arXiv subjects

Diptangshu Sen

Publications and source records attributed to Diptangshu Sen.

13 recordsLinked to original sources

arXiv2026

Effort Matters in Score-Based Admissions: How Retaking and Aggregation Shape Test Scores

Observed standardized test scores are the result of an endogenous process: students strategically allocate effort across multiple retake attempts to improve their outcomes. Because students differ in their ability to make these investments, the interaction between applicant strategy and institutional scoring rules---such as the widely used Single-Sitting and Superscoring policies---can disparately distort observed scores. We develop a strategic framework where students allocate effort in response to different scoring policies. We show that Superscoring---the practice of combining the best section scores across attempts---introduces systematic score inflation through order-statistic selection over noise draws. This degrades signal accuracy and amplifies wealth-based disparities by disproportionately rewarding applicants who can afford repeated testing. Conversely, Single-Sitting---which keeps the best overall score rather than section-level scores---preserves signal fidelity but excludes high-ability students who lack the resources to prepare for all subjects simultaneously. Neither rule uniformly dominates; instead, they force a structural trade-off between statistical precision and fair outcomes. Finally, to address this, we propose three algorithmic interventions which either modify how scores from multiple attempts are combined, or apply a post-hoc correction to observed scores. Using simulations calibrated to 2025 College Board data, we compare standard scoring rules against these proposed interventions.

cs.GT↗

arXiv2026

The Impact of Competition on Outcomes of Score-Based College Admissions

We study how the design of admissions policies affects the ability of students admitted to universities. In our model, applicants have a multi-dimensional ability, which is a combination of a "type" and a "soft skill." Universities may differ in how they evaluate quality and have differing preferences on type and soft skills. Then, university admissions rely on a single noisy aggregate signal, such as a test score, that may not fully align with the university's preferences, and a university evaluates applicants through the posterior expectations of their preference metric given the observed signal. Our main results highlight that the design of good admission policies can be counter-intuitive. Under a single university, when holding the number of qualified applicants constant, increasing the usefulness of the signal (by aligning it more closely with the university preferences) leads to a worse type and soft skill for admitted students. Further, a university cannot affect the composition of students that are strong on type versus soft skills by changing their preferences. The picture becomes even more complicated under competition between as few as two universities: self-selection effects among students admitted to both universities can lead to part of the applicant pool switching which university they prefer, even under small changes in the design of the noisy signal. This can, in particular, lead to sudden and non-monotonic loss in the quality of admitted students when changing the alignment between signal and university preferences. Further, a university can get more students by increasing their selectivity. Finally, when admissions rely on separate noisy scores for type and for soft skills, we show that universities that put more emphasis on type (respectively soft skills) end up, counter-intuitively, admitting students with higher soft skills (respectively type).

cs.GT↗

arXiv2026

Data Sharing with Endogenous Choices over Differential Privacy Levels

Motivated by the rapid push to decentralize sharing of data, we study whether large-scale data sharing coalitions can form in a decentralized manner under differential privacy when players have heterogeneous privacy preferences. We first consider a fully decentralized data-sharing mechanism in which each player decides whether to participate and how much privacy noise to add locally to their sensitive data before sharing. Privacy choices induce a fundamental trade-off: higher privacy lowers individual privacy costs but reduces data utility and statistical accuracy for the coalition. These choices generate externalities across players, making both participation and privacy levels strategic. Our goal is to understand which coalitions are stable, how privacy choices shape equilibrium outcomes, and how fully decentralized data-sharing compares to a centralized, socially optimal benchmark when the number of players is large. We provide a comprehensive analysis across multiple privacy-cost regimes corresponding to different attack/observation models in differential privacy, showing that full decentralization is highly inefficient in terms of both social welfare and estimator accuracy. Surprisingly, we find that a simple partially decentralized mechanism (where players still retain participation agency, but a central designer chooses a fixed privacy noise level for everyone) closes this efficiency gap down to constant factors across all privacy-cost regimes.

cs.GT↗

arXiv2025

Fixed Points and Stochastic Meritocracies: A Long-Term Perspective

We study group fairness in the context of feedback loops induced by meritocratic selection into programs that themselves confer additional advantage, like college admissions. We introduce a stylized, yet novel inter-generational model for the setting and analyze it in situations where there are no underlying differences between two populations. When the benefit of the program (or the harm of not getting into it) is completely symmetric, we show that disparities between the two populations will vanish on average in the long term, although in the short term disparities will continue to arise and dissipate cyclically. Further, the time an accumulated advantage takes to dissipate can be significant, and increases as a function of the relative importance of the program in conveying benefits. Interestingly, significant disparities can arise purely due to randomness even from completely symmetric initial conditions, especially when populations are small. The introduction of even a slight asymmetry, where the group that has accumulated an advantage becomes slightly preferred, leads to a completely different outcome. In these instances, starting from completely symmetric initial conditions, disparities between groups arise stochastically and then persist over time, yielding a permanent advantage for one group. Our analysis precisely characterizes conditions under which disparities persist or diminish, with a particular focus on the role of the scarcity of available spots in the program and its effectiveness. We also present extensive simulations in a richer model that further support our theoretical results in the simpler, stylized model. Our findings are relevant for the design and implementation of algorithmic fairness interventions in similar selection processes.

