The proportional ordinal Shapley solution for pure exchange economies

We define the proportional ordinal Shapley (the POSh) solution, an ordinal concept for pure exchange economies in the spirit of the Shapley value. Our construction is inspired by Hart and Mas-Colell's (1989) characterization of the Shapley value with the aid of a potential function. The POSh exists and is unique and essentially single-valued for a fairly general class of economies. It satisfies individual rationality, anonymity, and properties similar to the null-player and null-player out properties in transferable utility games. The POSh is immune to agents' manipulation of their initial endowments: It is not D-manipulable and does not suffer from the transfer paradox. Moreover, we characterize the POSh through a Harsanyi's (1959) system of dividends and, when agents' preferences are homothetic, through a weighted balanced contributions property à la Myerson (1980).