A. Heifetz The bayesian formulation of incomplete information — The non-compact case , 1993 .

[26]  Yi-Chun Chen,et al.  Universality of the Epstein-Wang type structure , 2010, Games Econ. Behav..

[27]  Dov Samet,et al.  Coherent beliefs are not always types , 1999 .

[28]  Lawrence S. Moss,et al.  Harsanyi Type Spaces and Final Coalgebras Constructed from Satisfied Theories , 2004, CMCS.

[29]  A. Heifetz,et al.  Topology-Free Typology of Beliefs , 1998 .

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

[31]  Eddie Dekel,et al.  Hierarchies of Beliefs and Common Knowledge , 1993 .

[32]  Alfredo Di Tillio,et al.  Subjective Expected Utility in Games , 2009 .

[33]  Sylvain Sorin,et al.  Repeated Games. Part A: Background Material , 1994 .

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

[35]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[36]  Brian Hill,et al.  An additively separable representation in the Savage framework , 2010, J. Econ. Theory.

[37]  Faruk Gul,et al.  Interdependent preference models as a theory of intentions , 2016, J. Econ. Theory.

[38]  Edi Karni,et al.  Subjective Expected Utility With Incomplete Preferences , 2013 .

[39]  Marciano M. Siniscalchi,et al.  Vector Expected Utility and Attitudes Toward Variation , 2008 .

[40]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[41]  D. Bergemann,et al.  Interdependent Preferences and Strategic Distinguishability , 2016 .

[42]  Efe A. Ok,et al.  Incomplete preferences under uncertainty: Indecisiveness in beliefs versus tastes , 2012 .

[43]  Peter P. Wakker,et al.  State Dependent Expected Utility for Savage's State Space , 1999, Math. Oper. Res..

[44]  W. Kets Bounded Reasoning and Higher-Order Uncertainty , 2012 .