arXiv subjects

Bhaskar Ray Chaudhury

Publications and source records attributed to Bhaskar Ray Chaudhury.

At least 19 recordsLinked to original sources

arXiv2026

The Stability of Data Exchange in Competitive Markets

We study the stability of data exchange among competing firms. Unlike tangible goods, data is non-rival: sharing it does not deprive the giver of its use. On one hand, competing firms-- often operating as machine-learning-driven predictors that collect observations from a shared environment to solve similar tasks-- can improve their predictive accuracies from pooling data. On the other hand, they compete for market share, which may depend on their relative predictive performance. This raises the central question of this paper: can there be a stable data exchange in such competitive environments? We formalize this via a model of $n$ firms exchanging fractions of their datasets, with predictive performance feeding into market competition. We adopt core stability as our solution concept, accounting for externalities via worst-case responses by non-participating firms. Our main results reveal a sharp contrast driven by demand structure: (i) in fully rational markets, where customers flock entirely to the top-performing firm, a core-stable exchange always exists for any monotone continuous prediction functions; (ii) in partially rational markets with logit-style demand, core-stable exchanges may fail to exist-and even approximate cores can be empty. Our impossibility results suggest that internal profit-sharing within coalitions can restore stability in partially rational markets. We formalize this intuition by showing that when co-operating coalitions equally redistribute market-share revenues among members, a core-stable data exchange exists. Finally, we propose a natural exchange dynamic and demonstrate empirically that it converges to a core-stable data exchange in fully rational markets on simulated instances derived from real datasets.

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arXiv2026

RARE: Response-Aware Rational Equilibrium in Pricing Games

We study a pricing game in markets with budget-constrained buyers, where each seller offers a single good at a price she sets, and each buyer chooses a utility-maximizing bundle subject to her budget. We consider both the rivalrous setting, such as markets for physical goods, and the non-rivalrous setting, such as markets for datasets. Pure Nash equilibria often fail to exist in this game. However, Nash equilibrium assumes that the other sellers keep their prices fixed when one seller deviates, whereas in practice, sellers harmed by a price change may respond, for example, by matching the new price. We propose a new equilibrium notion called Response-Aware Rational Equilibrium (RARE). At a RARE, every deviation by a seller can be deterred by a response from the other sellers, in which no responder earns less than she did right after the deviation. Every Nash equilibrium is a RARE. Assuming that buyers' purchases (among their optimal choices) change continuously with prices, we show that a RARE always exists for rivalrous goods, and for non-rivalrous goods when buyers have equal budgets. Moreover, the RARE that we construct extracts the buyers' entire budget. For non-rivalrous goods with unequal budgets, we show that an approximate RARE exists, where a deviating seller can increase her revenue by a factor of at most $b_{\mathrm{avg}}/b_{\min}$, the ratio of the average budget to the minimum budget. Our proof uses two nested applications of the KKM lemma. We also study a natural dynamic in which sellers repeatedly raise their prices to earn the revenue that they could guarantee themselves by deviating, and show that it reaches an approximate RARE, with additive error $δ$, within $\lfloor B/δ\rfloor$ rounds, where $B$ is the buyers' total budget. The main results of this paper are formally verified in the Lean 4 proof assistant (https://github.com/sharmaeklavya2/dm-rare).

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arXiv2026

Non-Linear Pricing Restores Tractability for a Data Seller

We consider a data seller who designs pricing mechanisms over multiple datasets to maximize revenue from budget-constrained buyers. The seller offers multiple datasets and assigns each a pricing function that maps the quantity purchased to a total payment. The goal is to design these pricing functions to maximize revenue, anticipating that buyers---who trade off accuracy gains against cost---choose bundles optimally subject to their budget constraints. Prior work [Chaudhury et al., 2026] studies such optimal pricing under the restriction that each dataset is assigned a linear price, and shows that computing optimal linear prices is computationally intractable. In contrast, we allow each dataset to be priced via a general function and show that this additional flexibility can not only increase the revenue but also restore tractability, yielding a surprising simultaneous improvement in economic performance and computational efficiency. Even when pricing functions are only required to be monotone and lower-continuous, optimal pricing admits a highly structured and simple form: each pricing function is piecewise linear and convex (PLC), and the optimal solution can be computed in polynomial time. Moreover, the total number of kinks across all pricing functions is bounded by the number of buyers. Consequently, when datasets significantly outnumber buyers, most pricing functions are effectively linear. We further empirically study the structure of optimal pricing by analyzing the number of kinks and the revenue gap between optimal nonlinear pricing and optimal linear pricing on simulations generated from a real dataset.

