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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 |
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.
References:
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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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [8] |
M. O. Jackson,
Allocation rules for network games, Game Econ Behav, 51 (2005), 128-154.
doi: 10.1016/j.geb.2004.04.009. |
| [9] |
R. B. Myerson,
Graphs and cooperation on games, Math Operations Res, 2 (1977), 225-229.
doi: 10.1287/moor.2.3.225. |
| [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.
|
| [11] |
A. van den Nouweland,
Games and graphs in economic situations Ph. D. thesis, Tilburg University, The Netherlands, 1993. |
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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [8] |
M. O. Jackson,
Allocation rules for network games, Game Econ Behav, 51 (2005), 128-154.
doi: 10.1016/j.geb.2004.04.009. |
| [9] |
R. B. Myerson,
Graphs and cooperation on games, Math Operations Res, 2 (1977), 225-229.
doi: 10.1287/moor.2.3.225. |
| [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.
|
| [11] |
A. van den Nouweland,
Games and graphs in economic situations Ph. D. thesis, Tilburg University, The Netherlands, 1993. |
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