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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 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
Harsanyi dividends are useful for analyzing both games and solution concepts, e.g. the Shapley value is obtained by distributing the dividend of each coalition among its members, i.e., the Shapley value () of player in game is given by summing up a player's share of the dividends of all coalitions that she belongs to, () =: / | |.
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 ...
Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in [9] uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar ...
For example, if student 1 prefers the house allocated to student 2 and vice versa, both of them will benefit by exchanging their houses. The goal is to find a core-stable allocation – a re-allocation of houses to students, such that all mutually-beneficial exchanges have been realized (i.e., no group of students can together improve their ...
Algorithms to solve the hospitals/residents problem can be hospital-oriented (as the NRMP was before 1995) [15] or resident-oriented. This problem was solved, with an algorithm, in the same original paper by Gale and Shapley, in which the stable marriage problem was solved. [9]
A stable matching always exists, and the algorithmic problem solved by the Gale–Shapley algorithm is to find one. [3] The stable matching problem has also been called the stable marriage problem, using a metaphor of marriage between men and women, and many sources describe the Gale–Shapley algorithm in terms of marriage proposals. However ...