ETES Seminar - David Delacretaz (University of Oxford)

Title: Endowed Assignment Valuations, the Walrasian Price Gap, and the Deficit under Ex Post Efficiency

Abstract: Assuming compact and identical type spaces for buyers and sellers, we first show that in any assignment game the sum of the Walrasian price gap, summed over all the objects traded under efficiency, is equal to the deficit a planner incurs who allocates efficiently and uses the profit maximizing dominant strategy mechanism that respect agents individual rationality constraints ex post. Generalizing beyond the single-unit demand and supply assumption of the assignment game, we also show that the sum of the Walrasian gap provides a lower bound for the deficit under efficiency for all models in which the agents' payoffs are endowed assignment valuations. To the best of our knowledge, this generalizes all results in the literature that relates the deficit under incentive compatibility and individual rationality to Walrasian prices.