Monotonic solutions of cooperative games

by: HP Young

International Journal of Game Theory, Vol. 14, No. 2. (1 June 1985), pp. 65-72.

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Abstract

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.

@article{game_coop_sol_young85, abstract = {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.}, author = {Young, H. P. }, citeulike-article-id = {2677658}, doi = {10.1007/BF01769885}, journal = {International Journal of Game Theory}, keywords = {game-theory, network-planning, wireless-comm}, month = {June}, number = {2}, pages = {65--72}, posted-at = {2008-04-16 12:33:42}, priority = {2}, title = {Monotonic solutions of cooperative games}, url = {http://dx.doi.org/10.1007/BF01769885}, volume = {14}, year = {1985} }

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TY - JOUR ID - game_coop_sol_young85 L3 - citeulike-article-id:2677658 TI - Monotonic solutions of cooperative games JF - International Journal of Game Theory VL - 14 IS - 2 SP - 65 EP - 72 N2 - 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. KW - game-theory KW - network-planning KW - wireless-comm AU - Young, HP PY - 1985/06/01/ UR - http://dx.doi.org/10.1007/BF01769885 ER -

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