| Title:
|
A value based on marginal contributions for multi–alternative games with restricted coalitions (English) |
| Author:
|
Masuya, Satoshi |
| Author:
|
Inuiguchi, Masahiro |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
50-67 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with cooperative games with $n$ players and $r$ alternatives which are called multi-alternative games. In the conventional multi-alternative games initiated by Bolger, each player can choose any alternative with equal possibilities. In actual social life, there exist situations in which players have some restrictions on their choice of alternatives. Considering such situations, we study restricted multi-alternative games. A value for a given game is proposed. (English) |
| Keyword:
|
game theory |
| Keyword:
|
cooperative game |
| Keyword:
|
multi-alternative game |
| Keyword:
|
restricted game |
| Keyword:
|
Banzhaf value |
| MSC:
|
91A06 |
| MSC:
|
91A12 |
| idZBL:
|
Zbl 1187.91016 |
| idMR:
|
MR2666894 |
| . |
| Date available:
|
2010-06-02T19:41:21Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140051 |
| . |
| Reference:
|
[1] J. F. Banzhaf: Weighted voting doesn’t work: a mathematical analysis.Rutgers Law Review 19 (1965), 317–343. |
| Reference:
|
[2] J. M. Bilbao, E. Lebrón, and N. Jiménez: Probabilistic values on convex geometries.Ann. Oper. Res. 84 (1998), 79–95. MR 1672378 |
| Reference:
|
[3] E. M. Bolger: Power indices for multicandidate voting games.Internat. J. Game Theory 15 (1986), 175–186. Zbl 0611.90106, MR 0857012 |
| Reference:
|
[4] E. M. Bolger: A value for games with $n$ players and $r$ alternatives.Internat. J. Game Theory 22 (1993), 319–334. Zbl 0793.90101, MR 1251183 |
| Reference:
|
[5] E. M. Bolger: A consistent value for games with $n$ players and $r$ alternatives.Internat. J. Game Theory 29 (2000), 93–99. Zbl 1034.91001, MR 1745874 |
| Reference:
|
[6] E. Lehrer: An axiomatization of the Banzhaf value.Internat J. Game Theory 17 (1988), 89–99. Zbl 0651.90097, MR 0944144 |
| Reference:
|
[7] R. B. Myerson: Graphs and cooperation in games.Math. Oper. Res. 2 (1977), 225–229. Zbl 0402.90106, MR 0459661 |
| Reference:
|
[8] R. Ono: Values for multialternative games and multilinear extensions.In: Power Indices and Coalition Formation (M. Holler and G. Owen, eds.), Kluwer Academic Publishers, Dordrecht 2001, pp. 63–86. |
| Reference:
|
[9] L. S. Shapley: A value for $n$-person games.In: Contributions to the Theory of Games II (H. Kuhn and A. Tucker, eds.), Princeton 1953, pp. 307–317. Zbl 0701.90097, MR 0053477 |
| Reference:
|
[10] M. Tsurumi, M. Inuiguchi, and T. Tanino: A solution for fuzzy generalized multi-alternative games.In: The 2006 NOLTA Proc. 2006, pp. 95–98. |
| . |