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arXiv2026

Equilibrium Pricing in Oligopolistic Data Markets

We study equilibrium pricing in oligopolistic data markets with budget-constrained buyers (e.g., machine learning companies purchasing data to improve model accuracy) and strategic data sellers. Sellers compete by setting prices for their datasets, giving rise to a pricing game whose pure Nash equilibria correspond to equilibrium prices. While equilibrium prices are guaranteed for rivalrous goods via competitive equilibrium, we show that the non-rivalry of data fundamentally alters this picture: an exact Nash equilibrium (NE) need not exist, and in fact, 1.363-approximate NE may also not exist under uniform pricing. We therefore investigate relaxed equilibrium notions. Allowing sellers to use beyond-uniform pricing---specifically, piecewise-linear convex pricing functions---guarantees approximate stability within a constant factor: there exists a pricing profile in which no seller can improve revenue by a factor of two by deviating to any uniform price (a 2-approximate NE against uniform deviations). Finally, our simulations demonstrate fast convergence and empirical approximation guarantees that outperform the worst-case bound of 2.

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arXiv2026

A Simple Polynomial-Time EFX Repair for Cancelable Valuations

The leximin++ proof of Plaut and Roughgarden for agents with identical monotone valuations gives a natural EFX-repair procedure: starting from an arbitrary partition, repeatedly transfer an eligible item to a minimum-valued bundle. The procedure terminates, but the standard argument gives no polynomial bound on the number of transfers, even for additive valuations. We show that a single deterministic tie-breaking rule makes this repair procedure polynomial for the broader class of cancelable valuations. Fix an ordering of the items consistent with their singleton values and always transfer the highest-ranked eligible item. Consecutive transferred items strictly decrease in this ordering, and hence the algorithm performs at most $m$ transfers, where $m$ is the number of items. Moreover, the repair procedure does not decrease the minimum bundle value or increase the maximum bundle value. As an application, for every fixed $\varepsilon>0$, we compute in polynomial time an allocation of restricted additive chores that is simultaneously EFX, $(1+\varepsilon)$-MMS, and a $2$-approximation to the optimal social cost. This improves upon the previous polynomial-time $4/3$-MMS guarantee. Finally, we exhibit a monotone cancelable ordering on five items with no additive representation, showing that the extension beyond additivity is genuine.

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arXiv2026

Fully Distributed Tâtonnement for Chores Markets

We study price-adjustment dynamics for computing competitive equilibria (CE) in Fisher markets with chores. Unlike in classical goods markets, prices in chores markets are payments for taking on undesirable tasks, and natural excess-demand dynamics can fail; even the naïve analogue of Walrasian tâtonnement may diverge. Recent work of Chaudhury et al. [2025] overcomes this obstacle via relative tâtonnement, which subtracts the average excess-demand signal from the excess demand vector. This recovers convergence, but at the cost of coupling the price updates across all chores. This leaves open whether such global coupling is inherent, or whether convergent tâtonnement can be recovered through a genuinely local update in which each chore reacts only to its own excess demand. We answer this question affirmatively through multiplicative tâtonnement, a fully distributed dynamics in which each chore price is updated using only its current price and its own excess-demand signal. Although the update contains no explicit normalization term, Walras' law and the multiplicative form of the update implicitly preserve the relevant aggregate price geometry. We prove that multiplicative tâtonnement converges to a CE in any chores Fisher market with continuous, convex, and $1$-homogeneous (CCH) disutilities. For convex CES disutilities, we further prove an approximate-CE convergence rate with the same $O(1/\varepsilon^2)$ dependence as relative tâtonnement, but with improved dependence on problem constants. Experiments on real-world and simulated instances show that multiplicative tâtonnement is substantially faster in practice, often by an order of magnitude.

