Béal, Sylvain and Lardon, Aymeric and Rémila, Eric and Solal, Philippe (2011): The Average Tree Solution for Multi-choice Forest Games.
Download (226kB) | Preview
In this article we study cooperative multi-choice games with limited cooperation possibilities, represented by an undirected forest on the player set. Players in the game can cooperate if they are connected in the forest. We introduce a new (single-valued) solution concept which is a generalization of the average tree solution defined and characterized by Herings et al.  for TU-games played on a forest. Our solution is characterized by component efficiency, component fairness and independence on the greatest activity level. It belongs to the precore of a restricted multi-choice game whenever the underlying multi-choice game is superadditive and isotone. We also link our solution with the hierarchical outcomes (Demange, 2004) of some particular TU-games played on trees. Finally, we propose two possible economic applications of our average tree solution.
|Item Type:||MPRA Paper|
|Original Title:||The Average Tree Solution for Multi-choice Forest Games|
|Keywords:||Average tree solution; Communication graph; (pre-)Core; Hierarchical outcomes; Multi-choice games.|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games|
|Depositing User:||Sylvain Béal|
|Date Deposited:||11. Feb 2011 18:03|
|Last Modified:||31. Dec 2015 18:41|
Albizuri, M.J. . The multichoice coalition value. Annals of Operations Research, 172, 363-474.
Albizuri, M.J., Aurrekoetxea, J., Zarzuelo, J.M. . Configuration values: Extensions of the coalitional Owen value. Games and Economic Behavior, 57, 1-17.
Aumann, R.J., Drèze, J.H. . Cooperative games with coalition structures. International Journal of Game Theory 3, 217-237.
Béal, S., Rémila, E., Solal, P. . Rooted-tree solutions for tree games. European Journal of Operational Research 203, 404-408.
Brink, R. van den. . Comparable axiomatizations of the Myerson value, the restricted Banzhaf value, hierarchical outcomes and the average tree Solution for cycle-free graph restricted games. Tinbergen Discussion Paper 09/108-1, Tinbergen Institute and Free University, Amsterdam.
Calvo, E., Santos, C.J. . A value for multichoice games. Mathematical Social Sciences, 40, 341-354.
Demange, G. . On group stability in hierarchies and networks. Journal of Political Economy, 112, 754-778.
Derks, J., Peters, H. . A Shapley value for games with restricted coalitions. International Journal of Game Theory, 21, 351-360.
Gilles, R., Owen, G., van den Brink, R. . Games with permission structures: the conjunctive approach. International Journal of Game Theory, 20, 277-293.
Grabisch, M. Lange, F. . Games on lattices, multichoice games and the Shapley value: a new approach. Mathematical Methods of Operations Research, 65 153-167.
Grabisch, M. Xie, L. . A new approach to the core and Weber set of multichoice games. Mathematical Methods of Operations Research, 66, 491-512.
Herings, P., van der Laan, G., Talman, D. . The average tree solution for cycle free games. Games and Economic Behavior, 62, 77-92.
Hotelling, H. . Stability in competition. Economic Journal}, 39, 40-57.
Hsiao, C.-R., Raghavan, T.E.S. . Shapley value for multi-choice cooperative games. Games and Economic Behavior, 5, 240-256.
Hwang Y-A., Liao Y-H. . Potential approach and characterizations of a Shapley value in multi-choice games. Mathematical Social Sciences, 56, 321-335.
Klijn, F., Slikker, M., Zarzuelo, J. . Characterizations of a multi-choice value. International Journal of Game Theory, 28, 521-532.
Mishra, D. Talman, D. . A characterization of the average tree solution for tree games. International Journal of Game Theory, 39,105-111.
Myerson, R. . Graphs and cooperation in games. Mathematics of Operations Research, 2, 225-229.
Nouweland van den, A., Potters, J., Tijs, S., Zarzuelo, J. . Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research, 41, 289-311.
Owen, G. . Values of games with a priori unions. In R. Hernn and O. Moschlin (Eds.), Lecture notes in economics and mathematical systems: Essays in honor of Oskar Morgenstern} (pp. 76-88). New York: Springer.
Peters, H., Zank, H. . The egalitarian solution for multichoice games. Annals of Operations Research,137, 399-409.
Shapley, L. S. . A value for n-person games. In A. W. Tucker and H. W. Kuhn (Eds.), Contributions to the theory of games II} (pp. 307-317). Princeton: Princeton University Press.