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A subjective spin on roulette wheels

Author

Listed:
  • Paolo Ghirardato
  • Fabio Maccheroni
  • Massimo Marinacci
  • Marciano Siniscalchi

Abstract

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.

Suggested Citation

  • Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
    • Handle: RePEc:icr:wpmath:17-2001
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    References listed on IDEAS

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    1. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin Expected Utility over Savage Acts with a Set of Priors," Journal of Economic Theory, Elsevier, vol. 92(1), pages 35-65, May.
    2. Casadesus-Masanell, Ramon & Klibanoff, Peter & Ozdenoren, Emre, 2000. "Maxmin expected utility through statewise combinations," Economics Letters, Elsevier, vol. 66(1), pages 49-54, January.
    3. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April.
    4. Ramon Casadesus-Masanell & Peter Klibanoff & Emre Ozdenoren, 1998. "Maximum Expected Utility over Savage Acts with a Set of Priors," Discussion Papers 1218, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
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