Abstract:

As both the Shapley and Winter values are averages of players' marginal contributions, this paper explores their analytic relationship. Specifically, the result that Shapley value is Winter value's expectation with respect to symmetric probability distributions on level structure set is proved. As a corollary, the argument that
Shapley value is Winter value's average with respect to any similar class in level structure set is also attested. Finally, the equivalence of this result and corollary is presented. The research results not only expand corresponding relationship between Shapley and Owen values, but also simplify the proofs of these correspondingrelationship enormously.

Key words: cooperative game, Shapley value, Owen value, Winter value, coalition structure, level structure