[UTMD-063] Strategy-proofness and competitive equilibrium with transferable utility: Gross substitutes revisited (by Keisuke Bando, Kenzo Imamura, Tomoya Kazumura)


Keisuke Bando, Kenzo Imamura, Tomoya Kazumura


We study the strategy-proofness (SP) of the competitive equilibrium selection (CE) mechanism in many-to-one matching with continuous transfers and quasilinear utility. The gross substitutes condition is known to guarantee the existence of CE and SP mechanisms. We show the converse: If a CE and SP mechanism exists, then the valuation of each firm must satisfy the gross substitutes condition. Various conditions for the existence of competitive equilibria have been proposed in the literature. Our results suggest that only the gross substitutes condition guarantees the existence of CE and SP mechanisms. We provide additional implications of our results for investment incentives and policy design. We also examine the two other models—the one with non-quasilinear utility and the one with discrete transfers. In contrast, the gross substitutes condition is not necessary in either model.