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Multiagent belief revision

Author

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  • Billot, Antoine
  • Vergnaud, Jean-Christophe
  • Walliser, Bernard

Abstract

An original epistemic framework is proposed for the modeling of beliefs and messages within a multiagent belief setting. This framework enables public, private and secret messages as well, even when the latter contains errors. A revising rule—i.e. the product rule—is introduced in pure epistemic terms in order to be applied to all structures and message. Since any syntactic structure can be expressed through various semantic ones, an equivalence principle is given by use of the semantic notion of bisimilarity. Thereafter, a robustness result proves that, for a given prior structure, bisimilar messages yield bisimilar posterior structures (Theorem 1). In syntax, the beliefs revised thanks to the product rule are then shown to be unique (Theorem 2). Finally, an equivalence theorem is established between the product rule and the Belief-Message Inference axiom (Theorem 3).

Suggested Citation

  • Billot, Antoine & Vergnaud, Jean-Christophe & Walliser, Bernard, 2015. "Multiagent belief revision," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 47-57.
  • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:47-57
    DOI: 10.1016/j.jmateco.2015.05.004
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    References listed on IDEAS

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    1. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1982. "We can't disagree forever," Journal of Economic Theory, Elsevier, vol. 28(1), pages 192-200, October.
    2. Board, Oliver, 2004. "Dynamic interactive epistemology," Games and Economic Behavior, Elsevier, vol. 49(1), pages 49-80, October.
    3. Giacomo Bonanno, 2004. "A simple modal logic for belief revision," Working Papers 45, University of California, Davis, Department of Economics.
    4. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107401396.
    5. Perea,Andrés, 2012. "Epistemic Game Theory," Cambridge Books, Cambridge University Press, number 9781107008915.
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    Keywords

    Belief; Belief revision; Epistemic logics; Game;

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