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文章基本信息

  • 标题:Least Square Approximations and Conic Values of Cooperative Games
  • 作者:Ulrich Faigle ; Michel Grabisch
  • 期刊名称:Documents de Travail du Centre d'Economie de la Sorbonne
  • 印刷版ISSN:1955-611X
  • 出版年度:2015
  • 出版社:Centre d'Economie de la Sorbonne
  • 摘要: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.
  • 关键词:least square approximation; cooperative game; pseudo-Boolean function; least square value; Shapley value; probabilistic value
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