The lattice of embedded subsets

Details The lattice of embedded subsets The lattice of embedded subsets

2010-02-19

arxiv.org/abs/1002.3814v1

Discrete Applied Mathematics 158 (2010) 479-488

Computer Science

Discrete Mathematics

Scientific paper

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.

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