A Reduced Harsanyi Power Solution for Cooperative Games with a Weight Vector
The Harsanyi power solution for cooperative games allocates dividends generated by coalitions proportionally to each player’s power index. Normally, cooperative games tacitly treat all players symmetric. However, the fact is that different players may be asymmetric and contribute to different efforts, bargaining powers, or stability in the process of cooperation. A weight vector is used to reflect players’ asymmetry. In view of these weights are possible to be less than 1, that is, not all players are absolutely important, a loss of dividends of coalitions can happen. We define and characterize a reduced Harsanyi power solution for cooperative games with a weight vector, which is relevant to a loss function of dividends. Moreover, when the loss function takes particular forms, the reduced Harsanyi power solution has a linear relationship with the Harsanyi power solution.
KeywordsHarsanyi dividend Loss function Reduced Harsanyi power solution
The research has been supported by the National Natural Science Foundation of China (Grant Nos. 71571143, 71601156, 71671140 and 71271171).
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