Extensions of group-valued modular maps
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The first theorem of this paper characterizes modular extensions of a group-valued modular map defined on a Boolean ring as maximal or minimal elements in the collection of all supermodular or submodular extensions, respectively. Using Zorn's lemma, we obtain results on the existence of a modular majorant or minorant of a supermodular or submodular map, respectively. The results are specialized to positive (super-)modular maps. The final remark includes an economic game theory application.
KeywordsGame Theory Final Remark Minimal Element Theory Application Boolean Ring
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