The \(\tau\)-value, the core and semiconvex games (Q1069867)

The notion of ''semiconvex game'' (of n persons, in characteristic function form) is introduced and it is proved that any exact game (in Schmeidler's sense) is semiconvex. Significant properties of Tijs' ''\(\tau\)-value'' \(\tau\) (v) associated with a semiconvex game v are pointed out. Among others: \(\tau\) (v) is contained into the core of v then \(n=4\) and \(\tau\) (v) is exactly the Shapley value when the gap function of v is a non- negative constant.