Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts

by M. Maschler, B. Peleg, Lloyd S. Shapley

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Explores the geometrical relationships between the kernel and nucleolus of an [n]-person game in characteristic-function form and a number of other cooperative solution concepts, most notably the core and the strong epsilon-core. As a result, many technical properties of these solutions are clarified and new light is shed on the intuitive interpretations. In games that are "zero-monotonic" (including all superadditive games), the kernel coincides with the pre-kernel, which is analytically simpler and can be described as a multi-bilateral equilibrium in which every pair of players bisects the difference between the outcomes that they, with the support of their best allies, could separately impose on each other. The nucleolus is a special point in the kernel, and for zero-monotonic games it lies in the least core as well.

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