In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a coopera- tive 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 (1946). In this paper we analyze the Shapley value (Shapley, 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. - 259:1(2017), pp. 1--19. [10.1007/s10479-017-2651-8]

The Shapley Value in the Knaster Gain Game

DALL'AGLIO, MARCO
;
2017

Abstract

In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a coopera- tive 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 (1946). In this paper we analyze the Shapley value (Shapley, 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.
Shapley value, Knaster procedure, Collusion
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. - 259:1(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: http://hdl.handle.net/11385/175505
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