Shapley value for differential network games: Theory and application

Leon Petrosyan; David Yeung

doi:10.3934/jdg.2020021

Article Contents

2021, Volume 8, Issue 2: 151-166. Doi: 10.3934/jdg.2020021

This issue Previous Article On the equal surplus sharing interval solutions and an application Next Article

Shapley value for differential network games: Theory and application

Leon Petrosyan^1, , and
David Yeung^2,

1.
St. Petersburg State University, Univereitetskaya Nab. 7/9 Saint-Petersburg, Russia
2.
SRS Consortium for Advanced Study in Cooperative Dynamic Games, Shue Yan University, 10 Wai Tsui Cres, North Point, Hong Kong

^* Corresponding author: Leon Petrosyan
^* Corresponding author: Leon Petrosyan

Received: December 2019

Revised: December 2019

Early access: July 2, 2020

Published online: July 2, 2020

The first author is supported by Russian Science Foundation the grant Optimal Behavior in Conflict-Controlled Systems 17-11-01079

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Abstract

This paper presents a time-consistent dynamic Shapley value imputation for a class of differential network games. A novel form for measuring the worth of coalitions – named as cooperative-trajectory characteristic function – is developed for the Shapley value imputation. This new class of characteristic functions is evaluated along the cooperative trajectory. It measures the worth of coalitions under the process of cooperation instead of under min-max confrontation or the Nash non-cooperative stance. The resultant dynamic Shapley value imputation yields a new cooperative solution in differential network games.

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Mathematics Subject Classification: Primary:91A23, 91A12;Secondary:90B10.

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References

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