A simple family of solutions for forest games. (English) Zbl 1391.91022
Summary: 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 eciency; generalized component fairness; TU-gameReferences:
| [1] | R. J. Aumann, Game theoretic analysis of a bankruptcy problem from the Talmud,, J Econ theory, 36, 195 (1985) · Zbl 0578.90100 · doi:10.1016/0022-0531(85)90102-4 |
| [2] | R. Baron, Average Tree solutions and the distribution of Harsanyi dividends,, Int. J. Game Theory, 40, 331 (2001) · Zbl 1220.91010 · doi:10.1007/s00182-010-0245-7 |
| [3] | S. Béal, The Average Tree solution for multi-choice forest games,, Annals of Operations Research, 196, 27 · Zbl 1259.91027 · doi:10.1007/s10479-012-1150-1 |
| [4] | S. Béal, Weighted component fairness for forest games,, Math Social Sci, 64, 144 · Zbl 1252.91027 · doi:10.1016/j.mathsocsci.2012.03.004 |
| [5] | K. Binmore, The Nash bargaining solution in economic modelling,, The RAND Journal of Economics, 176 (1986) · doi:10.2307/2555382 |
| [6] | P. Herings, The Average Tree solution for cycle-free graph games,, Game Econ Behav, 62, 77 (2008) · Zbl 1135.91316 · doi:10.1016/j.geb.2007.03.007 |
| [7] | P. Herings, The average tree solution for cooperative games with limited communication structure,, Game Econ Behav, 68, 626 (2010) · Zbl 1198.91067 · doi:10.1016/j.geb.2009.10.002 |
| [8] | M. O. Jackson, Allocation rules for network games,, Game Econ Behav, 51, 128 (2005) · Zbl 1114.91015 · doi:10.1016/j.geb.2004.04.009 |
| [9] | R. B. Myerson, Graphs and cooperation on games,, Math Operations Res, 2, 225 (1977) · Zbl 0402.90106 · doi:10.1287/moor.2.3.225 |
| [10] | L. S. Shapley, A value for n-person game,, in Contributions to the theory of games II, 28, 307 (1953) · Zbl 0050.14404 |
| [11] | A. van den Nouweland, <em>Games and graphs in economic situations</em>,, Ph.D. thesis (1993) |
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