ASPECTS OF EXCHANGEABILITY IN THE SHAPLEY VALUE

R Amit and Parthasarathy Ramachandran ()
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Parthasarathy Ramachandran: Department of Management Studies, Indian Institute of Science, Bangalore, India

International Game Theory Review (IGTR), 2013, vol. 15, issue 04, 1-11

Abstract: One of the important solution concepts in cooperative game theory is the Shapley value. The Shapley value is a probabilistic value in which each player subjectively assigns probabilities to the events which define their positions in a game. One of the most important concepts of subjective probability is the exchangeability. This paper characterizes the aspects of exchangeability in the Shapley value. We discuss exchangeability aspects in the Owen's multilinear characterization of the Shapley value; and, derive the Shapley value using exchangeability. We also link exchangeability to the Shapley's original derivation of the Shapley value. Lastly, we discuss exchangeability aspects in the semivalues. We show that, for a fixed finite set of players, the probability assignment in a semivalue cannot be a unique mixture of binomial distributions.

Keywords: Shapley value; exchangeability; de Finetti's theorem; JEL Classification: C71 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1142/S0219198913400288

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