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Updating non-additive probabilities-- a geometric approach

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  • Lehrer, Ehud

Abstract

A geometric approach, analogous to the approach used in the additive case, is proposed to determine the conditional expectation with non- additive probabilities. The conditional expectation is then applied for (i) updating the probability when new information becomes available; and (ii) defining the notion of independence of non-additive probabilities and Nash equilibrium.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4DXB98G-3/2/c2da0301429ddf82b691012dffc74b82
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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 50 (2005)
Issue (Month): 1 (January)
Pages: 42-57

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Handle: RePEc:eee:gamebe:v:50:y:2005:i:1:p:42-57

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
  2. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  3. Itzhak Gilboa & Ehud Lehrer, 1989. "The Value of Information -- An Axiomatic Approach," Discussion Papers 835, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Sarin, R. & Wakker, P.P., 1996. "Revealed likelihood and knightian uncertainty," Discussion Paper 1996-59, Tilburg University, Center for Economic Research.
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Cited by:
  1. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.
  2. André Lapied & Robert Kast, 2009. "Updating Choquet valuation and discounting information arrivals," Working Papers halshs-00410532, HAL.
  3. Dominiak, Adam & Duersch, Peter & Lefort, Jean-Philippe, 2012. "A dynamic Ellsberg urn experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 625-638.
  4. Jean-Philippe Lefort, 2006. "Comparison of experts in the non-additive case," Cahiers de la Maison des Sciences Economiques b06088, Université Panthéon-Sorbonne (Paris 1).
  5. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.

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