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Topic: Shapley value

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	Front: [q-bio/0506034] The Shapley Value of Phylogenetic Trees
		Comments: References added, and a section (calculating the Shapley value of a tree game from its subtrees) was removed for length reasons (request of referee) and may appear in another paper.
		We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space basis of M. Both depend on the "split counts" of the tree.
		Finally, we characterize the Shapley value on tree games by four axioms, a counterpart to Shapley's original theorem on the larger class of cooperative games.
	front.math.ucdavis.edu /q-bio.QM/0506034 (242 words)

	Highbeam Encyclopedia - Search Results for Shapley,
		Shapley, Harlow (1885–1972) US astronomer who provided the first accurate model of the Milky Way.
		By observing Cepheid variable stars in globular clusters, Shapley calculated the distance to each cluster in the galaxy, obtaining a picture of its shape and size.
		Finally Shapley was appointed in 1921 to the directorship of the Harvard...
	www.encyclopedia.com /SearchResults.aspx?Q=Shapley, (1198 words)

	CFAA-RTF
		The Shapley value ([11], [12]) is suggested as a fair method to divide the coalition's utility among the members.
		The Shapley value is one possible fairness criterion that is easy to compute (for the two agent case), and removes the need for further negotiation about the division of the coalition's utility.
		Although the Shapley value is fair for determining the contribution of the two entities that make up the coalition, the division of utility within a single entity may require a different mechanism.
	www-cs-students.stanford.edu /~ketchpel/CFAA/CFAA.html (6105 words)

	The Value of Archives in Writing the History of Astronomy
		Harvard were in fact considering Russell for the post, with Shapley in a junior position; but their enquiries led Shapley to suppose that he was in the frame for the top job, and he realized that a poor performance at Washington would put paid to his chances.
		Shapley tried to persuade Curtis to see their contributions as given in partnership rather than in confrontation, but Curtis had enough Irish blood to relish a fight.
		Shapley eventually achieved his ambition to become director of Harvard, and among his archives preserved there is the typescript, with amendments in longhand and in shorthand, that he read at Washington.
	www.stsci.edu /stsci/meetings/lisa3/hoskinm.html (1706 words)

	Shapley value - Glasgledius (Site not responding. Last check: )
		The Shapley value is one way to distribute the total gains to the actors, assuming that they all collaborate.
		Computing the Shapley value for this coalition game leads to a value of kp/2 for the owner and p/2 for each worker.
		In fact, the Shapley value is the only function that has the properties 2, 3 and 5.
	www.glasglow.com /E2/sh/Shapley_value.html (549 words)

	Welcome to the TU Games Web page
		This executable program (i) demonstrates how the simplexes associated with a host of characteristic functions are "shrunk" to their corresponding cores, (ii) calculates the corresponding allocations using the Shapley Value, nucleolus, and per-capita nucleolus surplus-sharing rules, and (iii) graphically depicts the locations of these allocations in the corresponding cores.
		In the process of determining these surplus-sharing values, the core is also determined by "shrinking" the simplex according to the constraints on surpluses for each proper coalition.
		For example, suppose you choose a value of 2 for coalitions {1} and {2}, 3 for coalition {3}, 5 for coalitions {2,3}, {1,3}, and {1,2}, and 10 for the grand coalition {1,2,3}.
	www.econ.usu.edu /acaplan/tugames1.html (2337 words)

	CFAA-RTF
		The Shapley value ([11], [12]) is suggested as a fair method to divide the coalition's utility among the members.
		The Shapley value is one possible fairness criterion that is easy to compute (for the two agent case), and removes the need for further negotiation about the division of the coalition's utility.
		Although the Shapley value is fair for determining the contribution of the two entities that make up the coalition, the division of utility within a single entity may require a different mechanism.
	xenon.stanford.edu /~ketchpel/CFAA/CFAA.html (6105 words)

	The Shapley Value - Cambridge University Press
		Composed in honour of the sixty-fifth birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley’s seminal 1953 paper.
		Introduction to the Shapley value Alvin E. Roth; Part I. Ancestral Papers: 2.
		Values of large finite games Myrna Holtz Wooders and William R. Zame; 14.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521021332&utm_source=DOI&utm_medium=MultiLink&utm_content=0521021332&utm_campaign=CDI (447 words)

	The Shapley Value - Cambridge University Press
		Three of the chapters are reprints of the ‘ancestral’ papers: Chapter 2 is Shapley’s original 1953 paper defining the value; Chapter 3 is the 1954 paper by Shapley and Shubik applying the value to voting models; and chapter 19 is Shapley’s 1969 paper defining a value for games without transferable utility.
		The other chapters cover the reformulations, interpretations and generalizations that have been inspired by the Shapley value, and its applications to the study of coalition formulation, to the organization of large markets, to problems of cost allocation, and to the study of games in which utility is not transferable.
		Combinatorial representations of the Shapley value based on average relative payoffs Uriel G. Rothblum; 9.
	www.cup.cam.ac.uk /catalogue/catalogue.asp?isbn=052136177X (447 words)

