On the bargaining set of three-player games
The description and the characterization of the (Aumann-Maschler) bargaining set are known, but its determination is still hard given a generic transferable utility cooperative game. We provide here an exhaustive determination of the bargaining set of any three-player game, balanced or not, superadditive or not.
The bargaining set of four-person balanced games
Abstract. It is well known that in three-person transferable-utility cooperative games the bargaining set ℳi1 and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set ℳi1 (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set ℳi1. Our discussion employs a generalization of balancedness to games with coalition structures.
ASYMPTOTIC PROPERTIES OF SOME CLASSES OF GENERALIZED FUNCTIONS
This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Ces?ro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.