### Working papers

On Dynamic Pricing (Job Market Paper)
with Rohit Lamba in November 2018
*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 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. More- over, the general optimal contract is shown to be backloaded and a theoretical bound is pro- vided 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 pro- cess, novel tools are developed to study dynamic models of mechanism design when global incentive constraints bind.
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Of Restarts and Shutdowns: Dynamic Contracts with Unequal Discounting
with Rohit Lamba and Thomas Schacherer in 2018
*Abstract:*
A large supplier (principal) contracts with a small firm (agent) to repeatedly provide
working capital in return for payments. The total factor productivity of the agent is
private and follows a Markov process. Moreover, the agent is less patient than the principal.
We solve for the optimal contract...
A large supplier (principal) contracts with a small firm (agent) to repeatedly provide
working capital in return for payments. The total factor productivity of the agent is
private and follows a Markov process. Moreover, the agent is less patient than the principal.
We solve for the optimal contract in this environment. Distortions are pervasive
and efficiency unattainable. The optimal contract is characterized by two key properties:
restart and shutdown, which capture various aspects of contracts offered in the marketplace.
The optimal distortions are completely pinned down by the number of low TFP
shocks since the last high shock. Once a high shock arrives, the contract loses memory
and repeats the same cycle, we call this endogenous resetting feature restart. If ex ante
agency frictions are high, the principal commits to not serving the low type, we call this
shutdown. The principal prefers a patient agent if the interim agency friction, as measured
by the persistence of the private information is large, and she prefers an impatient
agent if it is small. Finally, when global incentive constraints bind, we (i) provide the
complete recursive solution, and (ii) characterize a simpler incentive compatible contract
that is approximately optimal.
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A Theory of Dynamic Contracting with Financial Constraints
with Rohit Lamba in 2017
*Abstract:*
We study a dynamic principal-agent model where the agent has access to a persistent private
technology but is strapped for cash. Financial constraints are generated by the periodic interaction
between incentives (private information) and a strong notion of feasibility (being strapped
for cash)...
We study a dynamic principal-agent model where the agent has access to a persistent private
technology but is strapped for cash. Financial constraints are generated by the periodic interaction
between incentives (private information) and a strong notion of feasibility (being strapped
for cash). This interaction produces dynamic distortions that are a sum of two effects: backloading
of incentives and illiquidity. Bad technology shocks increase distortions and monotonically
push the optimal contract further away from efficiency. An endogenous number of good shocks
is required for the contract to become liquid, and then eventually efficient. Efficiency is an
absorbing state that is reached almost surely. Persistence of private information increases the
variance of total economic surplus generated by the model, and decreases the rate at which surplus
converges to its efficient value. The key predictions continue to hold in the continuous
time setting. A simple economic implementation of the optimal contract is also provided.
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### In Progress

Competition in Persuasion with Hard Evidence
with Ce Liu
Firm Dynamics with Inefficient Intermediation
with Rohit Lamba