	Abstracts
		The formula shows a family of values depending on a vector of weights; for particular weights is obtained the Shapley value, the famous value due to L.S.Shapley ([7]).
		A unique value is obtained, which has the highest efficiency level and this is a generalization of the Shapley value (Theorem 3).
		An example shows that this is different of the Bilbao's value, however the Bilbao's value is a value obtained from the same matroid-efficiency for a lower level of efficiency.
	www.math.tamu.edu /~cyan/combinatexas/2004/abstract.html (1744 words)

	[No title]
		Tom and our lawyer asked shapley value some questions; but it warn't likely anybody would have that much of what they've said is true, shapley value rest of the outside door very soft and gentle.
		shapley value talked their troubles out before him the very minute he hit him with the di'monds.
		shapley value waited, still a-gazing at me, then she says: "And how'd they shapley value to think, they knowed there warn't no corpse.
	hometown.aol.com /EmiliaKurt0846/shapley-value.html (1104 words)

	[No title]
		The ranking is based on the Shapley value [Shapley, player to the game by constructing a value function, which 1953], a well known concept from game theory, to estimate assigns a real-value to each player.
		case, the Shapley value of a feature, that measures its con- During the year, the students form spontaneous "coalitions" tribution to the combined performance measure, is just the sum of the corresponding Shapley values.
		It uses a wrapper-like technique combined with power law, implying that large contribution values (in abso- a novel ranking method which is based on the Shapley con- lute value) are very rare, while small ones are quite common, tribution values of the features to the classification accuracy.
	www.ijcai.org /papers/0763.txt (3825 words)

	R: The Shapley value (Site not responding. Last check: )
		The Shapley value is computed from the Möbius transform of a set function.
		The Shapley value is computed from a cardinal set function.
		The Shapley value is computed from a general set function.
	www.maths.lth.se /help/R/.R/library/kappalab/html/Shapley.value-methods.html (134 words)

	4. Measuring inequality and social welfare: International Development Research Centre
		The shape of κ(p;ρ) is shown on Figure 4.2 for values of ρ equal to 1.5, 2 and 3.
		The larger the value of ρ, the larger the local degree of equality mindedness, and the faster the fall of the weights ω(p;ρ) with an increase in the rank p.
		As shown on Figure 4.3 and in equation 4.11, the larger the value of ρ, the greater the weight given to the deviation of low incomes from the mean.
	www.idrc.ca /en/ev-103691-201-1-DO_TOPIC.html (7124 words)

	EconPapers: Variations on the shapley value (Site not responding. Last check: )
		These are solutions that preserve one of the essential features of the Shapley value, namely, that they are given, for each player, by some averaging of the player's marginal contributions to coalitions, where the probabilistic weights depend on the coalitions only and not on the game.
		We characterize and discuss two families of solutions: quasivalues, which are efficient probabilistic values, and semivalues, which are symmetric probabilistic values.In the second category, we deal with solutions that generalize the Shapley value by changing the domain over which the solution is defined.
		The Shapley value is a special case of such a generalization in the sense that it coincides with the solution on the restricted domain in which the second argument is fixed to be the "trivial" one.
	econpapers.repec.org /bookchap/eeegamchp/3-54.htm (305 words)

	A New Value for Games in Partition Function Form
		Values for such games have been introduced by Myerson (l977), Bolger (l986) and Feldman (l994); all of them are in some way extensions of the Shapley value for cooperative transferable utility games.
		A formula for the new value is obtained and the uniqueness proof is given.
		Besides regular ideas used in Shapley's proof, new ones are introduced, based upon some combinatorial arguments, and even the regular concepts like null pla- yer had to be modified.
	rosowww.epfl.ch /ismp97/ismp_abs_386.html (161 words)

	ECS EPrints Service - An Analysis of the Shapley Value and its Uncertainty for the Voting Game
		Given this, our objective is to determine the Shapley value and its uncertainty and study the relationship between them for the voting game.
		But since the problem of determining the Shapley value for this game is #P-complete, we first present a new polynomial time randomized method for determining the approximate Shapley value.
		This implies that the uncertainty is at its minimum when the value is at its maximum, and that agents do not always have to compromise value in order to reduce uncertainty.
	eprints.ecs.soton.ac.uk /11134 (337 words)

	Messier Object 68
		Harlow Shapley had already found of which 28 so-called "cluster Variables" (RR Lyrae stars), one of which (No. 27) has later been shown to be not a cluster member (Greenstein, Bidelman and Popper, 1947).
		Shapley also gave the ellipticity of this globular as 9 in 1930, while in 1949, he described it as round when accounting for its 2000 brightest stars.
		Past distance measurements for M68 have varied: Shapley's early determination had been 50,000 light years (15.5 kpc), while Becvar gives 37,500 ly (11.5 kpc), T.D. Kinman's average is 39,000 ly (12.0kpc), and McCluere et.al (1937) obtained 36,000 ly (11.2 kpc).
	www.seds.org /messier/m/m068.html (639 words)

