The lattice of embedded subsets

Michel Grabisch

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a partition of $N$ containing $S$. Despite the fact that many studies have been devoted to such games, surprisingly nobody clearly defined a structure (i.e., an order) on embedded coalitions, resulting in scattered and divergent works, lacking unification and proper analysis. The aim of the paper is to fill this gap, thus to study the structure of embedded coalitions (called here embedded subsets), and the properties of games in partition function form.

Keywords: Partition; Embedded subset; Game; Valuation; k-monotonicity (search for similar items in EconPapers)
Date: 2010-03
Note: View the original document on HAL open archive server: https://hal.science/hal-00457827v1
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Citations: View citations in EconPapers (14)

Published in Discrete Applied Mathematics, 2010, 158 (5), pp.479-488. ⟨10.1016/j.dam.2009.10.015⟩

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Working Paper: The lattice of embedded subsets (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00457827

DOI: 10.1016/j.dam.2009.10.015

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