Inspired by the two-step Shapley value, in this paper we introduce and axiomatize the multi-step Shapley value for cooperative games with levels structures. Moreover, we design a multi-step bidding mechanism, which implements the value strategically in subgame perfect Nash equilibrium for superadditve games.
Keywords: Multi-step shapley value, levels structure, implementation, SPNE
@article{RO_2021__55_3_1541_0,
author = {Li, Xianghui and Zheng, Wei and Li, Yang},
title = {An axiomatic and non-cooperative approach to the multi-step {Shapley} value},
journal = {RAIRO. Operations Research},
pages = {1541--1557},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/ro/2021073},
mrnumber = {4270857},
zbl = {1468.91011},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021073/}
}
TY - JOUR AU - Li, Xianghui AU - Zheng, Wei AU - Li, Yang TI - An axiomatic and non-cooperative approach to the multi-step Shapley value JO - RAIRO. Operations Research PY - 2021 SP - 1541 EP - 1557 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021073/ DO - 10.1051/ro/2021073 LA - en ID - RO_2021__55_3_1541_0 ER -
%0 Journal Article %A Li, Xianghui %A Zheng, Wei %A Li, Yang %T An axiomatic and non-cooperative approach to the multi-step Shapley value %J RAIRO. Operations Research %D 2021 %P 1541-1557 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021073/ %R 10.1051/ro/2021073 %G en %F RO_2021__55_3_1541_0
Li, Xianghui; Zheng, Wei; Li, Yang. An axiomatic and non-cooperative approach to the multi-step Shapley value. RAIRO. Operations Research, Tome 55 (2021) no. 3, pp. 1541-1557. doi: 10.1051/ro/2021073
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