VALUES FOR GAMES ON THE CYCLES OF A DIGRAPH

William Olvera-Lopez () and Francisco Sanchez-Sanchez ()
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William Olvera-Lopez: Centro de Investigación en Matemáticas A.C., Jalisco S/N, Valenciana. Guanajuato, México. A.P. 403, México
Francisco Sanchez-Sanchez: Centro de Investigación en Matemáticas A.C., Jalisco S/N, Valenciana. Guanajuato, México. A.P. 403, México

International Game Theory Review (IGTR), 2012, vol. 14, issue 02, 1-18

Abstract: In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes andr-efficient solutions, where the allocation amount is a real numberr, showing axiomatic solutions in both cases.

Keywords: Digraphs; cooperative games; allocation rules; 05C57; 91A12; 91A43 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S0219198912500089

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