Population monotonic allocation schemes for cooperative games with transferable utility.

*(English)*Zbl 0753.90083Summary: An allocation scheme for a cooperative game specifies how to allocate the worth of every coalition. It is population monotonic if each player’s payoff increases as the coalition to which he belongs grows larger. We show that, essentially, a game has a population monotonic allocation scheme (PMAS) if and only if it is a positive linear combination of monotonic simple games with veto control. A dual characterization is also provided. Sufficient conditions for the existence of a PMAS include convexity and “increasing average marginal contributions”. If the game is convex, its (extended) Shapley value is a PMAS.

##### MSC:

91A12 | Cooperative games |

##### Keywords:

allocation scheme; population monotonic allocation scheme; monotonic simple games; Shapley value
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\textit{Y. Sprumont}, Games Econ. Behav. 2, No. 4, 378--394 (1990; Zbl 0753.90083)

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