arXiv subjects

Jay Sethuraman

Publications and source records attributed to Jay Sethuraman.

17 recordsLinked to original sources

arXiv2026

Assortment and Procurement Design in Dual-Mode Content Platforms

We study assortment and procurement design for a digital content platform offering both ad-supported and subscription access. Users are heterogeneous in content preferences and ad tolerance and self-select between the two modes or an outside option. For a fixed common subscription price and ad load, the platform chooses assortment distributions specific to each user type and access mode, together with content-family-level buy-versus-rent decisions to maximize profit. Rental costs scale with realized consumption, whereas buying provides a reusable pool of titles whose cost depends on the largest induced requirement across user types and modes. We show that the resulting problem is NP-hard. We then develop a scalable approximation framework based on a candidate buy set, a relaxation of the procurement coupling, and a decomposition into linear programs with a single equality constraint. These subproblems are solved by dual bisection with cardinality-constrained assortment optimization, followed by restricted-master postprocessing to recover primal feasibility. The method yields computable optimality-gap bounds, an interpretable threshold-based procurement heuristic, and asymptotic optimality under proportional market scaling as market size and grid resolution increase. Numerical experiments show strong performance at moderate market scales and grid sizes.

cs.DS↗

arXiv2025

Teacher transfers: equalizing deficits across schools

The Right to Free and Compulsory Education Act (2009) (RTE) of the Government of India prescribes student-teacher ratios for state-run schools. One method advocated by the Act to achieve its goals is the redeployment of teachers from surplus to deficit (in teacher strength) schools. We consider a model where teachers can either remain in their initially assigned schools or be transferred to a deficit school in their acceptable set. The planner's objective is specified in terms of the post-transfer deficit vector that can be achieved. We show that there exists a transfer whose post-transfer deficit vector Lorenz dominates all achievable post-transfer deficit vectors. We provide a two-stage algorithm to derive the Lorenz-dominant post-transfer deficit vector, and show that this algorithm is strategy-proof for teachers.

econ.TH↗

arXiv2025

Gaming on Coincident Peak Shaving: Equilibrium and Strategic Behavior

Power system operators and electric utility companies often impose a coincident peak demand charge on customers when the aggregate system demand reaches its maximum. This charge incentivizes customers to strategically shift their peak usage away from the system's collective peak, which helps reduce stress on electricity infrastructure. In this paper, we develop a game-theoretic model to analyze how such strategic behavior affects overall system efficiency. We show that depending on the extent of customers' demand-shifting capabilities, the resulting coincident peak shaving game can exhibit concavity, quasi-concavity with discontinuities, or non-concavity with discontinuities. In a two-agent, two-period setting, we derive closed-form Nash equilibrium solutions for each scenario and generalize our findings to multi-agent contexts. We prove the stability of the equilibrium points and propose an algorithm for computing equilibrium outcomes under all game configurations. Our results indicate that the peak-shaving outcome at the equilibrium of the game model is comparable to the optimal outcome of the natural centralized model. However, there is a significant loss in efficiency. Under quasi-concave and non-concave conditions, this inefficiency grows with increased customer flexibility and larger disparities in marginal shifting costs; we also examine how the number of agents influences system performance. Finally, numerical simulations with real-world applications validate our theoretical insights.

eess.SY↗

arXiv2024

Scarf's Algorithm on Arborescence Hypergraphs

Scarf's algorithm--a pivoting procedure that finds a dominating extreme point in a down-monotone polytope--can be used to show the existence of a fractional stable matching in hypergraphs. The problem of finding a fractional stable matching in a hypergraph, however, is PPAD-complete. In this work, we study the behavior of Scarf's algorithm on arborescence hypergraphs, the family of hypergraphs in which hyperedges correspond to the paths of an arborescence. For arborescence hypergraphs, we prove that Scarf's algorithm can be implemented to find an integral stable matching in polynomial time. En route to our result, we uncover novel structural properties of bases and pivots for the more general family of network hypergraphs. Our work provides the first proof of polynomial-time convergence of Scarf's algorithm on hypergraphic stable matching problems, giving hope to the possibility of polynomial-time convergence of Scarf's algorithm for other families of polytope.

