# Least Square Approximations and Conic Values of Cooperative Games

Working paper

Issue number:

2015.47

Series:

Documents de travail du Centre d'Economie de la Sorbonne

Publisher:

Centre d'Economie de la Sorbonne

Year:

2015

The problem of least square approximation for set functions by set functions satisfying specified linear equality or inequality constraints is considered. The problem has important applications in the field of pseudo-Boolean functions, decision making and in cooperative game theory, where approximation by additive set functions yields so-called least square values. In fact, it is seem that every linear value for cooperative games arises from least square approximation. We provide a general approach and problem overview. In particular, we derive explicit formulas for solutions under mild constraints, which include and extend previous results in the literature.