The famous Indian manual on the management of kingdoms suggests an unusual tax that is based on a seller’s assessment of the price of the good to be sold. We show that this tax confronts the seller with an optimization problem. In translations, some interpretational issues have arisen that this paper claims to solve.

The aim of cooperative game theory is to suggest and defend payoffs for the players that depend on a coalition function (characteristic function) describing the economic, social, or political situation. We consider situations where the payoffs for some players are determined exogenously. For example, in many countries, lawyers or real-estate agents obtain a regulated fee or a regulated percentage of the business involved. The aim of this article is to suggest and axiomatize two values with exogenous payments, an unweighted one (...) and a weighted one. (shrink)