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Weak maximal elements and weak equilibria in ordinal games with applications to exchange economies

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  • Vincenzo Scalzo

    (University of Naples Federico II)

Abstract

We study binary relations (preferences) and ordinal games in the case where no continuity-like properties are assumed at all. We introduce generalizations of the maximal element and Nash equilibrium, called, respectively, the weak maximal element and weak equilibrium, and give existence results when binary relations satisfy only convexity conditions. The weak maximal element (weak equilibrium) is equivalent to the maximal element (Nash equilibrium) if and only if a generalization of continuity is given. Moreover, we obtain the existence of quasi-Pareto optimal allocations in exchange economies.

Suggested Citation

  • Vincenzo Scalzo, 2018. "Weak maximal elements and weak equilibria in ordinal games with applications to exchange economies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 29-39, April.
    • Handle: RePEc:spr:etbull:v:6:y:2018:i:1:d:10.1007_s40505-017-0121-8
    DOI: 10.1007/s40505-017-0121-8
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    References listed on IDEAS

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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Binary relations; Preference relations; Weak maximal element; Ordinal games; Weak equilibrium; Exchange economies; Quasi-Pareto optimality;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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