The Shapley value in the Knaster gain game

Federica Briata (), Andrea Dall’Aglio (), Marco Dall’Aglio () and Vito Fragnelli ()
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Federica Briata: University of Genova
Andrea Dall’Aglio: Sapienza University of Rome
Marco Dall’Aglio: LUISS University

Annals of Operations Research, 2017, vol. 259, issue 1, No 1, 19 pages

Abstract: Abstract In Briata et al. (AUCO Czech Econ Rev 6:199–208, 2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (Ann Soc Pol Math 19:228–230, 1946). In this paper we analyze the Shapley value (Shapley, in: Kuhn, Tucker (eds) Contributions to the theory of games II (Annals of Mathematics Studies 28), Princeton University Press, Princeton, 1953) of the game and propose its use as a measure of the players’ attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players’ evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism.

Keywords: Shapley value; Knaster procedure; Collusion (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-017-2651-8

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