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Solutions for network games and symmetric group representations

Sánchez-Pérez Joss

Operations Research and Decisions

2019

Vol. 29, No. 4

95--123

We present the relationship between network games and representation theory of the group of permutations of the set of players (nodes), and also offer a different perspective to study solutions for this kind of problems. We then provide several applications of this approach to the cases with three and four players.

An application of the representations of symmetric groups to characterizing solutions of games in partition function form

Sánchez-Pérez J.

Operations Research and Decisions

2014

Vol. 24, No. 2

97--122

A different perspective from the more “traditional” approaches to studying solutions of games in partition function form has been presented. We provide a decomposition of the space of such games under the action of the symmetric group, for the cases with three and four players. In particular, we identify all the irreducible subspaces that are relevant to the study of linear symmetric solutions. We then use such a decomposition to derive a characterization of the class of linear and symmetric solutions, as well as of the class of linear, symmetric and efficient solutions.