The probabilistic games and the Shapley function

Surajit Borkotokey; Sujata Goala; Rajnish Kumar

doi:10.1007/978-3-031-35668-1_32

The probabilistic games and the Shapley function

Surajit Borkotokey^*
, Sujata Goala
, Rajnish Kumar

^*Corresponding author for this work

Queen's Business School (QBS)

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

Abstract

Cooperative games with transferable utilities are studied in a probabilistic framework: call them probabilistic games. In this setup, each coalition has some probability of formation, and the worth of the grand coalition is the expectation over its sub-coalitions due to this probability distribution. We propose the Shapley function for the class of probabilistic games. A special subclass of probabilistic games is studied, and the Shapley function for this subclass is characterized. In this special subclass, players make coalitions in a sequential manner, where prior knowledge about their compatibility with one another in a preceding coalition is used to predict the worth of the succeeding coalitions. This is a natural assumption and is never being studied in the literature.

Original language	English
Title of host publication	Fuzzy optimization, decision-making and operations research
Editors	Chiranjibe Jana, Madhumangal Pal, Ghulam Muhiuddin, Peide Liu
Publisher	Springer Cham
Chapter	32
Pages	725-742
ISBN (Electronic)	9783031356681
ISBN (Print)	9783031356674
DOIs	https://doi.org/10.1007/978-3-031-35668-1_32
Publication status	Published - 06 Jun 2023

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The probabilistic games and the Shapley function. / Borkotokey, Surajit; Goala, Sujata; Kumar, Rajnish.
Fuzzy optimization, decision-making and operations research . ed. / Chiranjibe Jana; Madhumangal Pal; Ghulam Muhiuddin; Peide Liu. Springer Cham, 2023. p. 725-742.

Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed) › peer-review

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T1 - The probabilistic games and the Shapley function

AU - Borkotokey, Surajit

AU - Goala, Sujata

AU - Kumar, Rajnish

PY - 2023/6/6

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N2 - Cooperative games with transferable utilities are studied in a probabilistic framework: call them probabilistic games. In this setup, each coalition has some probability of formation, and the worth of the grand coalition is the expectation over its sub-coalitions due to this probability distribution. We propose the Shapley function for the class of probabilistic games. A special subclass of probabilistic games is studied, and the Shapley function for this subclass is characterized. In this special subclass, players make coalitions in a sequential manner, where prior knowledge about their compatibility with one another in a preceding coalition is used to predict the worth of the succeeding coalitions. This is a natural assumption and is never being studied in the literature.

AB - Cooperative games with transferable utilities are studied in a probabilistic framework: call them probabilistic games. In this setup, each coalition has some probability of formation, and the worth of the grand coalition is the expectation over its sub-coalitions due to this probability distribution. We propose the Shapley function for the class of probabilistic games. A special subclass of probabilistic games is studied, and the Shapley function for this subclass is characterized. In this special subclass, players make coalitions in a sequential manner, where prior knowledge about their compatibility with one another in a preceding coalition is used to predict the worth of the succeeding coalitions. This is a natural assumption and is never being studied in the literature.

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M3 - Chapter (peer-reviewed)

SN - 9783031356674

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A2 - Pal, Madhumangal

A2 - Muhiuddin, Ghulam

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PB - Springer Cham

ER -

The probabilistic games and the Shapley function

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