Publications
Contracting for Innovation under Ambiguity (Slides) (Short Slides)
Games and Economic Behavior, 2022. DOI: https://doi.org/10.1016/j.geb.2022.01.015
Abstract: Outsourcing of research is a large and growing trend in knowledge-intensive industries such as biotech, software industries. The smaller research-oriented contractees specialize in handling research specific uncertainties and ambiguities, and the contracts are typically very short term. I model innovation as an ambiguous stochastic process, and assume that the commercial firms and research labs differ in their attitude towards ambiguity. I characterize the sequence of short-term contracts between the ambiguity averse contractor and the ambiguity neutral contractee doing the research, and examine how the special features of the optimal contract facilitate ambiguity sharing. In this model, the commercial firm's ambiguity aversion acts as a commitment device and mitigates the dynamic moral hazard problem. This results in monotonically decreasing investment flow and prevents equilibrium delay. Also, experimentation stops earlier than the policymaker deems optimal, and there is a range of posterior beliefs for which the contracting parties choose to liquidate the project even after being granted a patent. I discuss the policy implications of these results, examining how patent law affects innovation produced in these research alliances.
Delegation using Forward Induction (pdf) (Slides)
International Game Theory Review, 2021. DOI: https://doi.org/10.1142/S0219198921500225
Abstract: This paper explores a potentially important role of delegation: as a signal to sustain cooperation in coordination games. I consider a static principal-agent model with two tasks, one of which requires cooperation between the principal and the agent. If there is asymmetric information about the agent's type, the principal with a private belief that the agent is a good type can delegate the first task as a signal of his private belief. This equilibrium is supported by the forward induction argument. I conduct laboratory experiments to test these theoretical predictions and to examine the role of information in equilibrium selection. I find that delegation is used only sometimes to facilitate cooperation; however, when the subjects have information about past sessions, there is a statistically significant increase in the use of delegation. This evidence suggests that information matters in equilibrium selection in Bayesian games.
The private solution trap in collective action problems across 34 nations (with E. Malthouse et. al. )
Proceedings of the National Academy of Sciences, U.S.A. 123 (12) e2504632123. DOI: https://doi.org/10.1073/pnas.2504632123 (2026).)
Abstract: Collective action problems emerge when individual incentives and group interests are misaligned, as in the case of climate change. Individuals involved in these problems are generally considered to have two options: contribute toward public solutions such as global warming mitigation or free ride. However, many collective action problems today involve a third option of investing in a “private solution” such as local adaptation. The availability of this third option can lead to a private solution trap whereby private solutions are adopted, collectively optimal public solutions are not provided, and existing inequalities are exacerbated. We investigated the private solution trap with a collective action game featuring private and public solutions, wealth inequality determined by luck or merit, and participants from 34 countries. We found that the joint existence of private solutions and wealth inequality had a consistent effect across countries: Participants given a higher endowment adopted private solutions almost twice as often as those given a lower endowment, regardless of whether it was determined by luck or merit, and contributed proportionally less toward public solutions. Wealth inequality increased in every country and those given lower endowments were often left unprotected as public solutions were not provided. Across countries, cultural values of hierarchy and harmony were associated with preferences for private and public solutions, respectively. We also identified two universal pathways toward public solution provision: early contributions and conditional cooperation. Our findings highlight the ubiquity of the private solution trap, its cultural underpinnings, and its potential consequences for global collective action problems.
Working Papers
Virtue of Simplicity in Asymmetric Auctions (with Shraman Banerjee) (Slides)
R&R at Review of Economic Design
In single object auctions when bidders are asymmetric, the Myersonian optimal auction is difficult to implement. In such situations, Hartline and Roughgarden (2009) proposes a "simple" auction that revenue approximates the optimal auction. This paper experimentally studies the performance of the simple auction vis-a-vis the optimal auction in terms of revenue generation. We find that under weak asymmetry, there is no statistically significant difference in the revenue generated through simple auction and optimal auction. With increasing asymmetry, simple auction generates less revenue, but the approximation is much closer than what the theory predicts. Simple auction consistently has a lower revenue. We analyse the discouragement and competitive effects due to the optimal auction rules.
