A Subjective Spin on Roulette Wheels

We provide a behavioral foundation to the notion of ‘mixture’ of acts, which is used to great advantage in he decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully sub-jective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may ‘distort’ the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley’s model of choice with incomplete preferences.

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

[2]  I. Gilboa.  Expected utility with purely subjective non-additive probabilities , 1987 .

[3]  Edi Karni,et al.  Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence , 1994 .

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

[5]  David M. Kreps.  Static choice in the presence of unforeseen contingencies , 1992 .

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

[7]  Massimo Marinacci,et al.  A Subjective Spin on Roulette Wheels , 2001 .

[8]  David Schmeidleis.  SUBJECTIVE PROBABILITY AND EXPECTED UTILITY WITHOUT ADDITIVITY , 1989 .

[9]  H. Raiffa,et al.  The Foundations of Decision under Uncertainty: An Elementary Exposition , 1964 .

[10]  Faruk Gul.  A Theory of Disappointment Aversion , 1991 .

[11]  Luigi Montrucchio,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESOn Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type ∗ , 2001 .

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

[13]  L. Montrucchio,et al.  Subcalculus for set functions and cores of TU games , 2003 .

[14]  G. Choquet.  Theory of capacities , 1954 .

[15]  D. Schmeidler,et al.  A More Robust Definition of Subjective Probability , 1992 .

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

[17]  Massimo Marinacci,et al.  Probabilistic Sophistication and Multiple Priors , 2002 .

[18]  Massimo Marinacci,et al.  Ambiguity Made Precise: A Comparative Foundation , 1998, J. Econ. Theory.

[19]  Klaus Nehring,et al.  Preference for Flexibility in a Savage Framework , 1999 .

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

[21]  A. Copeland.  Review: John von Neumann and Oskar Morgenstern, Theory of games and economic behavior , 1945 .

[22]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[23]  D. Schmeidler,et al.  Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice , 1995 .

[24]  Massimo Marinacci,et al.  Ambiguity from the Differential Viewpoint , 2002 .

[25]  Massimo Marinacci,et al.  Random Correspondences as Bundles of Random Variables , 2001 .

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

[27]  Mark J. Machina,et al.  Almost-objective uncertainty , 2001 .

[28]  Andrea Roncoroni.  Change of numéraire for affine arbitrage pricing models driven by multifactor marked point processes , 2001 .

[29]  Peter C. Fishburn,et al.  Utility theory for decision making , 1970 .

[30]  T. Bewley.  Knightian decision theory. Part I , 2002 .

[31]  Ramon Casadesus-Masanell,et al.  Maxmin Expected Utility over Savage Acts with a Set of Priors , 2000, J. Econ. Theory.

[32]  Faruk Gul,et al.  Savagés theorem with a finite number of states , 1992 .

[33]  Yutaka Nakamura.  Subjective expected utility with non-additive probabilities on finite state spaces , 1990 .

[34]  Emre Ozdenoren,et al.  Completing the State Space with Subjective States , 2002, J. Econ. Theory.

[35]  Ramon Casadesus-Masanell,et al.  Maxmin expected utility through statewise combinations , 2000 .

[36]  R. Luce.  Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches , 2000 .

[37]  Domenico Menicucci,et al.  APPLIED MATHEMATICS WORKING PAPER SERIESOptimal Two-Object Auctions with Synergies * , 2001 .