A simple family of solutions for forest games

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

A simple family of solutions for forest games

Oliver Juarez-Romero ^1,, , William Olvera-Lopez ^2, and Francisco Sanchez-Sanchez ^1,

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.

Keywords: Forest games, average tree solution, component efficiency, generalized component fairness.

Mathematics Subject Classification: Primary: 91A43, 91A46; Secondary: 05C57.

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

References:

[1]	R. J. Aumann and M. Maschler, Game theoretic analysis of a bankruptcy problem from the Talmud, J Econ theory, 36 (1985), 195-213. doi: 10.1016/0022-0531(85)90102-4. Google Scholar
[2]	R. Baron, S. Béal, E. Rémila and P. Solal, Average Tree solutions and the distribution of Harsanyi dividends, Int. J. Game Theory, 40 (2001), 331-349. doi: 10.1007/s00182-010-0245-7. Google Scholar
[3]	S. Béal, A. Lardon, E. Rémila and P. Solal, The Average Tree solution for multi-choice forest games, Annals of Operations Research, 196 (2012a), 27-51. doi: 10.1007/s10479-012-1150-1. Google Scholar
[4]	S. Béal, E. Rémila and P. Solal, Weighted component fairness for forest games, Math Social Sci, 64 (2012b), 144-151. doi: 10.1016/j.mathsocsci.2012.03.004. Google Scholar
[5]	K. Binmore, A. Rubinstein and A. Wolinsky, The Nash bargaining solution in economic modelling, The RAND Journal of Economics, (1986), 176-188. doi: 10.2307/2555382. Google Scholar
[6]	P. Herings, G. van der Laan and D. Talman, The Average Tree solution for cycle-free graph games, Game Econ Behav, 62 (2008), 77-92. doi: 10.1016/j.geb.2007.03.007. Google Scholar
[7]	P. Herings, G. van der Laan, D. Talman and Z. Yang, The average tree solution for cooperative games with limited communication structure, Game Econ Behav, 68 (2010), 626-633. doi: 10.1016/j.geb.2009.10.002. Google Scholar
[8]	M. O. Jackson, Allocation rules for network games, Game Econ Behav, 51 (2005), 128-154. doi: 10.1016/j.geb.2004.04.009. Google Scholar
[9]	R. B. Myerson, Graphs and cooperation on games, Math Operations Res, 2 (1977), 225-229. doi: 10.1287/moor.2.3.225. Google Scholar
[10]	L. S. Shapley, A value for n-person game Ⅱ, Annals of Mathematics Studies, (eds. Kuhn, H.W. and Tucker, A.W.), Princeton University Press, 28 (1953), 307-317. Google Scholar
[11]	A. van den Nouweland, Games and graphs in economic situations Ph. D. thesis, Tilburg University, The Netherlands, 1993.Google Scholar

show all references

References:

[1]	R. J. Aumann and M. Maschler, Game theoretic analysis of a bankruptcy problem from the Talmud, J Econ theory, 36 (1985), 195-213. doi: 10.1016/0022-0531(85)90102-4. Google Scholar
[2]	R. Baron, S. Béal, E. Rémila and P. Solal, Average Tree solutions and the distribution of Harsanyi dividends, Int. J. Game Theory, 40 (2001), 331-349. doi: 10.1007/s00182-010-0245-7. Google Scholar
[3]	S. Béal, A. Lardon, E. Rémila and P. Solal, The Average Tree solution for multi-choice forest games, Annals of Operations Research, 196 (2012a), 27-51. doi: 10.1007/s10479-012-1150-1. Google Scholar
[4]	S. Béal, E. Rémila and P. Solal, Weighted component fairness for forest games, Math Social Sci, 64 (2012b), 144-151. doi: 10.1016/j.mathsocsci.2012.03.004. Google Scholar
[5]	K. Binmore, A. Rubinstein and A. Wolinsky, The Nash bargaining solution in economic modelling, The RAND Journal of Economics, (1986), 176-188. doi: 10.2307/2555382. Google Scholar
[6]	P. Herings, G. van der Laan and D. Talman, The Average Tree solution for cycle-free graph games, Game Econ Behav, 62 (2008), 77-92. doi: 10.1016/j.geb.2007.03.007. Google Scholar
[7]	P. Herings, G. van der Laan, D. Talman and Z. Yang, The average tree solution for cooperative games with limited communication structure, Game Econ Behav, 68 (2010), 626-633. doi: 10.1016/j.geb.2009.10.002. Google Scholar
[8]	M. O. Jackson, Allocation rules for network games, Game Econ Behav, 51 (2005), 128-154. doi: 10.1016/j.geb.2004.04.009. Google Scholar
[9]	R. B. Myerson, Graphs and cooperation on games, Math Operations Res, 2 (1977), 225-229. doi: 10.1287/moor.2.3.225. Google Scholar
[10]	L. S. Shapley, A value for n-person game Ⅱ, Annals of Mathematics Studies, (eds. Kuhn, H.W. and Tucker, A.W.), Princeton University Press, 28 (1953), 307-317. Google Scholar
[11]	A. van den Nouweland, Games and graphs in economic situations Ph. D. thesis, Tilburg University, The Netherlands, 1993.Google Scholar

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