Least Square Approximations and Conic Values of Cooperative Games

Ulrich Faigle () and Michel Grabisch

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: 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

Keywords: least square approximation; cooperative game; pseudo-Boolean function; least square value; Shapley value; probabilistic value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2015-05
New Economics Papers: this item is included in nep-gth
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ftp://mse.univ-paris1.fr/pub/mse/CES2015/15047.pdf (application/pdf)

Related works:
Working Paper: Least Square Approximations and Conic Values of Cooperative Games (2015)
Working Paper: Least Square Approximations and Conic Values of Cooperative Games (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:15047

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