Difference between the position value and the myerson value is due to the existence of coalition structures. (English) Zbl 1211.91042
Summary: The study characterizes the position value and the Myerson value for communication situations. Each of these two values is represented by the Shapley value of a modified game obtained from the original communication situation. The difference between the two values comes from the existence of a coalition structure in the modified game.
References:
| [1] | Borm P, Owen G, Tijs S (1992) On the position value for communication situations. SIAM J Discr Math 5: 305–320 · Zbl 0788.90087 · doi:10.1137/0405023 |
| [2] | Casajus A (2007) The position value is the Myerson value, in a sense. Int J Game Theory 36: 47–55 · Zbl 1210.91013 · doi:10.1007/s00182-007-0086-1 |
| [3] | Casajus A (2008) The Myerson value in terms of the link agent form: a technical note. Working Paper, Wirtschaftswissenschaftliche Fakultät, Universität Leipzig, Germany. http://www.uni-leipzig.de/\(\sim\)micro/myersonlaf.pdf |
| [4] | Kamijo Y (2007) A two-step Shapley value in a cooperative game with a coalition structure. 21 COE-GLOPE Working Paper Series No. 28, Waseda University, Japan 2007. http://21coe-glope.com/paper/21COE_WP28.pdf |
| [5] | Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2: 225–229 · Zbl 0402.90106 · doi:10.1287/moor.2.3.225 |
| [6] | Myerson RB (1980) Conference structures and fair allocation rules. Int J Game Theory 9: 169–182 · Zbl 0441.90117 · doi:10.1007/BF01781371 |
| [7] | Owen G (1977) Value of games with a priori unions. In: Henn R, Moeschlin O (eds) Mathematical economics and game theory. Springer, Berlin · Zbl 0395.90095 |
| [8] | Peleg B, Sudhölter P (2003) Introduction to the theory of cooperative games. Kluwer, Dordrecht · Zbl 1193.91002 |
| [9] | Shapley LS (1953) A value for n-person games. In: Kuhn H, Tucker AW (eds) Contributions to the Theory of Games II. Princeton University Press, Princeton, pp 307–317 |
| [10] | Slikker M (2005) A characterization of the position value. Int J Game Theory 33: 505–514 · Zbl 1091.91006 · doi:10.1007/s00182-005-0211-y |
| [11] | van den Nouweland A (1993) Games and graphs in economic situations. PhD dissertation, Tilburg University, The Netherlands · Zbl 0795.90094 |
| [12] | Vazquez-Brage M, Garcia-Jurado I, Carreras F (1996) The Owen value applied to games with graph-restricted communication. Games Econ Behav 12: 42–53 · Zbl 0844.90124 · doi:10.1006/game.1996.0003 |
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.
