Some Remarks on Pseudotrees |
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Authors: | Carlos Alós-Ferrer Klaus Ritzberger |
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Institution: | (1) Department of Economics, University of Vienna, Hohenstaufengasse 9, 1010 Vienna, Austria;(2) Department of Economics and Finance, Institute for Advanced Studies, Stumpergasse 56, 1060 Vienna, Austria |
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Abstract: | This paper provides new results on pseudotrees. First, it is shown that pseudotrees are precisely those posets for which consistent
sets, directed sets, and nonempty chains coincide. Second, we show that chain-complete pseudotrees yield complete meet-semilattices.
Third, we prove that pseudotrees are precisely those posets that admit a set representation by sets of appropriate chains.
This latter result generalizes results needed for applications in game theory and economics. |
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