Associated consistency, value and graphs

Gérard Hamiache (1, 2) , Florian Navarro

1 EQUIPPE - Economie Quantitative, Intégration, Politiques Publiques et Econométrie
2 LEM - Lille économie management - UMR 9221

This article presents an axiomatic characterization of a new value for cooperative games with incomplete communication. The result is obtained by slight modifications of associated games proposed by Hamiache (Games Econ Behav 26:59–78, 1999; Int J Game Theory 30:279–289, 2001). This new associated game can be expressed as a matrix formula. We generate a series of successive associated games and show that its limit is an inessential game. Three axioms (associated consistency, inessential game, continuity) characterize a unique sharing rule. Combinatorial arguments and matrix tools provide a procedure to compute the solution. The new sharing rule coincides with the Shapley value when the communication is complete.

Domaines: Sciences de l'Homme et Société; Economies et finances

Gérard Hamiache, Florian Navarro. Associated consistency, value and graphs. International Journal of Game Theory, 2019, 49, pp.227-249. ⟨10.1007/s00182-019-00688-y⟩. ⟨hal-02501125⟩