On Harsanyi Payoff Vectors and the Weber Set

The paper discusses the set of Harsanyi payoff vectors,also known as the Selectope. First, we reconsider some results on Harsanyi payoff vectors, published by Vasil'ev in the late 1970's, within a more general framework. In particular, these results state already that the set of Harsanyi payoff vectors is given by the core of an associated convex game, a result that recently has been proven by Derks et. al.(2000). The marginal contribution vectors are examples of Harsanyi payoff vectors so that the Weber set, being the convex hull of the marginal contribution vectors, is a subset of the Harsanyi set, which denotes the set of Harsanyi payoff vectors. We provide two characterizations of those Harsanyi payoff vectors that are elements of the Weber set.