Abstract
This paper advances the idea that, in a variety of environments, it is natural to think of the solution of a (coalition form) game as an ordering of the players rather than as a division of the value of coalitions. Orderings that are characterized by an average of the desirability of one player to another across coalitions are axiomatized. This includes the rule where i is ranked above j if and only if the Shapley Value of i in the game without j is greater than the Shapley Value of j in the game without i. The result is applicable to arbitration schemes, scheduling problems, etc.
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