cs.DM↗

arXiv2024

Managing cascading disruptions through optimal liability assignment

Interconnected agents such as firms in a supply chain make simultaneous preparatory investments to increase chances of honouring their respective bilateral agreements. Failures cascade: if one fails their agreement, then so do all who follow in the chain. Thus, later agents' investments turn out to be pointless when there is an earlier failure. How losses are shared affects how agents invest to avoid the losses in the first place. In this way, a solution sets agent liabilities depending on the point of disruption and induces a supermodular investment game. We characterize all efficient solutions. These have the form that later agents -- who are not directly liable for the disruption -- still shoulder some of the losses, justified on the premise that they might have failed anyway. Importantly, we find that such indirect liabilities are necessary to avoid unbounded inefficiencies. Finally, we pinpoint one efficient solution with several desirable properties.

econ.TH↗

arXiv2023

Decentralized Finance: Protocols, Risks, and Governance

Financial markets are undergoing an unprecedented transformation. Technological advances have brought major improvements to the operations of financial services. While these advances promote improved accessibility and convenience, traditional finance shortcomings like lack of transparency and moral hazard frictions continue to plague centralized platforms, imposing societal costs. In this paper, we argue how these shortcomings and frictions are being mitigated by the decentralized finance (DeFi) ecosystem. We delve into the workings of smart contracts, the backbone of DeFi transactions, with an emphasis on those underpinning token exchange and lending services. We highlight the pros and cons of the novel form of decentralized governance introduced via the ownership of governance tokens. Despite its potential, the current DeFi infrastructure introduces operational risks to users, which we segment into five primary categories: consensus mechanisms, protocol, oracle, frontrunning, and systemic risks. We conclude by emphasizing the need for future research to focus on the scalability of existing blockchains, the improved design and interoperability of DeFi protocols, and the rigorous auditing of smart contracts.

q-fin.TR↗

arXiv2023

Scarf's algorithm and stable marriages

Scarf's algorithm gives a pivoting procedure to find a special vertex -- a dominating vertex -- in down-monotone polytopes. This paper studies the behavior of Scarf's algorithm when employed to find stable matchings in bipartite graphs. First, it proves that Scarf's algorithm can be implemented to run in polynomial time, showing the first positive result on its runtime in significant settings. Second, it shows an infinite family of instances where, no matter the pivoting rule and runtime, Scarf's algorithm outputs a matching from an exponentially small subset of all stable matchings, thus showing a structural weakness of the approach.

math.CO↗

arXiv2020

A note on the rationing of divisible and indivisible goods in a general network

The study of matching theory has gained importance recently with applications in Kidney Exchange, House Allocation, School Choice etc. The general theme of these problems is to allocate goods in a fair manner amongst participating agents. The agents generally have a unit supply/demand of a good that they want to exchange with other agents. On the other hand, Bochet et al. study a more general version of the problem where they allow for agents to have arbitrary number of divisible goods to be rationed to other agents in the network. In this current work, our main focus is on non-bipartite networks where agents have arbitrary units of a homogeneous indivisible good that they want to exchange with their neighbors. Our aim is to develop mechanisms that would identify a fair and strategyproof allocation for the agents in the network. Thus, we generalize the kidney exchange problem to that of a network with arbitrary capacity of available goods. Our main idea is that this problem and a couple of other related versions of non-bipartite fair allocation problem can be suitably transformed to one of fair allocations on bipartite networks for which we know of well studied fair allocation mechanisms.

cs.GT↗

arXiv2019

On optimal ordering in the optimal stopping problem

In the classical optimal stopping problem, a player is given a sequence of random variables $X_1\ldots X_n$ with known distributions. After observing the realization of $X_i$, the player can either accept the observed reward from $X_i$ and stop, or reject the observed reward from $X_i$ and continue to observe the next variable $X_{i+1}$ in the sequence. Under any fixed ordering of the random variables, an optimal stopping policy, one that maximizes the player's expected reward, is given by the solution of a simple dynamic program. In this paper, we investigate the relatively less studied question of selecting the order in which the random variables should be observed so as to maximize the expected reward at the stopping time. To demonstrate the benefits of order selection, we prove a novel prophet inequality showing that, when the support of each random variable has size at most 2, the optimal ordering can achieve an expected reward that is within a factor of 1.25 of the expected hindsight maximum; this is an improvement over the corresponding factor of 2 for the worst-case ordering. We also provide a simple $O(n^2)$ algorithm for finding an optimal ordering in this case. Perhaps surprisingly, we demonstrate that a slightly more general case - each random variable $X_i$ is restricted to have 3-point support of form $\{0, m_i, 1\}$ - is NP-hard, and provide an FPTAS for that case.

cs.DM↗

arXiv2014

Strategyproof Mechanisms for One-Dimensional Hybrid and Obnoxious Facility Location

