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The Probabilistic Games and the Shapley Function

In: Fuzzy Optimization, Decision-making and Operations Research

Author

Listed:
  • Surajit Borkotokey

    (Dibrugarh University, Department of Mathematics)

  • Sujata Goala

    (Dibrugarh University, Department of Mathematics)

  • Rajnish Kumar

    (Queen’s University Belfast, Queen’s Management School)

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.

Suggested Citation

  • Surajit Borkotokey & Sujata Goala & Rajnish Kumar, 2023. "The Probabilistic Games and the Shapley Function," Springer Books, in: Chiranjibe Jana & Madhumangal Pal & Ghulam Muhiuddin & Peide Liu (ed.), Fuzzy Optimization, Decision-making and Operations Research, chapter 0, pages 725-742, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-35668-1_32
    DOI: 10.1007/978-3-031-35668-1_32
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