Linear Transforms , Values and Least Square Approximation for Cooperation Systems

  title={Linear Transforms , Values and Least Square Approximation for Cooperation Systems},
  author={Ulrich Faigle and Michel Grabisch},
We study linear properties of TU-games, revisiting well-known issues like interaction transforms, the inverse Shapley value problem and the concept of semivalues and least square values. We embed TU-games into the model of cooperation systems and influence patterns, which allows us to introduce linear operators on games in a natural way. We focus on transforms, which are linear invertible maps, relate them to bases and investigate many examples (Möbius transform, interaction transform, Walsh… CONTINUE READING

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