We consider a strategic variant of the facility location problem. We would like to locate a facility on a closed interval. There are n agents located on that interval, divided into two types: type 1 agents, who wish for the facility to be as far from them as possible, and type 2 agents, who wish for the facility to be as close to them as possible. Our goal is to maximize a form of aggregated social benefit: maxisum- the sum of the agents' utilities, or the egalitarian objective- the minimal agent utility. The strategic aspect of the problem is that the agents' locations are not known to us, but rather reported to us by the agents- an agent might misreport his location in an attempt to move the facility away from or towards to his true location. We therefore require the facility-locating mechanism to be strategyproof, namely that reporting truthfully is a dominant strategy for each agent. As simply maximizing the social benefit is generally not strategyproof, our goal is to design strategyproof mechanisms with good approximation ratios. For the maxisum objective, in the deterministic setting, we provide a best-possible 3- approximate strategyproof mechanism; in the randomized setting, we provide a 23/13- approximate strategyproof mechanism and a lower bound of \frac{2}{\sqrt{3}}. For the egalitarian objective, we provide a lower bound of 3/2 in the randomized setting, and show that no bounded approximation ratio is attainable in the deterministic setting. To obtain our deterministic lower bounds, we characterize all deterministic strategyproof mechanisms when all agents are of type 1. Finally, we consider a generalized model that allows an agent to control more than one location, and provide best-possible 3- and 3/2- approximate strategyproof mechanisms for maxisum, in the deterministic and randomized settings respectively, when only type 1 agents are present.

cs.GT↗

arXiv2014

A Note on the Assignment Problem with Uniform Preferences

Motivated by a problem of scheduling unit-length jobs with weak preferences over time-slots, the random assignment problem (also called the house allocation problem) is considered on a uniform preference domain. For the subdomain in which preferences are strict except possibly for the class of unacceptable objects, Bogomolnaia and Moulin characterized the probabilistic serial mechanism as the only mechanism satisfying equal treatment of equals, strategyproofness, and ordinal efficiency. The main result in this paper is that the natural extension of the probabilistic serial mechanism to the domain of weak, but uniform, preferences fails strategyproofness, but so does every other mechanism that is ordinally efficient and treats equals equally. If envy-free assignments are required, then any (probabilistic or deterministic) mechanism that guarantees an ex post efficient outcome must fail even a weak form of strategyproofness.

cs.GT↗

arXiv2014

The size of the core in assignment markets

Assignment markets involve matching with transfers, as in labor markets and housing markets. We consider a two-sided assignment market with agent types and stochastic structure similar to models used in empirical studies, and characterize the size of the core in such markets. Each agent has a randomly drawn productivity with respect to each type of agent on the other side. The value generated from a match between a pair of agents is the sum of the two productivity terms, each of which depends only on the type but not the identity of one of the agents, and a third deterministic term driven by the pair of types. We allow the number of agents to grow, keeping the number of agent types fixed. Let $n$ be the number of agents and $K$ be the number of types on the side of the market with more types. We find, under reasonable assumptions, that the relative variation in utility per agent over core outcomes is bounded as $O^*(1/n^{1/K})$, where polylogarithmic factors have been suppressed. Further, we show that this bound is tight in worst case. We also provide a tighter bound under more restrictive assumptions. Our results provide partial justification for the typical assumption of a unique core outcome in empirical studies.

cs.GT↗

arXiv2014

Game Theory, Statistical Mechanics and Income Inequality

The widening inequality in income distribution in recent years, and the associated excessive pay packages of CEOs in the U.S. and elsewhere, is of growing concern among policy makers as well as the common person. However, there seems to be no satisfactory answer, in conventional economic theories and models, to the fundamental question of what kind of pay distribution we ought to see, at least under ideal conditions, in a free market environment and whether this distribution is fair. We propose a game theoretic framework that addresses these questions and show that the lognormal distribution is the fairest inequality of pay in an organization comprising of homogenous agents, achieved at equilibrium, under ideal free market conditions. We also show that for a population of two different classes of agents, the final distribution is a combination of two different lognormal distributions where one of them, corresponding to the top 3-5% of the population, can be misidentified as a Pareto distribution. Our theory also shows the deep and direct connection between potential game theory and statistical mechanics through entropy, which is a measure of fairness in a distribution. This leads us to propose the fair market hypothesis, that the self-organizing dynamics of the ideal free market, i.e., Adam Smith's "invisible hand", not only promotes efficiency but also maximizes fairness under the given constraints.

