Abstract: A new recursive definition of the weighted Solidarity value is provided based on the normalization weight system. The weighted Solidarity value not only supports the vulnerable players in payoff allocation problems, but also evaluates the difference of players and adjusts the degree of protection for the vulnerable participants flexibly applying the weight coefficient. Through defining the weighted symmetry for the expected variation, a new axiomatization for the weighted Solidarity value is proposed in the point of the view of algebra. Ultimately, we design the recursive algorithm to implement the weighted Solidarity value. The rationality of the weighted Solidarity is analyzed through comparing with other classical solutions in an actual case.

Key words: payoff distribution, the weighted Solidarity value, weighted symmetry for the expected variation, recursion