The Shapley value in the Knaster gain game

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 ). I...

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Bibliographic Details
Published in:Annals of operations research 2017-12, Vol.259 (1-2), p.1-19
Main Authors: Briata, Federica, Dall’Aglio, Andrea, Dall’Aglio, Marco, Fragnelli, Vito
Format: Article
Language:English
Subjects:
Analysis
Beliefs, opinions and attitudes
Business and Management
Combinatorics
Economic models
Game theory
Gamers
Methods
Operations research
Operations Research/Decision Theory
Original Paper
Players
Ranking
Theory of Computation
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-017-2651-8