More on Ausubel's Dynamic Double Auction

Abstract

This paper examines the incentive-compatibility of a close variant of Ausubel's (2006) dynamic auction for divisible heterogeneous goods. Assuming only quasi-linear, (weakly) concave utilities with private values, this paper removes Ausubel's assumptions that value functions are strictly concave and non-satiated, that demand functions are measurable, and that the price tâtonnement is continuous and reaches an equilibrium in finite time. Strict concavity is a problematic assumption when applying the auction design, for instance, to commodity exchanges between firms motivated by locally linear value functions. Since merely concave value functions may induce non-unique levels of optimal consumption, bidders in the design modification proposed here submit (set-valued) demand correspondences rather than (single-valued) demand functions. The auctioneer then selects a suitable vector of demand levels from these bids and feeds them into a discrete tatonnement process based Shor's (1985) subgradient algorithm. For quasi-linear, concave utilities, this algorithm converges to equilibrium prices for any starting point. This paper shows that misrepresentations of demand that lead the tâtonnement process away from the true price equilibrium are strictly inferior to truth-telling as the run-time of the process tends to infinity and as its step-size tends to zero. This result, based on only elementary techniques from convex analysis, is closely related to Ausubel's conclusion that truthful revelation of demand is a weakly dominating strategy.