The Weighted Surplus Division Value for Cooperative Games

Abstract

The weighted surplus division value is defined in this paper, which allocates to each player his individual worth and then divides the surplus payoff with respect to the weight coefficients. This value can be characterized from three different angles. First, it can be obtained analogously to the scenario of getting the procedural value whereby the surplus is distributed among all players instead of among the predecessors. Second, endowing the exogenous weight to the surplus brings about the asymmetry of the distribution. We define the disweighted variance of complaints to remove the effect of the weight and prove the weighted surplus division value is the unique solution of an optimization model. Lastly, the paper offers axiomatic characterizations of the weighted surplus division value through proposing new properties, including the ω -symmetry for zero-normalized game and individual equity.