Monotonic games are spanning network games. (English) Zbl 0795.90094
Summary: Spanning network games, which are a generalization of minimum cost spanning tree games, were introduced by D. Granot and M. Maschler [‘Network cost games and the reduced game property’, Working paper of the Rept. of Mathematics, The Hebrew University, Jerusalem, Israel], who showed that these games are always monotonic. In this paper a subclass of spanning network games is introduced, namely simplex games, and it is shown that every monotonic game is a simplex game. Hence, the class of spanning network games coincides with the class of monotonic games.
References:
| [1] | Borm P, and Tijs S (1992) ?Strategic claim games corresponding to an NTU-game?.Games and Economic Behavior 4, 58-71. · Zbl 0777.90088 · doi:10.1016/0899-8256(92)90005-D |
| [2] | Curiel I, Derks J, and Tijs S (1989) ?On balanced games and games with committee control?.OR Spektrum 11, 83-88. · Zbl 0678.90102 · doi:10.1007/BF01746002 |
| [3] | Curiel I, Maschler M, and Tijs S (1987) ?Bankruptcy games?.Zeitschrift für Oper. Res. 31, A143-A159. · Zbl 0636.90100 · doi:10.1007/BF02109593 |
| [4] | Dubey P (1975) ?On the uniqueness of the Shapley value?.Int. J. of Game Theory 4, 113-129. · Zbl 0352.90085 · doi:10.1007/BF01780630 |
| [5] | Granot D, and Huberman G (1981) ?Minimum cost spanning tree games?.Math. Prog. 21, 1-18. · Zbl 0461.90099 · doi:10.1007/BF01584227 |
| [6] | Granot D, and Maschler M (1991) ?Network cost games and the reduced game property?. Working paper of the Faculty of Commerce and Business Administration, University of British Colombia, Vancouver, Canada, and the Department of Mathematics, The Hebrew University, Jerusalem, Israel. |
| [7] | Kalai E, and Zemel E (1982) ?Totally balanced games and games of flow?.Math. Oper. Res. 7, 476-478. · Zbl 0498.90030 · doi:10.1287/moor.7.3.476 |
| [8] | Megiddo N (1978) ?Computational complexity and the game theory approach to cost allocation for a tree?.Math. of Oper. Res. 3, 189-196. · Zbl 0397.90111 · doi:10.1287/moor.3.3.189 |
| [9] | Neumann J von, and Morgenstern O (1944) Theory of Games and Economic Behavior, Princeton University Press, Princeton. · Zbl 0063.05930 |
| [10] | Peleg B (1968) ?On weights of constant-sum majority games?.SIAM J. Appl. Math. 16, 527-532. · Zbl 0155.29201 · doi:10.1137/0116042 |
| [11] | Shapley LS (1953) ?A value for n-person games?. In: Contributions to the Theory of Games II (Eds. Tucker A and Kuhn H), 307-317. |
| [12] | Shapley L, and Shubik M (1969) ?On market games?.J. Econ. Theory 1, 9-25. · doi:10.1016/0022-0531(69)90008-8 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
