Job Market Paper: Bidding against a buyout

We introduce two mechanisms that implement the Shapley value and the equal surplus value, respectively. The main feature of both mechanisms is that multiple proposers put forth allocation plans simultaneously. The implementation of a plan requires both consensus among proposers and acceptance of respondents. In case of disagreement among proposers, we use the bidding procedure introduced by Perez-Castrillo and Wettstein (J. Econ. Theory 100: 274-294, 2001), which facilitates a buyout of one proposer in each round. Then the difference between two values comes down to how proposers negotiate with respondents.

Value-free reductions, joint with D. Perez-Castrillo

We introduce the value-free (v-f ) reductions, which are operators that map a coalitional game played by a set of players to another “similar” game played by a subset of those players. We propose properties that v-f reductions may satisfy, we provide a theory of duality for them, and we characterize several v-f reductions (among which the value-free version of the reduced games propose by Hart and Mas-Colell, 1989, and Oishi et al., 2016). Unlike reduced games, which were introduced to characterize values in terms of consistency properties, v-f reductions are not defined in reference to values. However, a “path-independent” v-f reduction induces a value. We characterize v-f reductions that induce the Shapley value, the stand-alone value, and the Banzhaf value. Moreover, we can connect our approach to the literature on consistency because any value induced by a path-independent v-f reduction is consistent with that reduction.

The Proportional Ordinal Shapley Solution for Pure Exchange Economies, joint with D. Perez-Castrillo

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 (2006) that implements the POSh in subgame perfect Nash equilibrium for economies where agents have homothetic preferences and positive endowments.