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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 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 topology of the network or a special character of the problem.
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. [1] The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an n-player game. Players with the same ...
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 ...
When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player.
In 1962, David Gale and Lloyd Shapley proved that, for any equal number of men and women, it is always possible to solve the stable marriage problem and make all marriages stable. They presented an algorithm to do so. [9] [10] The Gale–Shapley algorithm (also known as the deferred acceptance algorithm) involves a number of "rounds" (or ...
The formula developed by Aumann and Shapley to construct a Shapley value for non atomic games with a continuum of players Topics referred to by the same term This disambiguation page lists articles associated with the title Diagonal formula .
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.