The Probabilistic Games and the Shapley Function

Surajit Borkotokey (), Sujata Goala and Rajnish Kumar ()
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Surajit Borkotokey: Dibrugarh University, Department of Mathematics
Sujata Goala: Dibrugarh University, Department of Mathematics
Rajnish Kumar: Queen’s University Belfast, Queen’s Management School

Chapter Chapter 32 in Fuzzy Optimization, Decision-making and Operations Research, 2023, pp 725-742 from Springer

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-35668-1_32

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

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