cs.CY↗

arXiv2025

Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty

We study strategic classification in binary decision-making settings where agents can modify their features in order to improve their classification outcomes. Importantly, our work considers the causal structure across different features, acknowledging that effort in a given feature may affect other features. The main goal of our work is to understand \emph{when and how much agent effort is invested towards desirable features}, and how this is influenced by the deployed classifier, the causal structure of the agent's features, their ability to modify them, and the information available to the agent about the classifier and the feature causal graph. In the complete information case, when agents know the classifier and the causal structure of the problem, we derive conditions ensuring that rational agents focus on features favored by the principal. We show that designing classifiers to induce desirable behavior is generally non-convex, though tractable in special cases. We also extend our analysis to settings where agents have incomplete information about the classifier or the causal graph. While optimal effort selection is again a non-convex problem under general uncertainty, we highlight special cases of partial uncertainty where this selection problem becomes tractable. Our results indicate that uncertainty drives agents to favor features with higher expected importance and lower variance, potentially misaligning with principal preferences. Finally, numerical experiments based on a cardiovascular disease risk study illustrate how to incentivize desirable modifications under uncertainty.

cs.GT↗

arXiv2025

When Should a Principal Delegate to an Agent in Selection Processes?

Decision-makers in high-stakes selection processes often face a fundamental choice: whether to make decisions themselves or to delegate authority to another entity whose incentives may only be partially aligned with their own. Such delegation arises naturally in settings like graduate admissions, hiring, or promotion, where a principal (e.g. a professor or worker) either reviews applicants personally or decisions are delegated to an agent (e.g. a committee or boss) that evaluates applicants efficiently, but according to a potentially misaligned objective. We study this trade-off in a stylized selection model with noisy signals. The principal incurs a cost for selecting applicants, but can evaluate applicants based on their fit with a project, team, workplace, etc. In contrast, the agent evaluates applicants solely on the basis of a signal that correlates with the principal's metric, but this comes at no cost to the principal. Our goal is to characterize when delegation is beneficial versus when decision-making should remain with the principal. We compare these regimes along three dimensions: (i) the principal's utility, (ii) the quality of the selected applicants according to the principal's metric, and (iii) the fairness of selection outcomes under disparate signal qualities.

cs.CY↗

arXiv2024

On Rider Strategic Behavior in Ride-Sharing Platforms

Over the past decade, ride-sharing services have become increasingly important, with U.S. market leaders such as Uber and Lyft expanding to over 900 cities worldwide and facilitating billions of rides annually. This rise reflects their ability to meet users' convenience, efficiency, and affordability needs. However, in busy areas and surge zones, the benefits of these platforms can diminish, prompting riders to relocate to cheaper, more convenient locations or seek alternative transportation. While much research has focused on the strategic behavior of drivers, the strategic actions of riders, especially when it comes to riders walking outside of surge zones, remain under-explored. This paper examines the impact of rider-side strategic behavior on surge dynamics. We investigate how riders' actions influence market dynamics, including supply, demand, and pricing. We show significant impacts, such as spillover effects where demand increases in areas adjacent to surge zones and prices surge in nearby areas. Our theoretical insights and experimental results highlight that rider strategic behavior helps redistribute demand, reduce surge prices, and clear demand in a more balanced way across zones.

cs.GT↗

arXiv2024

Differentially Private Data Release on Graphs: Inefficiencies and Unfairness

Networks are crucial components of many sectors, including telecommunications, healthcare, finance, energy, and transportation.The information carried in such networks often contains sensitive user data, like location data for commuters and packet data for online users. Therefore, when considering data release for networks, one must ensure that data release mechanisms do not leak information about individuals, quantified in a precise mathematical sense. Differential Privacy (DP) is the widely accepted, formal, state-of-the-art technique, which has found use in a variety of real-life settings including the 2020 U.S. Census, Apple users' device data, or Google's location data. Yet, the use of DP comes with new challenges, as the noise added for privacy introduces inaccuracies or biases and further, DP techniques can also distribute these biases disproportionately across different populations, inducing fairness issues. The goal of this paper is to characterize the impact of DP on bias and unfairness in the context of releasing information about networks, taking a departure from previous work which has studied these effects in the context of private population counts release (such as in the U.S. Census). To this end, we consider a network release problem where the network structure is known to all, but the weights on edges must be released privately. We consider the impact of this private release on a simple downstream decision-making task run by a third-party, which is to find the shortest path between any two pairs of nodes and recommend the best route to users. This setting is of highly practical relevance, mirroring scenarios in transportation networks, where preserving privacy while providing accurate routing information is crucial. Our work provides theoretical foundations and empirical evidence into the bias and unfairness arising due to privacy in these networked decision problems.

cs.CR↗

arXiv2024

Equilibria of Data Marketplaces with Privacy-Aware Sellers under Endogenous Privacy Costs

