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An elementary proof that additive i-likelihood characterizes the supports of consistent assessments

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  • Streufert, Peter A.

Abstract

I prove a convenient reformulation of Kreps and Wilson (1982, Lemma A1), whose proof has a nontrivial gap. Essentially, the support of a consistent assessment is characterized by the additive representability of the infinite-relative-likelihood relation that the support implies. My proof is unexpectedly elementary, for it relies solely on a classic result about additive representation, which in turn relies solely on Farkas’ Lemma.

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  • Streufert, Peter A., 2015. "An elementary proof that additive i-likelihood characterizes the supports of consistent assessments," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 37-46.
    • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:37-46
    DOI: 10.1016/j.jmateco.2015.03.003
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Giacomo Bonanno, 2013. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 567-592, August.
    3. Perea y Monsuwe, Andres & Jansen, Mathijs & Peters, Hans, 1997. "Characterization of Consistent Assessments in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 238-252, October.
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    7. Peter A. Streufert, 2012. "Specifying Nodes as Sets of Actions," University of Western Ontario, Departmental Research Report Series 20122, University of Western Ontario, Department of Economics.
    8. McLennan, Andrew, 1989. "Consistent Conditional Systems in Noncooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 141-174.
    9. Halpern, Joseph Y., 2010. "Lexicographic probability, conditional probability, and nonstandard probability," Games and Economic Behavior, Elsevier, vol. 68(1), pages 155-179, January.
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    11. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    12. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Peter A. Streufert, 2021. "A Category for Extensive-Form Games," Papers 2105.11398, arXiv.org.
    2. Peter A. Streufert, 2016. "The Category of Node-And-Choice Forms for Extensive-Form Games," University of Western Ontario, Departmental Research Report Series 20165, University of Western Ontario, Department of Economics.

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