The proportional ordinal Shapley solution for pure exchange economies

• Authors: Chaoran Sun and David Pérez-Castrillo.
• game theory
• Games and Economic Behavior
• Vol. 135 , 96-109, July, 2022.

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).