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Countably Additive Subjective Probabilities

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  • Stinchcombe, Maxwell B

Abstract

The subjective probabilities implied by L. J. Savage's (1954, 1972) postulates are finitely but not countably additive. The failure of countable additivity leads to two known classes of dominance paradoxes, money pumps and indifference between an act and one that pointwise dominates it. There is a common resolution to these classes of paradoxes and to any others that might arise from failures of countable additivity. It consists of reinterpreting finitely additive probabilities as the 'traces' of countably additive probabilities on larger state spaces. The new and larger state spaces preserve the essential decision-theoretic structures of the original spaces. Copyright 1997 by The Review of Economic Studies Limited.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 64 (1997)
Issue (Month): 1 (January)
Pages: 125-46

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Handle: RePEc:bla:restud:v:64:y:1997:i:1:p:125-46

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Cited by:
  1. João Correia-da-Silva, 2008. "Agreeing to disagree in a countable space of equiprobable states," FEP Working Papers 260, Universidade do Porto, Faculdade de Economia do Porto.
  2. Sarin, R. & Wakker, P.P., 1996. "A Single-Stage Approach to Anscombe and Aumann's Expected Utility," Discussion Paper 1996-45, Tilburg University, Center for Economic Research.
  3. João Correia-da-Silva, 2010. "Agreeing to disagree in a countable space of equiprobable states of nature," Economic Theory, Springer, vol. 45(1), pages 291-302, October.
  4. Stinchcombe, Maxwell B., 2005. "Nash equilibrium and generalized integration for infinite normal form games," Games and Economic Behavior, Elsevier, vol. 50(2), pages 332-365, February.
  5. Martin Dumav & Maxwell B. Stinchcombe, 2013. "The von Neumann/Morgenstern approach to ambiguity," Working Papers 480, Bielefeld University, Center for Mathematical Economics.
  6. Stinchcombe, Maxwell B., 2011. "Correlated equilibrium existence for infinite games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 146(2), pages 638-655, March.

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