Conferences at Department of Economics, University of Toronto, Canadian Economic Theory Conference 2019

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On Dynamic Pricing

Ilia Krasikov*, Rohit Lamba

Date: 2019-05-03 4:30 pm – 5:00 pm
Last modified: 2019-04-14

Abstract


This paper studies a canonical model of dynamic price discrimination- when firms can endogenously discriminate amongst consumers based on the timing of information arrival and/or the timing of purchase. A seller and buyer trade repeatedly. Buyer’s valuation for the trade is private information and it evolves over time according to a renewal Markov process. The seller offers a dynamic pricing contract which options a sequence of forwards. As a first step, we show that this relatively simple dynamic pricing contract achieves the optimum in the two period repeated sales model. We then show that this contract is (a) the optimum when a single object is sold at a fixed time and (b) the optimum under strong monotonicity in the repeated sales model. The gap between the full optimum and our mechanism of simple dynamic pricing instruments is explained through buybacks. Moreover, the general optimal contract is shown to be backloaded and a theoretical bound is provided for the fraction of optimal revenue that can be extracted by the seller from using our mechanism: it achieves more than 70% of the total profit uniformly across distributions, and more than 90% for standard ones such as the power distribution. The construction of the mechanism and bounds is then extended to multiple players to study repeated auctions. At every step of the analysis a mapping is established between the pricing model (indirect mechanisms) and the dynamic mechanism design toolkit (direct mechanisms). In this process, novel tools are developed to study dynamic models of mechanism design when global incentive constraints bind.

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