The Proportional Ordinal Shapley Solution for Pure Exchange Economies

Abstract

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. Moreover, the POSh is immune to agents' manipulation of their initial endowments: It is not D-manipulable and does not suffer from the transfer paradox. Finally, we construct a bidding mechanism à la Pérez-Castrillo and Wettstein (2001) that implements the POSh in subgame perfect Nash equilibrium for economies where agents have homothetic preferences and positive endowments.