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arXiv2026

Competitive Equilibrium in Labor Economies through the Lens of Goods and Chores Fisher Markets

In this paper, we study a two-sided labor market that couples the classical Fisher market with goods and the Fisher market with bads into a single unified framework. In our model, users demand tasks in order to derive utility, while workers supply labor to perform these tasks in exchange for earnings. Each task thus plays a dual role: it is a good for the user side of the market and a chore for the worker side. Given prices for tasks, users choose utility-maximizing bundles subject to budgets, while workers choose disutility-minimizing task bundles subject to earning requirements; the resulting choices induce demand and supply endogenously for each task, and a CE corresponds to prices at which these coincide. We show that such markets are guaranteed to admit a CE in a very general setting, and the first and second welfare theorems hold for our labor market model. We next study the computation of equilibria under linear preferences. We show that, similar to the chores setting, equilibria correspond to KKT points of an Eisenberg-Gale-like non-convex program. Despite the non-convex characterization, we go on to show a set of surprisingly positive results. First, we show that there exists a polynomial-time combinatorial algorithm for computing CE, which relies on a natural Walrasian scheme for updating prices. In the "CEEI-like" case, this yields a strongly polynomial-time algorithm. We next show that our market admits a natural dual program, and this non-convex labor-market program admits a change of variables that transforms it into a linear program (albeit with irrational coefficients). Finally, leveraging this LP, we give yet another polynomial-time algorithm while deriving an approach for addressing the irrational coefficients in an efficient manner. We note that, even for goods-only linear Fisher markets, obtaining such an LP formulation remains open.

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arXiv2026

Revenue-Optimal Pricing for Budget-Constrained Buyers in Data Markets

We study revenue-optimal pricing in data markets with rational, budget-constrained buyers. Such a market offers multiple datasets for sale, and buyers aim to improve the accuracy of their prediction tasks by acquiring data bundles. The market's objective is to price datasets to maximize total revenue, considering that buyers with quasi-linear utilities choose their bundles optimally under budget constraints. We allow the buyers to purchase fractions of datasets, and the amount they pay is proportional to the fraction they receive. Although competitive equilibrium gives revenue-optimal pricing in rivalrous markets with quasi-linear buyers, we show that revenue maximization in data markets is APX-hard. Despite the hardness, we design a 2-approximation algorithm when datasets arrive online, and a $(1-1/e)^{-1}$-approximation algorithm for the offline setting.

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arXiv2026

Maximizing Nash Social Welfare in 2-Value Instances: Delineating Tractability

We study the problem of allocating a set of indivisible goods among a set of agents with \emph{2-value additive valuations}. In this setting, each good is valued either $1$ or $p/q$, for some fixed co-prime numbers $p,q\in \mathbb{N}$ such that $1\leq q < p$. Our goal is to find an allocation maximizing the \emph{Nash social welfare} (\NSW), i.e., the geometric mean of the valuations of the agents. In this work, we give a complete characterization of polynomial-time tractability of \NSW\ maximization that solely depends on the values of $q$. We start by providing a rather simple polynomial-time algorithm to find a maximum \NSW\ allocation when the valuation functions are \emph{integral}, that is, $q=1$. We then exploit more involved techniques to get an algorithm producing a maximum \NSW\ allocation for the \emph{half-integral} case, that is, $q=2$. Finally, we show it is \classNP-hard to compute an allocation with maximum \NSW\ whenever $q\geq3$.

