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Minimum norm solutions for cooperative games. (English) Zbl 1131.91008
Summary: A solution \(f\) for cooperative games is a minimum norm solution, if the space of games has a norm such that \(f (v)\) minimizes the distance (induced by the norm) between the game \(v\) and the set of additive games. We show that each linear solution having the inessential game property is a minimum norm solution. Conversely, if the space of games has a norm, then the minimum norm solution w.r.t. this norm is linear and has the inessential game property. Both claims remain valid also if solutions are required to be efficient. A minimum norm solution, the least square solution, is given an axiomatic characterization.

91A12 Cooperative games
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