We study a two-sided online data ecosystem comprised of an online platform, users on the platform, and downstream learners or data buyers. The learners can buy user data on the platform (to run a statistic or machine learning task). Potential users decide whether to join by looking at the trade-off between i) their benefit from joining the platform and interacting with other users and ii) the privacy costs they incur from sharing their data. First, we introduce a novel modeling element for two-sided data platforms: the privacy costs of the users are endogenous and depend on how much of their data is purchased by the downstream learners. Then, we characterize marketplace equilibria in certain simple settings. In particular, we provide a full characterization in two variants of our model that correspond to different utility functions for the users: i) when each user gets a constant benefit for participating in the platform and ii) when each user's benefit is linearly increasing in the number of other users that participate. In both variants, equilibria in our setting are significantly different from equilibria when privacy costs are exogenous and fixed, highlighting the importance of taking endogeneity in the privacy costs into account. Finally, we provide simulations and semi-synthetic experiments to extend our results to more general assumptions. We experiment with different distributions of users' privacy costs and different functional forms of the users' utilities for joining the platform.

cs.GT↗

arXiv2023

Pricing in Ride-sharing Markets : Effects of network competition and autonomous vehicles

Autonomous vehicles will be an integral part of ride-sharing services in the future. This setting differs from traditional ride-sharing marketplaces because of the absence of the supply side (drivers). However, it has far-reaching consequences because in addition to pricing, players now have to make decisions on how to distribute fleets across network locations and re-balance vehicles in order to serve future demand. In this paper, we explore a duopoly setting in the ride-sharing marketplace where the players have fully autonomous fleets. Each ride-service provider (RSP)'s prices depend on the prices and the supply of the other player. We formulate their decision-making problems using a game-theoretic setup where each player seeks to find the optimal prices and supplies at each node while considering the decisions of the other player. This leads to a scenario where the players' optimization problems are coupled and it is challenging to find the equilibrium. We characterize the types of demand functions (e.g.: linear) for which this game admits an exact potential function and can be solved efficiently. For other types of demand functions, we propose an iterative algorithm to compute the equilibrium. We conclude by providing numerical insights into how different kinds of equilibria would play out in the market when the players are asymmetric. Our numerical evaluations also provide insights into how the regulator needs to consider network effects while deciding regulation in order to avoid unfavorable outcomes.

cs.GT↗

arXiv2021

Discriminatory Price Mechanism for Smart Grid

We consider a scenario where a retailer can set different prices for different consumers in a smart grid. The retailer's objective is to maximize the revenue, minimize the operating cost, and maximize the consumer's welfare. The retailer wants to optimize a convex combination of the above objectives using price signals specific to each consumer. However, variability in unit prices across consumers is bounded by a parameter $η$, hence limiting the discrimination. We formulate the pricing problem as a Stackelberg game where the retailer is the leader and consumers are followers. Since the retailer's optimization problem turns out to be non-convex, we convexify it via relaxations. We provide performance guarantees for the relaxations in the asymptotic sense (when number of consumers tends to $\infty$). Further, we show that despite the variability in pricing, the pricing scheme proposed by our model is fair as higher prices are charged to consumers who have higher willingness for demand. We extend our analysis to the scenario where consumers can feed energy back to the grid via net-metering. We show that our pricing policy promotes fairness even in this scenario as prosumers who contribute more to the grid, are given large cuts on buying rates. The policy is also found to incentivize more prosumers to invest in renewable energy, thus encouraging sustainability.

math.OC↗

arXiv2021

Optimal minimal-contact routing of randomly arriving agents through connected networks

Collision-free or contact-free routing through connected networks has been actively studied in the industrial automation and manufacturing context. Contact-free routing of personnel through connected networks (e.g., factories, retail warehouses) may also be required in the COVID-19 context. In this context, we present an optimization framework for identifying routes through a connected network that eliminate or minimize contacts between randomly arriving agents needing to visit a subset of nodes in the network in minimal time. We simulate the agent arrival and network traversal process, and introduce stochasticity in travel speeds, node dwell times, and compliance with assigned routes. We present two optimization formulations for generating optimal routes - no-contact and minimal-contact - on a real-time basis for each agent arriving to the network given the route information of other agents already in the network. We generate results for the time-average number of contacts and normalized time spent in the network.

math.OC↗

arXiv2021

Design of Incentive Mechanisms Using Prospect Theory to Promote Better Sell-back Behavior among Prosumers

Users can now give back energies to the grid using distributed resources. Proper incentive mechanisms are required for such users, also known as prosumers, in order to maximize the sell-back amount while maintaining the retailer's profit. However, all the existing literature considers expected utility theory (EUT) where they assume that prosumers maximize their expected payoff. We consider prospect theory (PT) which models the behavior of humans in the face of uncertainty in a better manner. We show that in a day-ahead contract pricing mechanism, the actual optimal value of contract and the sell-back amount may be smaller compared to the one computed by the EUT. We also propose a lottery-based mechanism and show that such a mechanism can increase the sell-back amount while increasing the retailer's savings compared to day-ahead contract pricing.

math.OC↗