On Harsanyi Dividends and Asymmetric Values

The concept of dividend in transferable utility games was introduced by Harsanyi [1959]. It offers a unifying framework for studying various valuation concepts, from the Shapley value (symmetric as well as weighted) to the different notions of values introduced by Weber [1988]. Using the decomposition of the characteristic function used by Shapley [1953] to prove uniqueness of his value, the idea of Harsanyi was to associate to each coalition a dividend to be distributed among its members to define an allocation. Many authors have contributed to that question. Here, we offer a synthesis of their work, with a particular attention to restrictions on dividend distributions, starting with the seminal contributions of Vasil'ev [1978], Hammer, Peled and Sorensen [1977] and Derks, Haller and Peters [2000], until the recent paper of van den Brink, van der Laan and Vasil'ev [2014].