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On The Completeness Of The Universal Knowledge–Belief Space: A Technical Note

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  • MIKLÓS PINTÉR

    (Department of Mathematics, Corvinus University of Budapest and MTA-BCE "Lendület" Strategic Interactions Research Group, Fővám tér 13-15, Budapest, 1093, Hungary)

Abstract

Meier [Games Econ. Behav.62, 53–66] shows that the universal knowledge–belief space exists. However, besides the universality there is an other important property might be imposed on knowledge–belief spaces, inherited also from type spaces, the completeness. In this paper, we introduce the notion of complete knowledge–belief space, and demonstrate that the universal knowledge–belief space is not complete, that is, some subjective beliefs (probability measures) on the universal knowledge–belief space are not knowledge–belief types.

Suggested Citation

  • Miklós Pintér, 2014. "On The Completeness Of The Universal Knowledge–Belief Space: A Technical Note," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-6.
    • Handle: RePEc:wsi:igtrxx:v:16:y:2014:i:01:n:s0219198914400064
    DOI: 10.1142/S0219198914400064
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    Keywords

    Belief; knowledge; uncertainty; complete type space; complete knowledge–belief space; universal type space; universal knowledge–belief space; games with incomplete information; C70; C72; D80; D82; D83;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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