The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012.[1][2] To each cooperative game it assigns a unique distribution (among the players) of a total surplus generated by the coalition of all players. The Shapley value is characterized by a collection of desirable properties. Hart (1989) provides a survey of the subject.[3][4]
^Shapley, Lloyd S. (August 21, 1951). "Notes on the n-Person Game -- II: The Value of an n-Person Game" (PDF). Santa Monica, Calif.: RAND Corporation.
^Roth, Alvin E., ed. (1988). The Shapley Value: Essays in Honor of Lloyd S. Shapley. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511528446. ISBN 0-521-36177-X.
^Hart, Sergiu (1989). "Shapley Value". In Eatwell, J.; Milgate, M.; Newman, P. (eds.). The New Palgrave: Game Theory. Norton. pp. 210–216. doi:10.1007/978-1-349-20181-5_25. ISBN 978-0-333-49537-7.
^Hart, Sergiu (May 12, 2016). "A Bibliography of Cooperative Games: Value Theory".
The Shapleyvalue is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel...
of 92. Shapley was an expert Kriegspiel player, and an avid baseball fan. Along with the Shapleyvalue, stochastic games, the Bondareva–Shapley theorem...
concepts, e.g. the Shapleyvalue is obtained by distributing the dividend of each coalition among its members, i.e., the Shapleyvalue ϕ i ( v ) {\displaystyle...
stochastic games, the Shapleyvalue, and repeated games. Together with Jean-Francois Mertens, he proved the existence of the uniform value of zero-sum undiscounted...
M(F)\neq 0} . In game theory, the Shapleyvalue or Shapley index is used to indicate the weight of a game. Shapleyvalues can be calculated for fuzzy measures...
optimizes the best-case outcomes (the price of stability), is precisely the Shapleyvalue cost-sharing rule. A symmetrical statement is similarly valid for utility-sharing...
Harlow Shapley (November 2, 1885 – October 20, 1972) was an American scientist, head of the Harvard College Observatory (1921–1952), and political activist...
factors corresponding to particular values (e.g., high or low) of the output. Shapley effects rely on Shapleyvalues and represent the average marginal...
chess; sometimes called "the father of information theory" Lloyd Shapley – Shapleyvalue and core concept in coalition games (Nobel Memorial Prize in Economic...
first described by Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is...
game-theory. The approach proposed in uses the Shapleyvalue. Because of the time-complexity hardness of the Shapleyvalue calculation, most efforts in this domain...
Aumann, 1985, JET "The Consistent ShapleyValue for Hyperplane Games", with G. Owen, 1989, IJGT "The Consistent ShapleyValue for Games without Side Payments"...
of the game when door 1 was chosen by the player: the host's action adds value to the door not eliminated, but not to the one chosen by the contestant...
common knowledge in game theory. He collaborated with Lloyd Shapley on the Aumann–Shapleyvalue. He is also known for Aumann's agreement theorem, in which...
the axioms characterizing the Shapleyvalue. The payoff allocation for each sub-game is perceived as fair, so the Shapley-based payoff allocation for the...
Foundation for Research in Economics at Yale. "On the Uniqueness of the ShapleyValue" (1975) International Journal of Game Theory Vol. 4, pp. 131–139. "Trade...
the extensive form game, fictitious play, repeated games, and the Shapleyvalue were developed. The 1950s also saw the first applications of game theory...
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