The impressive amount of papers concerning the Shapley value, seems to well reflect the success of the method to convert the information contained in a cooperative game into a personal attribution that players may use as a "prospect" in the game. On the other hand, in order to guarantee the effective evaluation of a cooperative game in practice, players are also faced with a concrete challenge related to the difficulty of the calculation of a "sensible" value . Luckily, for many classes of games studied in the literature of cooperative games, the computation of the Shapley value becomes surprisingly easy. The objective of this survey is to present some examples of this type, where the exact Shapley value of a game can be obtained avoiding the complex calculation of a weighted average of all the players' marginal contributions, as suggested by the original formula introduced by Shapley himself. Looking at these examples, we argue that the linearity of the Shapley value plays an important role to establish a clever computational procedure for its calculus. The majority of the algorithms onsidered in this paper, rely on the decomposition of a given characteristic function as a sum of games where the marginal contribution of each player over all possible coalitions is driven by properties tailored to specific applications. In many cases, these properties restore axioms used in the literature for the alternative axiomatic characterizations of the Shapley value.
Sometimes the computation of the Shapley value is simple / Dall'Aglio, Marco; Fragnelli, Vito; Moretti, Stefano. - (2019), pp. 441-462.
|Titolo:||Sometimes the computation of the Shapley value is simple|
Dall'Aglio, Marco [Membro del Collaboration Group]
|Data di pubblicazione:||2019|
|Citazione:||Sometimes the computation of the Shapley value is simple / Dall'Aglio, Marco; Fragnelli, Vito; Moretti, Stefano. - (2019), pp. 441-462.|
|Appare nelle tipologie:||02.1 - Capitolo o saggio su monografia (Monograph’s Chapter/Essay)|