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arXiv2025

Tâtonnement Dynamics for Fisher Markets with Chores

In this paper, we initiate the study of tâtonnement dynamics in markets with chores. Tâtonnement is a fundamental market dynamics, capturing how prices evolve when they are adjusted in proportion of their excess demand. While its convergence to a competitive equilibrium (CE) is well understood in goods markets for broad classes of utilities, no analogous results are known for chore markets. Analyzing tâtonnement in the chores market presents new challenges. Several elegant structural properties that facilitate convergence in goods markets-such as convexity of the equilibrium price set and monotonicity of excess demand under the tâtonnement price updates-fail to hold in the chore setting. Consistent with these difficulties, we first show that naïve tâtonnement diverges. To overcome this, we propose a modified process called relative tâtonnement, where prices are updated according to normalized excess demand. We prove its convergence to a CE under suitable step-size choices for a broad class of disutility functions, namely continuous, convex, and 1-homogeneous (CCH) disutilities. This class includes many standard forms such as linear and convex CES disutilities. Our proof proceeds by introducing a nonsmooth, nonconvex yet regular objective function-a generalization of the objective in the Eisenberg-Gale-type dual program introduced by [CKMN24]. For convex CES disutilities, where disutility is the weighted $p$-norm of the individual chore disutilities for $p \in (1, \infty)$, we show that relative tâtonnement converges to an $\varepsilon$-CE in $O(1/\varepsilon^2)$ iterations. This quadratic convergence rate is established by leveraging the polar gauge (or gauge dual) of the disutility function. Finally, following the framework of [AH58], we analyze the stability of CE and provide a complete characterization of local stability.

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arXiv2025

Human-AI Collaboration with Misaligned Preferences

In many real-life settings, algorithms play the role of assistants, while humans ultimately make the final decision. Often, algorithms specifically act as curators, narrowing down a wide range of options into a smaller subset that the human picks between: consider content recommendation or chatbot responses to questions with multiple valid answers. Crucially, humans may not know their own preferences perfectly either, but instead may only have access to a noisy sampling over preferences. Algorithms can assist humans by curating a smaller subset of items, but must also face the challenge of misalignment: humans may have different preferences from each other (and from the algorithm), and the algorithm may not know the exact preferences of the human they are facing at any point in time. In this paper, we model and theoretically study such a setting. Specifically, we show instances where humans benefit by collaborating with a misaligned algorithm. Surprisingly, we show that humans gain more utility from a misaligned algorithm (which makes different mistakes) than from an aligned algorithm. Next, we build on this result by studying what properties of algorithms maximize human welfare when the goals could be either utilitarian welfare or ensuring all humans benefit. We conclude by discussing implications for designers of algorithmic tools and policymakers.

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arXiv2025

On the Existence and Complexity of Core-Stable Data Exchanges

The rapid growth of data-driven technologies and the emergence of various data-sharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents -- or groups of agents -- from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data. The net utility of an agent is payoff minus the cost. We adapt the classical notion of core-stability from cooperative game theory to data exchange. A data exchange is core-stable if no subset of agents has any incentive to deviate to a different exchange. We show that a core-stable data exchange is guaranteed to exist when agents have concave payoff functions and convex cost functions -- a setting typical in domains like PAC learning and random discovery models. We show that relaxing either of the foregoing conditions may result in the nonexistence of core-stable data exchanges. Then, we prove that finding a core-stable exchange is PPAD-hard, even when the potential blocking coalitions are restricted to constant size. To the best of our knowledge, this provides the first known PPAD-hardness result for core-like guarantees in data economics. Finally, we show that data exchange can be modelled as a balanced $n$-person game. This immediately gives a pivoting algorithm via Scarf's theorem \cite{Scarf1967core}. We show that the pivoting algorithm works well in practice through our empirical results.

