TY - JOUR
A2 - Nie, Pu-yan
AU - Arribillaga, R. Pablo
AU - MassÃ³, Jordi
AU - Neme, Alejandro
PY - 2014
DA - 2014/04/30
TI - On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game
SP - 190614
VL - 2014
AB - We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) assignment game. We consider the Core, three other notions of group stability, and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related to the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated with the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.
SN - 1110-757X
UR - https://doi.org/10.1155/2014/190614
DO - 10.1155/2014/190614
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -