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 Mat. Teor. Igr Pril., 2018, Volume 10, Issue 1, Pages 23–39 (Mi mgta211)

Applying cooperative game theory with coalitional structure for data clustering

Vladimir M. Bure, Kseniya Yu. Staroverova

Saint Petersburg State University

Abstract: In the work a cooperative game where distance or similarity of players may be defined is considered. A characteristic function is defined in such a way that it is high for such coalitions which consist of more similar objects than objects from other coalitions. We consider the function which may not be superadditive that is why not only the grand coalition but smaller ones can be formed and considering a game with coalitional structure is reasonable. Therefore, we have a natural transformation from a cooperative game to a clustering problem. Several single-valued cooperative solution concepts are considered with this type of a characteristic function and stability conditions are found.

Keywords: coalition, stable coalitional structure, clustering, Shapley value, Aumann-Dreze value, ES-value.

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Document Type: Article
UDC: 519.834
BBK: 22.18

Citation: Vladimir M. Bure, Kseniya Yu. Staroverova, “Applying cooperative game theory with coalitional structure for data clustering”, Mat. Teor. Igr Pril., 10:1 (2018), 23–39

Citation in format AMSBIB
\Bibitem{BurSta18} \by Vladimir~M.~Bure, Kseniya~Yu.~Staroverova \paper Applying cooperative game theory with coalitional structure for data clustering \jour Mat. Teor. Igr Pril. \yr 2018 \vol 10 \issue 1 \pages 23--39 \mathnet{http://mi.mathnet.ru/mgta211}