A Reduced Harsanyi Power Solution for Cooperative Games with a Weight Vector

Abstract

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.