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Compactness in the choice and game theories: a characterization of rationality

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  • Athanasios Andrikopoulos

    (University of Ioannina)

Abstract

Compactness is an important topological property as it enables us to apply minimax theorems in economic theory. The theory of optimal choice sets is a solution theory that has a long and well-established tradition in social choice and game theories. A general solution concept of choice problems when the set of best alternatives does not exist (this problem occurs when the preferences yielded by an economic process are cyclic) is the Schwartz set. This set is one of the most popular solution concepts since it insures rationality. The Schwartz set is equivalent to the admissible set that appears in the game theory literature. The present note shows that the feasible set is compact if and only if every generalized upper tc-semicontinuous preference has non-empty Schwartz (admissible) set.

Suggested Citation

  • Athanasios Andrikopoulos, 2013. "Compactness in the choice and game theories: a characterization of rationality," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 105-110, November.
    • Handle: RePEc:spr:etbull:v:1:y:2013:i:2:d:10.1007_s40505-013-0002-8
    DOI: 10.1007/s40505-013-0002-8
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    References listed on IDEAS

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    Cited by:

    1. Carlos Alós-Ferrer & Klaus Ritzberger, 2015. "On the characterization of preference continuity by chains of sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 115-128, October.

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    More about this item

    Keywords

    Schwartz set; Admissible set; Maximal element; Minimal undominated set;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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