TY - GEN
T1 - Marginal games and characterizations of the shapley value in TU games
AU - Kongo, Takumi
AU - Funaki, Yukihiko
N1 - Funding Information:
Acknowledgments. The authors thank Rodica Branzei, Irinel Dragan, and Stef Tijs for their helpful comments. This work was supported by JSPS KAKENHI Grant Number 15K17031 (Kongo), 24220033 (Funaki), 26245026 (Funaki), and 26380247 (Funaki).
Publisher Copyright:
© Springer Nature Singapore Pte Ltd. 2017.
PY - 2017
Y1 - 2017
N2 - Axiomatizations and recursive representations of the Shapley value on the class of all cooperative games with transferable utilities are given. Marginal games, which are closely related to dual games, play central roles in our results. Our axiomatizations are based on axioms that are marginal game variations of the well-known balanced contributions property, so that they are interpreted as fair treatment between two players in games as the balanced contributions property is. Our general recursive representation enables us to represent the Shapley value for n-person games by those for r-person and (n − r)-person games with fixed r < n. The particular case of r = 1 has a clear contrasting interpretation to the existing recursive formula.
AB - Axiomatizations and recursive representations of the Shapley value on the class of all cooperative games with transferable utilities are given. Marginal games, which are closely related to dual games, play central roles in our results. Our axiomatizations are based on axioms that are marginal game variations of the well-known balanced contributions property, so that they are interpreted as fair treatment between two players in games as the balanced contributions property is. Our general recursive representation enables us to represent the Shapley value for n-person games by those for r-person and (n − r)-person games with fixed r < n. The particular case of r = 1 has a clear contrasting interpretation to the existing recursive formula.
KW - Balanced contribution
KW - Dual game
KW - Marginal game
KW - Recursive representation
KW - Shapley value
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U2 - 10.1007/978-981-10-6753-2_12
DO - 10.1007/978-981-10-6753-2_12
M3 - Conference contribution
AN - SCOPUS:85032659784
SN - 9789811067525
T3 - Communications in Computer and Information Science
SP - 165
EP - 173
BT - Game Theory and Applications - 3rd Joint China-Dutch Workshop and 7th China Meeting, GTA 2016, Revised Selected Papers
A2 - Yang, Xiao-Guang
A2 - Li, Deng-Feng
A2 - Uetz, Marc
A2 - Xu, Gen-Jiu
PB - Springer Verlag
T2 - 3rd Joint China-Dutch Workshop on Game Theory and Applications and 7th China Meeting on Game Theory and Applications, GTA 2016
Y2 - 20 November 2016 through 23 November 2016
ER -