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arXiv2025

Polyline Simplification has Cubic Complexity

In the classic polyline simplification problem we want to replace a given polygonal curve $P$, consisting of $n$ vertices, by a subsequence $P'$ of $k$ vertices from $P$ such that the polygonal curves $P$ and $P'$ are as close as possible. Closeness is usually measured using the Hausdorff or Fréchet distance. These distance measures can be applied "globally", i.e., to the whole curves $P$ and $P'$, or "locally", i.e., to each simplified subcurve and the line segment that it was replaced with separately (and then taking the maximum). This gives rise to four problem variants: Global-Hausdorff (known to be NP-hard), Local-Hausdorff (in time $O(n^3)$), Global-Fréchet (in time $O(k n^5)$), and Local-Fréchet (in time $O(n^3)$). Our contribution is as follows. - Cubic time for all variants: For Global-Fréchet we design an algorithm running in time $O(n^3)$. This shows that all three problems (Local-Hausdorff, Local-Fréchet, and Global-Fréchet) can be solved in cubic time. All these algorithms work over a general metric space such as $(\mathbb{R}^d,L_p)$, but the hidden constant depends on $p$ and (linearly) on $d$. - Cubic conditional lower bound: We provide evidence that in high dimensions cubic time is essentially optimal for all three problems (Local-Hausdorff, Local-Fréchet, and Global-Fréchet). Specifically, improving the cubic time to $O(n^{3-ε} \textrm{poly}(d))$ for polyline simplification over $(\mathbb{R}^d,L_p)$ for $p = 1$ would violate plausible conjectures. We obtain similar results for all $p \in [1,\infty), p \ne 2$. In total, in high dimensions and over general $L_p$-norms we resolve the complexity of polyline simplification with respect to Local-Hausdorff, Local-Fréchet, and Global-Fréchet, by providing new algorithms and conditional lower bounds.

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arXiv2024

On the Theoretical Foundations of Data Exchange Economies

The immense success of ML systems relies heavily on large-scale, high-quality data. The high demand for data has led to many paradigms that involve selling, exchanging, and sharing data, motivating the study of economic processes with data as an asset. However, data differs from classical economic assets in terms of free duplication: there is no concept of limited supply since it can be replicated at zero marginal cost. This distinction introduces fundamental differences between economic processes involving data and those concerning other assets. We study a parallel to exchange (Arrow-Debreu) markets where data is the asset. Here, agents with datasets exchange data fairly and voluntarily, aiming for mutual benefit without monetary compensation. This framework is particularly relevant for non-profit organizations that seek to improve their ML models through data exchange, yet are restricted from selling their data for profit. We propose a general framework for data exchange, built on two core principles: (i) fairness, ensuring that each agent receives utility proportional to their contribution to others; contributions are quantifiable using standard credit-sharing functions like the Shapley value, and (ii) stability, ensuring that no coalition of agents can identify an exchange among themselves which they unanimously prefer to the current exchange. We show that fair and stable exchanges exist for all monotone continuous utility functions. Next, we investigate the computational complexity of finding approximate fair and stable exchanges. We present a local search algorithm for instances with monotone submodular utility functions, where each agent contributions are measured using the Shapley value. We prove that this problem lies in CLS under mild assumptions. Our framework opens up several intriguing theoretical directions for research in data economics.

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arXiv2024

Competitive Equilibrium for Chores: from Dual Eisenberg-Gale to a Fast, Greedy, LP-based Algorithm

We study the computation of competitive equilibrium for Fisher markets with $n$ agents and $m$ divisible chores. Competitive equilibria for chores are known to correspond to the nonzero KKT points of a program that minimizes the product of agent disutilities, which is a non-convex program whose zero points foil iterative optimization methods. We introduce a dual-like analogue of this program, and show that a simple modification to our "dual" program avoids such zero points, while retaining the correspondence between KKT points and competitive equilibria. This allows, for the first time ever, application of iterative optimization methods over a convex region for computing competitive equilibria for chores. We next introduce a greedy Frank-Wolfe algorithm for optimization over our program and show a new state-of-the-art convergence rate to competitive equilibrium. Moreover, our method is significantly simpler than prior methods: each iteration of our method only requires solving a simple linear program. We show through numerical experiments that our method is extremely practical: it easily solves every instance we tried, including instances with hundreds of agents and up to 1000 chores, usually in 10-30 iterations, is simple to implement, and has no numerical issues.

