Harsanyi power solution for games with restricted cooperation

This paper discusses the Harsanyi power solution for cooperative games in which cooperation among players is based on an arbitrary collection of feasible coalitions. We define the Harsanyi power solution as a value which distributes the Harsanyi dividends such that the dividend shares of players in each feasible coalition are proportional to the corresponding players’ participation index, (i.e., a power measure for players in the cooperation restrictions). When all coalitions can be formed in a game, the Harsanyi power solution coincides with the Shapley value. We provide two axiomatic characterizations for the Harsanyi power solution: one uses component efficiency and participation fairness, and the other uses efficiency and participation balanced contributions. Meanwhile, we show that the axioms of each axiomatization are logically independent. The study also shows that the Harsanyi power solution satisfies several other properties such as additivity and inessential player out. In addition, the Harsanyi power solution is the unique value that admits the $$\lambda $$ λ -potential.