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Monotonic solutions of cooperative games

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The principle of monotonicity for cooperative games states that if a game changes so that some player's contribution to all coalitions increases or stays the same then the player's allocation should not decrease. There is a unique symmetric and efficient solution concept that is monotonic in this most general sense — the Shapley value. Monotonicity thus provides a simple characterization of the value without resorting to the usual “additivity” and “dummy” assumptions, and lends support to the use of the value in applications where the underlying “game” is changing, e.g. in cost allocation problems.

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This work was supported in part by the National Science Foundation under Grant MCS-82-07672 at the University of Maryland.

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Young, H.P. Monotonic solutions of cooperative games. Int J Game Theory 14, 65–72 (1985).

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