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Probabilities on streams and reflexive games

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  • Andrew Schumann

Abstract

Probability measures on streams (e.g. on hypernumbers and p-adic numbers) have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann’s agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level.

Suggested Citation

  • Andrew Schumann, 2014. "Probabilities on streams and reflexive games," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(1), pages 71-96.
  • Handle: RePEc:wut:journl:v:1:y:2014:p:71-96:id:1074
    DOI: 10.5277/ord140105
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    References listed on IDEAS

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    1. Heifetz, Aviad, 1996. "Non-well-founded-Type Spaces," Games and Economic Behavior, Elsevier, vol. 16(2), pages 202-217, October.
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