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Ankur A. Kulkarni

Publications and source records attributed to Ankur A. Kulkarni.

At least 19 recordsLinked to original sources
arXiv2026

Nonlocal Teams and Information Structures

We look at Bell inequalities from the lens of information structures in stochastic teams. We consider the usual CHSH game and a dynamic variant of the same to study how various classes of strategies, classical, projective and quantum, behave under team theoretic solution concepts. We find that projective strategies (where each player performs projective measurements) enjoy important properties in the usual CHSH game, but they do not carry over to its dynamic version. These results shed light on the delicate interplay of information structure in quantum strategies and the fragility of some well known ideas under changes of information structure.

quant-ph↗
arXiv2025

Achievable Rates for Information Extraction from a Strategic Sender

We consider a setting of non-cooperative communication where a receiver wants to recover randomly generated sequences of symbols that are observed by a strategic sender. The sender aims to maximize an average utility that may not align with the recovery criterion of the receiver, whereby the signals it sends may not be truthful. The rate of communication is defined as the number of reconstructions corresponding to the sequences recovered correctly while communicating with the sender. We pose this problem as a sequential game between the sender and the receiver with the receiver as the leader and determine strategies for the receiver that attain vanishing probability of error and compute the rates of such strategies. We show the existence of such strategies under a condition on the utility of the sender. For the case of the binary alphabet, this condition is also necessary, in the absence of which, the probability of error goes to one for all choices of strategies of the receiver. We show that for reliable recovery, the receiver chooses to correctly decode only a $\textit{subset}$ of messages received from the sender and deliberately makes an error on messages outside this subset. Despite a clean channel, our setting exhibits a non-trivial $\textit{maximum}$ rate of communication, which is in general strictly less than the capacity of the channel. This implies the impossibility of strategies that correctly decode sequences of rate greater than the maximum rate while also achieving reliable communication. This is a key point of departure from the usual setting of cooperative communication.

cs.IT↗
arXiv2024

Informativeness and Trust in Bayesian Persuasion

A persuasion policy successfully persuades an agent to pick a particular action only if the information is designed in a manner that convinces the agent that it is in their best interest to pick that action. Thus, it is natural to ask, what makes the agent trust the persuader's suggestion? We study a Bayesian persuasion interaction between a sender and a receiver where the sender has access to private information and the receiver attempts to recover this information from messages sent by the sender. The sender crafts these messages in an attempt to maximize its utility which depends on the source symbol and the symbol recovered by the receiver. Our goal is to characterize the \textit{Stackelberg game value}, and the amount of true information revealed by the sender during persuasion. We find that the SGV is given by the optimal value of a \textit{linear program} on probability distributions constrained by certain \textit{trust constraints}. These constraints encode that any signal in a persuasion strategy must contain more truth than untruth and thus impose a fundamental bound on the extent of obfuscation a sender can perform. We define \textit{informativeness} of the sender as the minimum expected number of symbols truthfully revealed by the sender in any accumulation point of a sequence of $\varepsilon$-equilibrium persuasion strategies, and show that it is given by another linear program. Informativeness is a fundamental bound on the amount of information the sender must reveal to persuade a receiver. Closed form expressions for the SGV and the informativeness are presented for structured utility functions. This work generalizes our previous work where the sender and the receiver were constrained to play only deterministic strategies and a similar notion of informativeness was characterized. Comparisons between the previous and current notions are discussed.

cs.GT↗
arXiv2024

Revisiting Common Randomness, No-signaling and Information Structure in Decentralized Control

This work revisits the no-signaling condition for decentralized information structures. We produce examples to show that within the no-signaling polytope exist strategies that cannot be achieved by passive common randomness but instead require agents to either share their observations with a mediator or communicate directly with each other. This poses a question mark on whether the no-signaling condition truly captures the decentralized information structure in the strictest sense.

cs.IT↗
arXiv2023

Signalling for Electricity Demand Response: When is Truth Telling Optimal?

Utilities and transmission system operators (TSO) around the world implement demand response programs for reducing electricity consumption by sending information on the state of balance between supply demand to end-use consumers. We construct a Bayesian persuasion model to analyse such demand response programs. Using a simple model consisting of two time steps for contract signing and invoking, we analyse the relation between the pricing of electricity and the incentives of the TSO to garble information about the true state of the generation. We show that if the electricity is priced at its marginal cost of production, the TSO has no incentive to lie and always tells the truth. On the other hand, we provide conditions where overpricing of electricity leads the TSO to provide no information to the consumer.

eess.SY↗
arXiv2023

The Quantum Advantage in Binary Teams and the Coordination Dilemma: Part I

We have shown that entanglement assisted stochastic strategies allow access to strategic measures beyond the classically correlated measures accessible through passive common randomness, and thus attain a quantum advantage in decentralised control. In this two part series of articles, we investigate the decision theoretic origins of the quantum advantage within a broad superstructure of problem classes. Each class in our binary team superstructure corresponds to a parametric family of cost functions with a distinct algebraic structure. In this part, identify the only problem classes that benefit from quantum strategies. We find that these cost structures admit a special decision-theoretic feature -- `the coordination dilemma'. Our analysis hence reveals some intuition towards the utility of non-local quantum correlations in decentralised control.

eess.SY↗
arXiv2023

The Quantum Advantage in Decentralized Control

It is known in the context of decentralised control that there exist control strategies consistent with the requirements of a given information structure, yet physically unimplementable through any amount of passive common randomness. This imposes a natural set of limitations on what is achievable through common randomness in both cooperative and competitive settings. We show that it is possible to breach these limitations with the use of quantum-physical architectures. In particular, we present a class of stochastic strategies that leverage quantum entanglement to produce strategic distributions which compose a strict superclass of strategies implemented through passive common randomness. We investigate numerically, the `quantum advantage' offered by this new class over a parametric family of cooperative decision problems with static information structure. We demonstrate through variations across the parametric family that fundamental decision theoretic elements such as information and the cost determine the manifestation of quantum advantage in a given control problem. Our work motivates a novel decision and control paradigm with an enlarged space of control policies achievable by means of quantum architectures.

