Shapley-like values without symmetry
Following the work of Shapley on the Shapley value , and further work of Owen , we offer an alternative formulation of and path to and through the work of Weber in his paper on efficient but not symmetric cooperative games . We accomplish this by offering alternative conditions to replace the standard axiomatic assumptions. This is accomplished by introducing conditions, "reasonableness" and "efficiency" on the output of the games themselves, and using this to find properties of the linear maps that describe the games themselves. This results in a special class of linear maps for which any other "reasonable, efficient" map can be written as a convex combination of special ones.
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