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Many important values for cooperative games are known to arise from leastsquare optimization problems. The present investigation develops anoptimization framework to explain and clarify this phenomenon in a generalsetting. The main result shows that every linear value results from some leastsquare approximation problem and that, conversely, every least squareapproximation problem with linear constraints yields a linear value.  This approach includes and extends previous results on so-called least squarevalues and semivalues in the literature. In particular, is it demonstrated howknown explicit formulas for solutions under additional assumptions easilyfollow from the general results presented here.

Least Square Approximations and Linear Values of Cooperative Games