# American Institute of Mathematical Sciences

April  2017, 4(2): 87-96. doi: 10.3934/jdg.2017006

## A simple family of solutions for forest games

 1 CIMAT, A. C., Jalisco S/N, Valenciana, C.P. 36240, Guanajuato, Gto, México 2 UASLP, School of Economics, Av. Pintores S/N, Burócratas del Estado, C.P. 78213, San Luis Potosí, SLP, México

* Corresponding author: Tel. +52 473 73 27155, Ext 4991

Received  April 2016 Revised  December 2016 Published  March 2017

In this paper we study TU-games where the cooperation structure among the players is modeled by a forest. Using the classical component efficiency axiom and a generalized version of the component fairness axiom we obtain a family of solutions. We show that every solution in this family is based on a process of transfers among the players, and the average tree solution belongs to the family. Finally, we obtain a solution based on the degree of the nodes and we study a set of properties satisfied by this family.

Citation: Oliver Juarez-Romero, William Olvera-Lopez, Francisco Sanchez-Sanchez. A simple family of solutions for forest games. Journal of Dynamics & Games, 2017, 4 (2) : 87-96. doi: 10.3934/jdg.2017006
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##### References:
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