Research Interests in Marketing:

Topics: pricing

Methodology: Analytical  

Working Papers:

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I) ``Heterogeneous Value Uncertainty in Online Channels: Dynamic Mechanism Design of Price and Return Policies"with K. Sudhir, Amit Pazgal.  

Consumers differ in their match uncertainty when buying through online retail channels. Generous return policies can encourage purchasing in the presence of significant ex-ante match uncertainty, but need higher prices to support them. Given heterogeneity in match uncertainty among consumers, retailers can jointly discriminate over a menu of upfront retail price and post-purchase refund costs. As consumer uncertainty over matching is resolved over time only after purchase, discrimination using a menu over retail price and refund costs is a sequential screening problem that requires a dynamic mechanism design based analysis. Further, since returns are costly to retailers, manufacturers can find it optimal to share risk with the retailer by optimizing over their wholesale prices and refunds to retailers on items returned. We model the channel in a leader-follower framework with the manufacturer as the leader choosing wholesale pricing and refund terms and retailer as the follower  solving a sequential screening problem to price discriminate on uncertainty. To the best of our knowledge, we are the first to introduce the sequential screening problem in a dynamic mechanism design framework into marketing. We find that the retailer finds it optimal to price discriminate on price paths only if manufacturers offer refunds on returned products or there is some salvage value for the product.

II) ``Pricing with Valuation Uncertainty using Dynamic Mechanism Design"with K. Sudhir, Amit Pazgal.  

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The paper studies price discrimination in price paths over first and subsequent purchase in settings where consumers have uncertainty over their valuation distributions for the product at the time of first purchase and realize their valuation after first purchase by incurring a learning cost that is different from price. Consumers pay (get paid or receive free) the product to try in the first period, incur an additional learning cost to realize their valuation before deciding to purchase the product in the second period. We propose and solve a sequential screening model based on dynamic mechanism design where forward looking consumers are offered an optimal menu of price paths over the two periods that price discriminates over the valuation uncertainty and learning costs. Price discrimination is feasible when learning costs are higher for the high valuation uncertainty segment. The firm offers a relatively lower first period price (including free or subsidies) for the higher learning cost-higher uncertainty segment, but a higher second period price; overall their total cost across both periods are higher. More consumers are excluded from second period purchase among the higher valuation uncertainty segment--as the firm seeks to obtain greater profits from those with the highest valuations from the higher uncertainty segment. Our model offers a dynamic screening explanation for the use of freemiums, even in settings without cross-customer externalities. We find that online reviews that reduce the variance in prior valuation distributions can dampen seller profits and the ability to offer upgrades in the second period can enhance the ability to price discriminate on valuation uncertainty more effectively and increase seller profits.

III) ``The Effect of Switching Cost on The Competition Between Local and Online Firms"with Amit Pazgal.  

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In this paper we study the competition between local and online firms in a two-period model where switching costs are present in the second time period. In contrast to the standard switching cost literature, both the ``lock in and ripoff" and the ``lock in and no ripoff" patterns are found to exist in equilibrium. All firms prefer to lower their first-period prices in order to attract more consumers. However, in the second period, when the disutility of using the online provider is high, the local retailers prefer to charge their previous customers a higher price. The online provider tends to charge a lower price to maintain its previous customers and maybe attract new ones, which forms the ``ripoff" pattern for the local retailers and ``no ripoff" pattern for the online provider. Conversely, when the online disutility is low, ``no ripoff" pattern is established for the local retailers and the ``ripoff" pattern is developed for the online provider. Furthermore, we also find that when the firm is better off with switching costs it prefers to increase the switching costs further resulting in even higher profits. Not only do we find the monotonic relationships between the revenue and switching costs but we also observe the more general U-shape relationship. We offer two extensions of our model: one considers the effect of loyal consumers and the other studies the competition between n>= 2 local retailers and an online provider.

Ongoing Project: 

I) ``The Effect of Switching Cost on The Competition Between Local and Online Firms"with Amit Pazgal, Dinha Cohen-Vernik.  

In this paper we study the competition between local and online firms in a two-period model where switching costs are present in the second time period. In contrast to the standard switching cost literature, both the ``lock in and ripoff" and the ``lock in and no ripoff" patterns are found to exist in equilibrium. All firms prefer to lower their first-period prices in order to attract more consumers. However, in the second period, when the disutility of using the online provider is high, the local retailers prefer to charge their previous customers a higher price. The online provider tends to charge a lower price to maintain its previous customers and maybe attract new ones, which forms the ``ripoff" pattern for the local retailers and ``no ripoff" pattern for the online provider. Conversely, when the online disutility is low, ``no ripoff" pattern is established for the local retailers and the ``ripoff" pattern is developed for the online provider. Furthermore, we also find that when the firm is better off with switching costs it prefers to increase the switching costs further resulting in even higher profits. Not only do we find the monotonic relationships between the revenue and switching costs but we also observe the more general U-shape relationship. We offer two extensions of our model: one considers the effect of loyal consumers and the other studies the competition between n>= 2 local retailers and an online provider.

Research Interests in Mathematics:

Topics: dynamical system, PDE, stochastic PDE, numerical analysis

Ph.D. thesis: 

``Existence of Homoclinic Connections Corresponding to Bilayer Structures in Amphiphilic Polymer Systems "

Publication: 

``Convergence of the Spectral Galerkin Method for the Stochastic Reaction-Diffusion-Advection Equation", with Yanzhi Zhang, Journal of Mathematical Analysis and Applications, 446(2): 1230-1254, 2017.

``Existence of Compressible Bilayers in the Functionalized Cahn-Hilliard Equation", with Keith Promislow, SIAM Applied Dynamical System, 13(2):629-657, 2014.

``Curvature Driven Flow of Bi-Layer Interfaces", with Keith Promislow, Nir Gavish, Gurgen Hayrapetyan, Physica D: Nonlinear Phenomena, 240(7):675-693, 2010.

``Efficient and Accurate Numerical Methods for the Klein-Gordon-Schroedinger Equations", with Weizhu Bao, Jounral of Computational Physics, 225(2):1863-1893, 2007.