Czédli, Gábor; Pollák, György When do coalitions form a lattice? (English) Zbl 0829.06003 Acta Sci. Math. 60, No. 1-2, 197-206 (1995). Summary: Given a finite partially ordered set \(P\), for subsets or, in other words, coalitions \(X\), \(Y\) of \(P\) let \(X\leq Y\) mean that there exists an injection \(\varphi: X\to Y\) such that \(x\leq \varphi (x)\) for all \(x\in X\). The set \({\mathcal L} (P)\) of all subsets of \(P\) equipped with this relation is a partially ordered set. All partially ordered sets \(P\) such that \({\mathcal L} (P)\) is a lattice are determined, and this result is extended to quasiordered sets \(P\) versus \(q\)-lattices \({\mathcal L} (P)\) as well. Some elementary properties of distributive lattices \({\mathcal L} (P)\) are also given. Cited in 3 ReviewsCited in 2 Documents MSC: 06A06 Partial orders, general 06B99 Lattices 91A99 Game theory Keywords:partially ordered set; subsets; coalitions; lattice; quasiordered sets; \(q\)-lattice; distributive lattices PDFBibTeX XMLCite \textit{G. Czédli} and \textit{G. Pollák}, Acta Sci. Math. 60, No. 1--2, 197--206 (1995; Zbl 0829.06003)