Rahul Deb

Dynamic Screening with Limited Commitment

We examine a model of dynamic screening and price discrimination in which the seller has limited commitment power. Two cohorts of anonymous, patient, and risk-neutral buyers arrive over two periods. Buyers in the first cohort arrive in period one, are privately informed about the distribution of their values, and then privately learn the value realizations in period two. Buyers in the second cohort are “last-minute shoppers” that already know their values upon their arrival in period two. The seller can fully commit to a long-term contract with buyers in the first cohort, but cannot commit to the future contractual terms that will be offered to second-cohort buyers. The expected second-cohort contract serves as an endogenous type-dependent outside option for first-cohort buyers, reducing the sellers ability to extract rents via sequential contracts. We derive the seller-optimal equilibrium and show that, when the seller cannot condition on future contractual terms (either explicitly or implicitly), she endogenously generates a commitment to maintaining high future prices by manipulating the timing of contracting.

A testable model of consumption with externalities

This paper presents a nonparametric model of interdependent preferences, where an individuals consumption may act as an externality on the preferences of other consumers. We assume that individual price consumption data is observed for all consumers. It is known that the general consumption model with externalities imposes few restrictions on the observed data, where the consistency requirement is Nash rationalizability. We motivate potential games as an important sub class of games where the family of concave potential games is refutable and imposes stronger restrictions on observed data. We use this framework to extend the analysis of Brown and Matzkin [D. Brown, R. Matzkin, Testable restrictions on the equilibrium manifold, Econometrica 64 (1996) 1249-1262] on refutable pure exchange economies to pure exchange economies with externalities. Finally, we discuss an application of this model to inter-household consumption data.

An Efficient Nonparametric Test of the Collective Household Model

Recently Cherchye et al. (2007a) provided a nonparametric characterization of a general collective model for household consumption which includes externalities and public consumption. This characterization involved different testable necessary and sufficient conditions. We discuss the special case of the household model for which their sufficient conditions are also necessary. We show that verification of this sufficient condition is NP Complete and discuss the relevance of this result for empirical testing. We observe that testing this condition is equivalent to solving the acyclic partitioning problem on a directed graph. We devise an efficient algorithm which approximately solves the minimum acyclic partitioning problem on directed graphs. Hence, we compute an approximate solution to the problem of finding the minimum number K, so that the observed data is consistent with K decision makers. We implement our algorithm on a randomly generated price consumption data set and report the results.

Optimal Contracting of New Experience Goods

We model new experience goods in the context of dynamic mechanism design. These are goods for which an agent is unsure of her valuation but can learn it through consumption experience. We consider a dynamic environment with a single buyer and seller in which contracting occurs over T periods, where each time the agent consumes the object, she receives a signal which allows her to revise her valuation. In this setting, experimentation with the product is strategic both for the buyer and seller. We derive the efficient and seller optimal contracts and compare them. We present a simple two period example which highlights some of the key features of the model. Finally, the methodology developed in the paper can be used to design efficient and optimal contracts in a multi-buyer setting with learning, where each buyer has single unit demand and there is a single object for sale in each period.

Implementation With Contingent Contracts

We study dominant strategy incentive compatibility in a mechanism design setting with contingent contracts where the payoff of each agent is observed by the principal and can be contracted upon. Our main focus is on the class of linear contracts (one of the most commonly used contingent contracts) which consist of a transfer and a flat rate of profit sharing. We characterize outcomes implementable by linear contracts and provide a foundation for them by showing that, in finite type spaces, every social choice function that can be implemented using a more general nonlinear contingent contract can also be implemented using a linear contract. We then qualitatively describe the set of implementable outcomes. We show that a general class of social welfare criteria can be implemented. This class contains social choice functions (such as the Rawlsian) which cannot be implemented using (uncontingent) transfers. Under additional conditions, we show that only social choice functions in this class are implementable.

Interdependent Preferences, Potential Games and Household Consumption

This paper presents a nonparametric model of interdependent preferences, where an individual’s consumption may be an externality on the preferences of other consumers. We assume that individual price consumption data is observed for all consumers and prove that the general model imposes few restrictions on the observed data, where the consistency requirement is Nash rationalizability. We motivate potential games as an important sub class of games where the family of concave potential games is refutable and imposes stronger restrictions on observed data. As an application of this model, we discuss inter-household consumption data. Finally, we use this framework to extend the analysis of Brown and Matzkin (1996) on refutable pure exchange economies to pure exchange economies with externalities.

Revealed Price Preference: Theory and Stochastic Testing

We develop a model of demand where consumers trade-off the utility of consumption against the disutility of expenditure. This model is appropriate whenever a consumer’s demand over a strict subset of all available goods is being analyzed. Data sets consistent with this model are characterized by the absence of revealed preference cycles over prices. The model is readily generalized to the random utility setting, for which we develop nonparametric statistical tests. Our application on national household consumption data provides support for the model.

Evaluating Strategic Forecasters

Motivated by the question of how one should evaluate professional election forecasters, we study a novel dynamic mechanism design problem without transfers. A principal who wishes to hire only high-quality forecasters is faced with an agent of unknown quality. The agent privately observes signals about a publicly observable future event, and may strategically misrepresent information to inflate the principal’s perception of his quality. We show that the optimal deterministic mechanism is simple and easy to implement in practice: it evaluates a single, optimally timed prediction. We study the generality of this result and its robustness to randomization and noncommitment.