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arXiv · 1602.08068

The Shapley Value in the Knaster Gain Game

Federica Briata·Andrea Dall'Aglio·Marco Dall'Aglio·Vito Fragnelli
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Abstract

In Briata, Dall'Aglio and Fragnelli (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 (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.

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Federica Briata, Andrea Dall'Aglio, Marco Dall'Aglio, Vito Fragnelli. 2017-03-23. The Shapley Value in the Knaster Gain Game. https://doi.org/10.1007/s10479-017-2651-8

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