econ.GN↗

arXiv2013

Approximation Algorithms for the Incremental Knapsack Problem via Disjunctive Programming

In the incremental knapsack problem ($\IK$), we are given a knapsack whose capacity grows weakly as a function of time. There is a time horizon of $T$ periods and the capacity of the knapsack is $B_t$ in period $t$ for $t = 1, \ldots, T$. We are also given a set $S$ of $N$ items to be placed in the knapsack. Item $i$ has a value of $v_i$ and a weight of $w_i$ that is independent of the time period. At any time period $t$, the sum of the weights of the items in the knapsack cannot exceed the knapsack capacity $B_t$. Moreover, once an item is placed in the knapsack, it cannot be removed from the knapsack at a later time period. We seek to maximize the sum of (discounted) knapsack values over time subject to the capacity constraints. We first give a constant factor approximation algorithm for $\IK$, under mild restrictions on the growth rate of $B_t$ (the constant factor depends on the growth rate). We then give a PTAS for $\IIK$, the special case of $\IK$ with no discounting, when $T = O(\sqrt{\log N})$.

cs.DS↗

arXiv2013

Approximately Optimal Mechanisms for Strategyproof Facility Location: Minimizing $L_p$ Norm of Costs

We consider the problem of locating a single facility on the real line. This facility serves a set of agents, each of whom is located on the line, and incurs a cost equal to his distance from the facility. An agent's location is private information that is known only to him. Agents report their location to a central planner who decides where to locate the facility. The planner's objective is to minimize a "social" cost function that depends on the agent-costs. However, agents might not report truthfully; to address this issue, the planner must restrict himself to {\em strategyproof} mechanisms, in which truthful reporting is a dominant strategy for each agent. A mechanism that simply chooses the optimal solution is generally not strategyproof, and so the planner aspires to use a mechanism that effectively {\em approximates} his objective function. In our paper, we study the problem described above with the social cost function being the $L_p$ norm of the vector of agent-costs. We show that the median mechanism (which is known to be strategyproof) provides a $2^{1-\frac{1}{p}}$ approximation ratio, and that is the optimal approximation ratio among all deterministic strategyproof mechanisms. For randomized mechanisms, we present two results. First, we present a negative result: we show that for integer $\infty>p>2$, no mechanism---from a rather large class of randomized mechanisms--- has an approximation ratio better than that of the median mechanism. This is in contrast to the case of $p=2$ and $p=\infty$ where a randomized mechanism provably helps improve the worst case approximation ratio. Second, for the case of 2 agents, we show that a mechanism called LRM, first designed by Procaccia and Tennenholtz for the special case of $L_{\infty}$, provides the optimal approximation ratio among all randomized mechanisms.

cs.GT↗

arXiv2013

Strategyproof and Consistent Rules for Bipartite Flow Problems

We continue the study of Bochet et al. and Moulin and Sethuraman on fair allocation in bipartite networks. In these models, there is a moneyless market, in which a non-storable, homogeneous commodity is reallocated between agents with single-peaked preferences. Agents are either suppliers or demanders. While the egalitarian rule of Bochet et al. satisfies pareto optimality, no envy and strategyproof, it is not consistent. On the other hand, the work of Moulin and Sethuraman is related to consistent allocations and rules that are extensions of the uniform rule. We bridge the two streams of work by introducing the edge fair mechanism which is both consistent and groupstrategyproof. On the way, we explore the "price of consistency" i.e. how the notion of consistency is fundamentally incompatible with certain notions of fairness like Lorenz Dominance and No-Envy. The current work also introduces the idea of strong invariance as desideratum for groupstrategyproofness and generalizes the proof of Chandramouli and Sethuraman to a more broader class of mechanisms. Finally, we conclude with the study of the edge fair mechanism in a transshipment model where the strategic agents are on the links connecting different supply/demand locations.

math.OC↗

arXiv2011

Groupstrategyproofness of the Egalitarian Mechanism for Constrained Rationing Problems

The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is, in fact, peak group strategyproof : no coalition of agents can (weakly) benefit from jointly misreporting their peaks. Furthermore, we show that the egalitarian mechanism cannot be manipulated by any coalition of suppliers (or any coalition of demanders) in the model where both the suppliers and demanders are agents. Our proofs shed light on the structure of the two models and simpify some of the earlier proofs of strategyproofness in the earlier papers. An implication of our results is that the well known algorithm of Megiddo to compute a lexicographically optimal flow in a network is group strategyproof with respect to the source capacities (or sink capacities).

cs.GT↗