The expected Shapley value on a class of probabilistic TU games

Surajit Borkotokey; Sujata Goala; Rajnish Kumar

doi:10.1142/S0219198925500112

The expected Shapley value on a class of probabilistic TU games

Surajit Borkotokey^*
, Sujata Goala
, Rajnish Kumar

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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Abstract

We study the class of probabilistic cooperative games and obtain the Expected Shapley value as a solution concept. This is an extension of the classical cooperative games with transferable utilities where we assume that each coalition has an ex-ante probability of being formed. The Expected Shapley value is the expectation of the Shapley values of all the coalitions with respect to their probability distribution and is calculated before the realization of the state. We present five characterizations of our proposed value. Finally, we introduce a bidding mechanism under a non-cooperative setup and show that the Expected Shapley value is a subgame perfect Nash equilibrium under this setup.

Original language	English
Article number	2550011
Number of pages	30
Journal	International Game Theory Review
Early online date	21 Aug 2025
DOIs	https://doi.org/10.1142/S0219198925500112
Publication status	Early online date - 21 Aug 2025
Externally published	Yes

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Keywords

expected Shapley value
implementation
probabilistic TU games
Shapley value
TU game

ASJC Scopus subject areas

General Computer Science
Business and International Management
Statistics, Probability and Uncertainty

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10.1142/S0219198925500112Licence: Unspecified

The expected Shapley value on a class of probabilistic TU games
Copyright 2025 the authors. This is an accepted manuscript distributed under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Accepted author manuscript, 718 KBLicence: CC BY

Cite this

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abstract = "We study the class of probabilistic cooperative games and obtain the Expected Shapley value as a solution concept. This is an extension of the classical cooperative games with transferable utilities where we assume that each coalition has an ex-ante probability of being formed. The Expected Shapley value is the expectation of the Shapley values of all the coalitions with respect to their probability distribution and is calculated before the realization of the state. We present five characterizations of our proposed value. Finally, we introduce a bidding mechanism under a non-cooperative setup and show that the Expected Shapley value is a subgame perfect Nash equilibrium under this setup.",

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AB - We study the class of probabilistic cooperative games and obtain the Expected Shapley value as a solution concept. This is an extension of the classical cooperative games with transferable utilities where we assume that each coalition has an ex-ante probability of being formed. The Expected Shapley value is the expectation of the Shapley values of all the coalitions with respect to their probability distribution and is calculated before the realization of the state. We present five characterizations of our proposed value. Finally, we introduce a bidding mechanism under a non-cooperative setup and show that the Expected Shapley value is a subgame perfect Nash equilibrium under this setup.

KW - expected Shapley value

KW - implementation

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DO - 10.1142/S0219198925500112

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SN - 0219-1989

JO - International Game Theory Review

JF - International Game Theory Review

M1 - 2550011

ER -

The expected Shapley value on a class of probabilistic TU games

Abstract

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Keywords

ASJC Scopus subject areas

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