Least Square Approximations and Conic Values of Cooperative Games

Ulrich Faigle () and Michel Grabisch

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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; approximation par les moindres carrés; jeu coopératif; fonction pseudo-booléenne; valeur aux moindre carrés; valeur de Shapley; valeur probabiliste (search for similar items in EconPapers)
Date: 2015-05
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01169281v1
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Published in 2015

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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:hal:cesptp:halshs-01169281

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