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

Vincenzo Scalzo ()
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Vincenzo Scalzo: University of Naples Federico II

Economic Theory Bulletin, 2018, vol. 6, issue 1, No 3, 29-39

Abstract: 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.

Keywords: Binary relations; Preference relations; Weak maximal element; Ordinal games; Weak equilibrium; Exchange economies; Quasi-Pareto optimality (search for similar items in EconPapers)
JEL-codes: C72 D51 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s40505-017-0121-8

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