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The Shapley value is one way to distribute the total gains to the players, assuming that they all collaborate. It is a "fair" distribution in the sense that it is the only distribution with certain desirable properties listed below. According to the Shapley value, [5] the amount that player i is given in a coalitional game (,) is
The Shapley value is the unique payoff vector that is efficient, symmetric, and satisfies monotonicity. [14] It was introduced by Lloyd Shapley (Shapley 1953) who showed that it is the unique payoff vector that is efficient, symmetric, additive, and assigns zero payoffs to dummy players.
The Shapley value is mainly applicable to the following situation: the contribution of each actor is not equal, but each participant cooperates with each other to obtain profit or return. The efficiency of the resource allocation and combination of the two distribution methods are more reasonable and fair, and it also reflects the process of ...
The Bondareva–Shapley theorem: the core of a game is nonempty if and only if the game is "balanced". [5] [6] Every Walrasian equilibrium has the core property, but not vice versa. The Edgeworth conjecture states that, given additional assumptions, the limit of the core as the number of consumers goes to infinity is a set of Walrasian equilibria.
Let be the number of players, the set of action profiles over the action sets of each player and : be the payoff function for player .. Given a game = (, = …,:), we say that is a potential game with an exact (weighted, ordinal, generalized ordinal, best response) potential function if : is an exact (weighted, ordinal, generalized ordinal, best response, respectively) potential function for .
The ingredients of a stochastic game are: a finite set of players ; a state space (either a finite set or a measurable space (,)); for each player , an action set (either a finite set or a measurable space (,)); a transition probability from , where = is the action profiles, to , where (,) is the probability that the next state is in given the current state and the current action profile ; and ...
The Shapley value is the only value that satisfies this property, plus 2, 3, and 5. —Preceding unsigned comment added by 193.147.86.254 17:26, 14 September 2007 (UTC) You are right. Just take v(N) and divide it evenly among the players. This is another solution, different from the Shapley value, that satisfies 2, 3, and 5.
The solution concept authority distribution was formulated by Lloyd Shapley and his student X. Hu in 2003 to measure the authority power of players in a well-contracted organization. [1] The index generates the Shapley-Shubik power index and can be used in ranking, planning and organizational choice.