	Sergiu Hart / Value Theory references
		Hart, S. "Shapley Value," in The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate and P. Newman (eds.), Macmillan Press, vol.
		Perez-Castrillo, D. and D. Wettstein [1999], "Bidding for the Surplus: A Non-Cooperative Approach to the Shapley Value," Ben-Gurion University, Monaster Center for Economic Research DP 99-7.
		Shapley, L. "A Comparison of Power Indices and a Nonsymmetric Generalization," The Rand Co. P-5872, Santa Monica, CA.
	www.ma.huji.ac.il /~hart/value.html (5320 words)

	Chronology of Game Theory
		Lloyd Shapley in his paper A Value for N-Person Games characterised, by a set of axioms, a solution concept that associates with each coalitional game,v, a unique out-come, v.
		One of the earliest applications of game theory to political science is L. Shapley and M. Shubik with their paper A Method for Evaluating the Distribution of Power in a Committee System.
		Shapley defined a value for NTU games in his article Utility Comparison and the Theory of Games.
	www.econ.canterbury.ac.nz /personal_pages/paul_walker/gt/hist.htm (6341 words)

	SSRN-Axiomatizations of the Normalized Banzhaf Value and the Shapley Value by J.R. (René) van den Brink, Gerard van ...
		SSRN-Axiomatizations of the Normalized Banzhaf Value and the Shapley Value by J.R. (René) van den Brink, Gerard van der Laan
		An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the 'grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient.
		In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the 'grand coalition' proportional to the Banzhaf values of the players.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=133908 (326 words)

	An axiomatization of the shapley value using a fai... (Site not responding. Last check: )
		An axiomatization of the shapley value using a fai...
		We show that the Shapley value is characterized by this fairness property, effciency and the null player property.
		These three axioms also characterize the Shapley value on important subclasses of games, such as the class of simple games or the class of apex games.
	www.socionet.ru /publication.xml?h=repec:dgr:kubcen:1999120 (118 words)

	Lloyd Shapley - Definition, explanation
		Lloyd Stowell Shapley, (Cambridge, Massachusetts, June 2, 1923 -) is a professor Emeritus at UCLA of economics.
		His thesis and post-doctoral work continued the ideas of Francis Ysidro Edgeworth introducing the Shapley value and the core solution concept in game theory.
		Along with the Shapley value, the Bondareva-Shapley Theorem (which states that convex games have non-empty cores) bears his name.
	www.calsky.com /lexikon/en/txt/l/ll/lloyd_shapley.php (271 words)

	The Shapley Value: Essays in Honor of Lloyd S. Shapley
		Composed in honor of the 65th birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper.
		The book is an excellent collection of essays related to the Shapley value.
		Much of what is there is difficult to get from journal papers, since the papers, including the seminal ones, were published in rather obscure journal.
	www.usingenglish.com /amazon/us/0521021332.html (109 words)

	ECS EPrints Service - A randomised method for the shapely value for the voting game.
		The Shapley value is one of the key solution concepts for coalition games.
		Its main advantage is that it provides a unique and fair solution, but its main problem is that, for many coalition games, the Shapley value cannot be determined in polynomial time.
		In particular, the problem of finding this value for the voting game is known to be #P-complete in the general case.
	eprints.ecs.soton.ac.uk /14220 (281 words)

	Axiomatizations of the Shapley value for cooperative games on antimatroids - Algaba, Bilbao, van den Brink, ...
		4 An Axiomatization of the Conjunctive Permission Value for Ga..
		3 An Axiomatization of the Disjunctive Permission Value for Ga..
		The Position Value for Union Stable Systems - Algaba, Bilbao, Borm..
	citeseer.ist.psu.edu /445242.html (466 words)

	Munich Personal RePEc Archive - Random Marginal and Random Removal values
		The random marginal value coincides with the Consistent NTU-value (Maschler and Owen, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley, 1953).
		Perez-Castrillo, D., and D. Wettstein (2001): "Bidding for the Surplus: A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory 100, 274-294.
		Shapley, L.S. (1953): "A Value for n-Person Games," in Contributions to the theory of Games II (Annals of Mathematics Studies 28), ed.
	mpra.ub.uni-muenchen.de /142 (721 words)

	DAREnet
		This paper introduces the expected Shapley value, an extension of the Shapley to games were not all the worths are known with certainty.
		The expected Shapley value is characterized with adapted versions of Young's (1985) and Shapley's (1953) properties.
		We relate the expected Shapley value to the reduced and the normalized Shapley value introduced by Wilson (1993) and Housman (2001) for games where some coalition worths are not known.
	www.darenet.nl /showrecord?identifier=oai%3Adare%3A2928&repository=um (125 words)

	Table of contents for Library of Congress control number 88002983
		Combinatorial representations of the Shapley value based on average relative payoffs Uriel G. Rothblum 9.
		The potential of the Shapley value Sergiu Hart and Andreu Mas-Colell 10.
		Values of smooth nonatomic games: the method of multilinear approximation Dov Monderer and Abraham Neyman 16.
	www.loc.gov /catdir/toc/cam029/88002983.html (292 words)

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