Communicating Bias (with Srijita Ghosh and Suraj Shekhar)
Submitted
Abstract: We consider a cheap talk model where the sender's bias is her private information. Before the sender learns the state, she sends a cheap talk message about her bias to the receiver. Subsequently, the receiver gets a state relevant cheap talk message from the sender. We find that there is no full bias revealing informative equilibrium. Even when partial bias revelation is considered, at most one bias type can be revealed in the bias revelation stage of any informative equilibrium. The cheap talk literature routinely assumes that bias is common knowledge. Our results show that this assumption should not be taken for granted. Finally, we find a novel trade-off between revealing bias and revealing information about the state.
Communicating Bias with two senders (with Srijita Ghosh and Suraj Shekhar)
Submitted
Abstract: We study a cheap talk model with two senders whose biases are privately known. Prior to learning the state, each sender sends a cheap talk message about her bias to the receiver, who then hires one sender to provide state-relevant advice. In our companion paper \cite{SSS1}, we show that with a single sender, no bias-revealing equilibrium exists. Competition between two senders changes this: the combination of rivalry for the single position and each sender's uncertainty about her opponent's bias can sustain a bias-revealing equilibrium. Moreover, we find parametric conditions under which the revelation equilibrium generates higher welfare compared to any equilibrium without bias revelation. Competition thus enhances communication through a novel channel: not by directly improving information transmission about the state, but by enabling bias revelation that would otherwise be unattainable.
Wisdom of the Crowds: Social Learning with Online Ratings (with Shraman Banerjee)
Despite a large number of reviews nowadays freely available online, the "wisdom of the crowds" in the form of these reviews do not always lead to efficient social learning. I build a continuous time framework to analyse the dynamics of online reviews. Given the behavioral assumption that the buyers leave feedback only if their experience with the product is very different from their prior expectation, I show the range of beliefs for which reviews can not efficiently aggregate information. I find the optimal buyer sequencing if the sellers can determine the sequence.
Wisdom of the Crowd vs Expert: Online Review Context
R&R at Marketing Intelligence and Planning
Abstract: This paper analyzes the self-reporting bias present in online reviews and discusses the welfare implications of this bias. It endogenizes the process in which reviews are generated and shows that reviewers’ incentive to be "pivotal" leads to only extreme reviews being posted, which is an empirically observed phenomenon. If consumers update their belief about the product using Bayes rule, failing to correct for this bias results in a loss of expected utility. However, if consumers can adjust for the bias, even in the presence of the bias, a large number of reviews is preferred by the consumers compared to the expensive expert opinion. If consumers do not take this bias into account, the value of "wisdom of the crowd" is lower.
Student Feedback and Performance Evaluation in Sequential Learning (with Parimal Bag)
How to conduct performance evaluation of lecturers in universities? With modules structured vertically moving from lower level to higher ups, learning externalities run in one direction. The planner has access only to the student feedback, which is a noisy signal of the effort and standard of the instructor, but the feedback is also sequential in nature. We show that ignoring this externality and designing a bonus structure treating the courses as exogenous leads to loss in welfare. We solve for the optimal contract design under this vertical externality.
Venture Capital Investment under Ambiguity
Abstract: A central feature of Venture Capital financing is the extensive use of control rights as an instrument as part of the dynamic contract signed at the beginning of the project. In this paper, I present an explanation of the shift in control rights based on the contextual ambiguity present in such financing environment. In a multiple priors model with ambiguity-averse capitalist and ambiguity-neutral entrepreneur, I show how control rights shift to mitigate possible hold-up issues. As the signal precision falls, venture capitalist acquires control rights more often.
Work in Progress
Asymmetric Auctions with Anonymous Reserve Prices (with Shraman Banerjee)