Volume 55, Number 3, May-June 2021
|Page(s)||1541 - 1557|
|Published online||11 June 2021|
An axiomatic and non-cooperative approach to the multi-step Shapley value
Department of Mathematics, School of Sciences, Henan University of Technology, Zhengzhou 450001, Henan, PR China
2 School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, PR China
3 School of Sciences, Henan University of Technology, Zhengzhou 450001, Henan, PR China
* Corresponding author: firstname.lastname@example.org
Accepted: 30 April 2021
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.
Mathematics Subject Classification: 91A10 / 91A12
Key words: Multi-step shapley value / levels structure / implementation / SPNE
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
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