A new solution for \(n\)-person games using coalitional theory. I: The conditions (Q2748145)

Let \(v\) be an \(n\)-person transferable utility game in coalition function form, and let \(S(v)\) be the Shapley value of \(v\). This paper studies \(v\) from the standpoint of coalition trees. The split-the-difference (STD) solution is applied when any coalition tree is equally likely, and any 2-player coalition splits its coalition value equally. The paper shows that the STD solution of \(v\) is \(S(v)\). In addition, a sufficient condition is given for the STD solution to be in the core of \(v\).