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.

The Shapley value in the Knaster gain game / Briata, Federica; Dall’Aglio, Andrea; Dall’Aglio, Marco; Fragnelli, Vito. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - STAMPA. - 259:1-2(2017), pp. 1-19. [10.1007/s10479-017-2651-8]

The Shapley value in the Knaster gain game

Dall’Aglio, Andrea;
2017

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.
2017
Collusion; Knaster procedure; Shapley value; decision sciences (all); management science and operations research
01 Pubblicazione su rivista::01a Articolo in rivista
The Shapley value in the Knaster gain game / Briata, Federica; Dall’Aglio, Andrea; Dall’Aglio, Marco; Fragnelli, Vito. - In: ANNALS OF OPERATIONS RESEARCH. - ISSN 0254-5330. - STAMPA. - 259:1-2(2017), pp. 1-19. [10.1007/s10479-017-2651-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1120412
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