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arXiv2023

Fair and Efficient Allocation of Indivisible Chores with Surplus

We study fair division of indivisible chores among $n$ agents with additive disutility functions. Two well-studied fairness notions for indivisible items are envy-freeness up to one/any item (EF1/EFX) and the standard notion of economic efficiency is Pareto optimality (PO). There is a noticeable gap between the results known for both EF1 and EFX in the goods and chores settings. The case of chores turns out to be much more challenging. We reduce this gap by providing slightly relaxed versions of the known results on goods for the chores setting. Interestingly, our algorithms run in polynomial time, unlike their analogous versions in the goods setting. We introduce the concept of $k$ surplus which means that up to $k$ more chores are allocated to the agents and each of them is a copy of an original chore. We present a polynomial-time algorithm which gives EF1 and PO allocations with $(n-1)$ surplus. We relax the notion of EFX slightly and define tEFX which requires that the envy from agent $i$ to agent $j$ is removed upon the transfer of any chore from the $i$'s bundle to $j$'s bundle. We give a polynomial-time algorithm that in the chores case for $3$ agents returns an allocation which is either proportional or tEFX. Note that proportionality is a very strong criterion in the case of indivisible items, and hence both notions we guarantee are desirable.

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arXiv2022

EFX Allocations: Simplifications and Improvements

The existence of EFX allocations is a fundamental open problem in discrete fair division. Given a set of agents and indivisible goods, the goal is to determine the existence of an allocation where no agent envies another following the removal of any single good from the other agent's bundle. Since the general problem has been illusive, progress is made on two fronts: $(i)$ proving existence when the number of agents is small, $(ii)$ proving existence of relaxations of EFX. In this paper, we improve results on both fronts (and simplify in one of the cases). We prove the existence of EFX allocations with three agents, restricting only one agent to have an MMS-feasible valuation function (a strict generalization of nice-cancelable valuation functions introduced by Berger et al. which subsumes additive, budget-additive and unit demand valuation functions). The other agents may have any monotone valuation functions. Our proof technique is significantly simpler and shorter than the proof by Chaudhury et al. on existence of EFX allocations when there are three agents with additive valuation functions and therefore more accessible. Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX allocations and EFX allocations with few unallocated goods (charity). Chaudhury et al. showed the existence of $(1-ε)$-EFX allocation with $O((n/ε)^{\frac{4}{5}})$ charity by establishing a connection to a problem in extremal combinatorics. We improve their result and prove the existence of $(1-ε)$-EFX allocations with $\tilde{O}((n/ ε)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used to prove improved upper-bounds on a problem in zero-sum combinatorics introduced by Alon and Krivelevich.

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arXiv2022

Fairness in Federated Learning via Core-Stability

Federated learning provides an effective paradigm to jointly optimize a model benefited from rich distributed data while protecting data privacy. Nonetheless, the heterogeneity nature of distributed data makes it challenging to define and ensure fairness among local agents. For instance, it is intuitively "unfair" for agents with data of high quality to sacrifice their performance due to other agents with low quality data. Currently popular egalitarian and weighted equity-based fairness measures suffer from the aforementioned pitfall. In this work, we aim to formally represent this problem and address these fairness issues using concepts from co-operative game theory and social choice theory. We model the task of learning a shared predictor in the federated setting as a fair public decision making problem, and then define the notion of core-stable fairness: Given $N$ agents, there is no subset of agents $S$ that can benefit significantly by forming a coalition among themselves based on their utilities $U_N$ and $U_S$ (i.e., $\frac{|S|}{N} U_S \geq U_N$). Core-stable predictors are robust to low quality local data from some agents, and additionally they satisfy Proportionality and Pareto-optimality, two well sought-after fairness and efficiency notions within social choice. We then propose an efficient federated learning protocol CoreFed to optimize a core stable predictor. CoreFed determines a core-stable predictor when the loss functions of the agents are convex. CoreFed also determines approximate core-stable predictors when the loss functions are not convex, like smooth neural networks. We further show the existence of core-stable predictors in more general settings using Kakutani's fixed point theorem. Finally, we empirically validate our analysis on two real-world datasets, and we show that CoreFed achieves higher core-stability fairness than FedAvg while having similar accuracy.

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