1973
DOI: 10.1287/mnsc.20.3.370
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A Simple Expression for the Shapley Value in a Special Case

Abstract: We present a simple and easily calculated expression for the Shapley value whenever the characteristic function is a "cost" function with the property that the cost of any subset of players is equal to the cost of the "largest" player in that subset. It turns out that a simple rule previously proposed for calculating airport landing charges generates precisely the Shapley value for an appropriately defined game.

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Cited by 408 publications
(207 citation statements)
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“…In the literature, various classes of games that are fully determined by the worths of these special coalitions can be found. For example, in auction games (see Graham et al, 1990) and bankruptcy games (see O'Neill, 1982;Aumann and Maschler, 1985), the game is fully described by the worth of the 'grand coalition' N and the worths of all coalitions of size n − 1, while an airport game (see Littlechild and Owen, 1973) is fully described by the n worths of the singletons. Although the solutions studied in this article are especially useful for these classes of games, we support these solutions also in other applications of games, even if the game depends on the worths of more coalitions.…”
Section: Discussionmentioning
confidence: 99%
“…In the literature, various classes of games that are fully determined by the worths of these special coalitions can be found. For example, in auction games (see Graham et al, 1990) and bankruptcy games (see O'Neill, 1982;Aumann and Maschler, 1985), the game is fully described by the worth of the 'grand coalition' N and the worths of all coalitions of size n − 1, while an airport game (see Littlechild and Owen, 1973) is fully described by the n worths of the singletons. Although the solutions studied in this article are especially useful for these classes of games, we support these solutions also in other applications of games, even if the game depends on the worths of more coalitions.…”
Section: Discussionmentioning
confidence: 99%
“…In this paper we consider this issue in the context of cooperative games with transferable utility. Cooperative games are widely applied in economic allocation problems such as auction games (see Graham et al 1990), airport landing fee problems (see Littlechild and Owen 1973), water distribution problems (see Ambec and Sprumont 2002), polluted river problems (see Ni and Wang 2007), sequencing problems (see Curiel et al 1989) and queueing problems (see Maniquet 2003). For these games the trade-off between marginalism and egalitarianism can be seen as the trade-off between allocating according to the Shapley value or the equal division solution.…”
Section: Introductionmentioning
confidence: 99%
“…The Harsanyi constrained core is always nonempty and generalizes 1 Besides the examples discussed in Section 3, other examples are, e.g. auction games (see Graham et al (1990)), dual airport games (see Littlechild and Owen (1973)), telecommunication games (see van den Nouweland et al (1996)) and queueing games (see Maniquet (2003)). …”
Section: Introductionmentioning
confidence: 89%
“…In the DR polluted river game v the worth of a coalition S is equal to the sum of all costs from the most upstream player in S to the most downstream player n. In fact, v is the airport game corresponding to the airport situation with costs ∑ n j=i c j for player (airplane) i ∈ N , see Littlechild and Owen (1973). 13 In general an airport game, and so v, is not totally positive.…”
Section: Polluted River Gamesmentioning
confidence: 99%