Economic Theory Bulletin

, Volume 6, Issue 1, pp 29–39 | Cite as

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

  • Vincenzo Scalzo
Research Article


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.


Binary relations Preference relations Weak maximal element Ordinal games Weak equilibrium Exchange economies Quasi-Pareto optimality 

JEL Classification

C72 D51 


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Copyright information

© Society for the Advancement of Economic Theory 2017

Authors and Affiliations

  1. 1.Department of Economics and Statistics (DISES)University of Naples Federico IINapoliItaly

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