Open Access
Generalized Shapley Values by Simplicial Sampling
B. von Hohenbalken,T. Levesque +1 more
- 01 Jan 1978
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TL;DR: In this paper, the authors extend the Shapley value to a class of abstract games for which the roles that players assume are determinants of the likelihood of particular coalitions and for which they can be found as a special case.
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Abstract: Characteristic function representation of n-person cooperative games precludes the modeling of structural properties of a game other than the relationship between coalition structure and the worth of a game. This means that the Shapley value, a measure of expected return to a player from playing the game, is restricted as a solution concept to only those games satisfying the condition that all coalitions of the same cardinality are equiprobable. By contrast, as we demonstrate below, Shapley's three axioms are satisfied for Shapley-like measures based on richer characterizations of a game. In particular, we extend the Shapley value to a class of abstract games for which the roles that players assume are determinants of the likelihood of particular coalitions and for which the original Shapley value can be found as a special case.
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Citations
Uniform sampling on simplices and spheres
Abstract: The increasing use of 120-cps terminals and the growth of APL are placing increasing strains on current APL notation. For those people who think verbally rather than visually, a phonetic notation is preferable to a logograph~c notation. A notation is proposed for use specifically on ASCII terminals. Specific solutions are offered to the problems of (a) ambiguities in parsing (upper and lower case), (b) recognition of operator sequences (periods as separators), and (c) reserved-word name conflicts (name spaces). The change in notation is accomplished with almost no change to the underlying language.
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Cooperation Preference Aware Shapley Value: Modeling, Algorithms and Applications
Hong Biao Xie,John C. S. Lui +1 more
TL;DR: In this paper , the authors developed mathematical models to solicit two types of cooperation preferences, i.e., group-wise preferences and pairwise preferences, and extended the classical Shapley value to capture this feature.
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References
Evaluation of a Presidential Election Game
TL;DR: In this paper, the Shapley value of the presidential election game is approximated by the method of multilinear extensions; the likely error in this approximation is computed by studying the error in the electoral college game.
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Values of large games. 6: evaluating the electoral college exactly
Irwin Mann,Lloyd S. Shapley +1 more
- 01 Jan 1962
TL;DR: In this paper, the electoral college is used as an application for the theory of games and the use of the power index, and the results have some sociological, as well as mathematical, interest; they are given for three different cases.