2016/01/12 by Ulrich Faigle, Michel Grabisch, Faigle, Ulrich +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Optimization Algorithms Research #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Game Theory and Voting Systems #Optimization and Control (math.OC) #Optimization and Variational Analysis #cs.GT #math.OC
paper · pdf · doi:10.48550/arxiv.1601.02831
arxiv created 2016/01/12 · openalex publication_date 2016/01/12 · arxiv updated 2016/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Many important values for cooperative games are known to arise from least square optimization problems. The present investigation develops an optimization framework to explain and clarify this phenomenon in a general setting. The main result shows that every linear value results from some least square approximation problem and that, conversely, every least square approximation problem with linear constraints yields a linear value. This approach includes and extends previous results on so-called least square values and semivalues in the literature. In particular, is it demonstrated how known explicit formulas for solutions under additional assumptions easily follow from the general results presented here.