In Chap. 16 set-valued solution concepts for games with transferable utilities were studied: the imputation set, core, domination core, and stable sets. In this chapter, a one-point (single-valued) solution concept is discussed: the Shapley value. It may again be helpful to first study the relevant parts of Chaps. 1 and 9.
Section 17.1 introduces the Shapley value by several formulas and presents (a variation on) Shapley’s axiomatic characterization using additivity. In Sect. 17.2 we present three other characterizations of the Shapley value: a description in terms of Harsanyi dividends; an axiomatic characterization of Young based on strong monotonicity; and Owen’s formula for the Shapley value based on a multilinear extension of games. Section 11.3 discusses Hart and Mas-Colell’s approach to the Shapley value based on potential and reduced games.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). The Shapley Value. In: Game Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69291-1_17
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DOI: https://doi.org/10.1007/978-3-540-69291-1_17
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