The Myerson value introduced by Mayerson (Math Oper Res 2:225-229, 1977) is a solution for cooperative games under the partial cooperation structures described by graphs, in which feasible coalitions are connected but their structures are ignored. To extend the Myerson value, we define a mapping to describe local structures of coalitions and obtain a new solution for cooperative games, called Myerson value with local structures. We propose an axiomatic characterization of the Myerson value associated with local cooperative structures.
Daniel Li Li, Er-Fang Shan
. The Myerson Value on Local Structures of Coalitions[J]. Journal of the Operations Research Society of China, 2019
, 7(3)
: 461
-473
.
DOI: 10.1007/s40305-019-00254-z
[1] Béal, S., Rémila, E., Solal, P.:Fairness and fairness for neighbors:the difference between the Myerson value and component-wise Egalitarian solutions. Econ. Lett. 117, 263-267(2012)
[2] Bollobás, B.:Random Graphs, 2nd edn. Cambridge University Press, London (2001)
[3] Calvo, E., Lasaga, J., Nouweland, A.:Values of games with probabilistic graphs. Math. Soc. Sci. 37, 79-95(1999)
[4] Erdös, P., Rényi, A.:On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17-61(1960)
[5] González-Arangüena, E., Manuel, C.M., Pozo, M.D.:Values of games with weighted graphs. Eur. J. Oper. Res. 243, 248-257(2015)
[6] Jackson, M.:Allocation rules for network games. Games Econ. Behav. 51, 128-154(2005)
[7] Jackson, M., Wolinsky, A.:A strategic model of social and economic networks. J. Econ. Theory 71, 44-74(1996)
[8] Khmelnitskaya, A., Selçuk, Ö., Talman, D.:The Shapley value for directed graph games. Oper. Res. Lett. 44, 143-147(2016)
[9] Myerson, R.B.:Graphs and cooperation in games. Math. Oper. Res. 2, 225-229(1977)
[10] Myerson, R.B.:Conference structures and fair allocation rules. Int. J. Game Theory 9, 169-182(1980)
[11] Shan, E., Zhang, G., Dong, Y.:Component-wise proportional solutions for communication graph games. Math. Soc. Sci. 81, 22-28(2016)
[12] Shapley, L.S.:A value for n-person games. In:Tucker, A.W., Kuhn, H.W. (eds.) Contributions to the theory of games Ⅱ, pp. 307-317. Princeton University Press, Princeton (1953)
[13] van den Brink, R., Khmelnitskaya, A., van der Laan, G.:An efficient and fair solution for communication graph games. Econ. Lett. 117, 786-789(2012)
[14] van den Nouweland, A., Borm, P., Tijs, S.:Allocation rules for hypergraph communication situations. Int. J. Game Theory 20, 255-268(1992)
