Ilia Krasikov

Assistant professor at Higher School of Economics
Ilia_Krasikov_CV.pdf
krasikovis.main@gmail.com

Working papers

On Dynamic Pricing (New draft coming soon) with Rohit Lamba 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... 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. More Hide
Implications of Unequal Discounting in Dynamic Contracting (Submitted) with Rohit Lamba and Thomas Mettral Abstract: This paper studies a canonical dynamic screening model where the principal’s discount factor is larger than the agent, the agent has limited commitment and payoff relevant private information that follows a Markov process. The interaction of unequal discounting and limited commitment with... This paper studies a canonical dynamic screening model where the principal’s discount factor is larger than the agent, the agent has limited commitment and payoff relevant private information that follows a Markov process. The interaction of unequal discounting and limited commitment with persistent agency frictions produces a novel tradeoff: (i) new intertemporal costs of incentive provision emerge, and (ii) the net present value of the standard information rent decreases. The former ensure that the shadow price of incentive constraints are permanently positive, and the latter contributes towards decreasing distortions since principal and agent evaluate future payoffs differently. The optimal contract mostly exhibits a rather simple cyclical form that we term restart: (i) distortions decrease monotonically in the consecutive number of low shocks; (ii) a high shock erases all previous history of distortions, and then (iii) for every consecutive low shock, distortions follow the same path as before. Invoking an automaton inspired definition, restart contracts are shown to be simple. The optimal restart contract is (globally) optimal when the relaxed approach works, and approximately optimal otherwise. The setup admits a host of applications where one party is "financially bigger" and the other is armed with some private information. Examples include a venture capitalist-entrepreneur relationship, loan contracts between the International Monetary Fund and emerging markets, and governments redistributing amongst heterogeneous citizens. More Hide
A Theory of Dynamic Contracting with Financial Constraints (R&R at JET) with Rohit Lamba Abstract: Financial constraints preclude many surplus producing economic transactions, and inhibit the growth of many others. This paper models financial constraints through the interaction of persistent private information and borrowing limitations for the agent. Specifically in a canonical model of dynamic... Financial constraints preclude many surplus producing economic transactions, and inhibit the growth of many others. This paper models financial constraints through the interaction of persistent private information and borrowing limitations for the agent. Specifically in a canonical model of dynamic screening with Markov types, the requirement of positivity of per-period utility is added as a stronger feasibility constraint. The distortions, defined as the wedge between optimal and efficient allocation, thus produced, increase over time with each successive "bad shock" and decrease with each "good shock". This overturns the standard result of decreasing distortions in dynamic mechanism design without financial constraints. At any point in the contract, an en- dogenous number of "good shocks" are required for the principal to provide some liquidity and then eventually for the contract to become efficient. Efficiency is reached almost surely. The av- erage rate at which contract become efficient is decreasing in persistence of shocks; in particular, the iid model predicts a quick dissolution of financial constraints. This speaks to the relevance of modeling persistence in dynamic models of agency. A conceptual point is made on the fragile interpretation of positivity of stage utility as a limited liability constraint, and an extension where the principal can terminate the contract is provided. The problem is solved recursively, and build- ing on the literature, a technical tool of finding the minimal subset of the recursive domain that houses the optimal contract is further developed. More Hide

In Progress

Competition in Persuasion with Hard Evidence with Ce Liu
Optimal Dynamic Allocation with Costly Verification with Rohit Lamba and Yunan Lee
Firm Dynamics with Inefficient Intermediation with Rohit Lamba