Constrained core solutions for totally positive games with ordered players

Rene van den Brink (), Gerard Laan () and Valeri Vasil’ev ()
Authors registered in the RePEc Author Service: Valery Alexandrovich Vasil'ev ()

International Journal of Game Theory, 2014, vol. 43, issue 2, 368 pages

Abstract: In many applications of cooperative game theory to economic allocation problems, such as river-, polluted river- and sequencing games, the game is totally positive (i.e., all dividends are nonnegative), and there is some ordering on the set of the players. A totally positive game has a nonempty core. In this paper we introduce constrained core solutions for totally positive games with ordered players which assign to every such a game a subset of the core. These solutions are based on the distribution of dividends taking into account the hierarchical ordering of the players. The Harsanyi constrained core of a totally positive game with ordered players is a subset of the core of the game and contains the Shapley value. For special orderings it coincides with the core or the Shapley value. The selectope constrained core is defined for acyclic orderings and yields a subset of the Harsanyi constrained core. We provide a characterization for both solutions. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Totally positive TU-game; Digraph; Harsanyi dividends; Core; Shapley value; Harsanyi set; Selectope; Polluted river games; C71 (Cooperative games) (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (16)

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DOI: 10.1007/s00182-013-0382-x

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