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Generalized additive games

Giulia Cesari (), Roberto Lucchetti and Stefano Moretti
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Giulia Cesari: Politecnico di Milano
Roberto Lucchetti: Politecnico di Milano
Stefano Moretti: CNRS UMR7243, PSL, Université Paris-Dauphine

International Journal of Game Theory, 2017, vol. 46, issue 4, 919-939

Abstract: Abstract A transferable utility (TU) game with n players specifies a vector of $$2^n-1$$ 2 n - 1 real numbers, i.e. a number for each non-empty coalition, and this can be difficult to handle for large n. Therefore, several models from the literature focus on interaction situations which are characterized by a compact representation of a TU-game, and such that the worth of each coalition can be easily computed. Sometimes, the worth of each coalition is computed from the values of single players by means of a mechanism describing how the individual abilities interact within groups of players. In this paper we introduce the class of Generalized additive games (GAGs), where the worth of a coalition $$S { \subseteq } N$$ S ⊆ N is evaluated by means of an interaction filter, that is a map $$\mathcal {M}$$ M which returns the valuable players involved in the cooperation among players in S. Moreover, we investigate the subclass of basic GAGs, where the filter $$\mathcal {M}$$ M selects, for each coalition S, those players that have friends but not enemies in S. We show that well-known classes of TU-games can be represented in terms of such basic GAGs, and we investigate the problem of computing the core and the semivalues for specific families of GAGs.

Keywords: TU-games; Core; Semivalues; Airport games; Peer games; Argumentation games (search for similar items in EconPapers)
Date: 2017
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