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.File | Dimensione | Formato | |
---|---|---|---|
Briata_The-Shapley-Value_2017.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
479.23 kB
Formato
Adobe PDF
|
479.23 kB | Adobe PDF | Contatta l'autore |
Briata_preprint_The-Shapley-Value_2017.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
321.93 kB
Formato
Adobe PDF
|
321.93 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.