eess.SY↗
arXiv2022

Information Revelation Through Signalling

This paper studies a Stackelberg game wherein a sender (leader) attempts to shape the information of a less informed receiver (follower) who in turn takes an action that determines the payoff for both players. The sender chooses signals to maximize its own utility function while the receiver aims to ascertain the value of a source that is privately known to the sender. It is well known that such sender-receiver games admit a vast number of equilibria and not all signals from the sender can be relied on as truthful. Our main contribution is an exact characterization of the minimum number of distinct source symbols that can be correctly recovered by a receiver in \textit{any} equilibrium of this game; we call this quantity the \textit{informativeness} of the sender. We show that the informativeness is given by the \textit{vertex clique cover number} of a certain graph induced by the utility function, whereby it can be computed based on the utility function alone without the need to enumerate all equilibria. We find that informativeness characterizes the existence of well-known classes of separating, pooling and semi-separating equilibria. We also compare informativeness with the amount of information obtained by the receiver when it is the leader and show that the informativeness is always greater than the latter, implying that the receiver is better off being a follower. Additionally, we also show that when the players play behavioral strategies, an equilibrium may not exist.

cs.GT↗
arXiv2022

Shannon meets Myerson: Information Extraction from a Strategic Sender

We study a setting where a receiver must design a questionnaire to recover a sequence of symbols known to strategic sender, whose utility may not be incentive compatible. We allow the receiver the possibility of selecting the alternatives presented in the questionnaire, and thereby linking decisions across the components of the sequence. We show that, despite the strategic sender and the noise in the channel, the receiver can recover exponentially many sequences, but also that exponentially many sequences are unrecoverable even by the best strategy. We define the growth rate of the number of recovered sequences as the information extraction capacity. A generalization of the Shannon capacity, it characterizes the optimal amount of communication resources required. We derive bounds leading to an exact evaluation of the information extraction capacity in many cases. Our results form the building blocks of a novel, noncooperative regime of communication involving a strategic sender.

cs.IT↗
arXiv2022

A Scalable Bayesian Persuasion Framework for Epidemic Containment on Heterogeneous Networks

During an epidemic, the information available to individuals in the society deeply influences their belief of the epidemic spread, and consequently the preventive measures they take to stay safe from the infection. In this paper, we develop a scalable framework for ascertaining the optimal information disclosure a government must make to individuals in a networked society for the purpose of epidemic containment. This problem of information design problem is complicated by the heterogeneous nature of the society, the positive externalities faced by individuals, and the variety in the public response to such disclosures. We use a networked public goods model to capture the underlying societal structure. Our first main result is a structural decomposition of the government's objectives into two independent components -- a component dependent on the utility function of individuals, and another dependent on properties of the underlying network. Since the network dependent term in this decomposition is unaffected by the signals sent by the government, this characterization simplifies the problem of finding the optimal information disclosure policies. We find explicit conditions, in terms of the risk aversion and prudence, under which no disclosure, full disclosure, exaggeration and downplay are the optimal policies. The structural decomposition results are also helpful in studying other forms of interventions like incentive design and network design.

eess.SY↗
arXiv2022

Refinement of the Equilibrium of Public Goods Games over Networks: Efficiency and Effort of Specialized Equilibria

Recently Bramoulle and Kranton presented a model for the provision of public goods over a network and showed the existence of a class of Nash equilibria called specialized equilibria wherein some agents exert maximum effort while other agents free ride. We examine the efficiency, effort and cost of specialized equilibria in comparison to other equilibria. Our main results show that the welfare of a particular specialized equilibrium approaches the maximum welfare amongst all equilibria as the concavity of the benefit function tends to unity. For forest networks a similar result also holds as the concavity approaches zero. Moreover, without any such concavity conditions, there exists for any network a specialized equilibrium that requires the maximum weighted effort amongst all equilibria. When the network is a forest, a specialized equilibrium also incurs the minimum total cost amongst all equilibria. For well-covered forest networks we show that all welfare maximizing equilibria are specialized and all equilibria incur the same total cost. Thus we argue that specialized equilibria may be considered as a refinement of the equilibrium of the public goods game. We show several results on the structure and efficiency of equilibria that highlight the role of dependants in the network.

cs.GT↗
arXiv2020

Optimal Questionnaires for Screening of Strategic Agents

During the COVID-$19$ pandemic the health authorities at airports and train stations try to screen and identify the travellers possibly exposed to the virus. However, many individuals avoid getting tested and hence may misreport their travel history. This is a challenge for the health authorities who wish to ascertain the truly susceptible cases in spite of this strategic misreporting. We investigate the problem of questioning travellers to classify them for further testing when the travellers are strategic or are unwilling to reveal their travel histories. We show there are fundamental limits to how many travel histories the health authorities can recover.% can be correctly classified by any probing mechanism.

cs.IR↗
arXiv2020

Duopolistic platform competition for revenue and throughput

We consider two competing platforms operating in a two-sided market and offering identical services to their customers at potentially different prices. The objective of each platform is to maximize its throughput or revenue by suitably pricing its services. We assume that customers have a preference or loyalty to the platforms while the workers freelance for the two platforms. Assuming that the resulting interaction between the users is such that their aggregate utility is maximized, we show that for each value of the loyalty, there exists a pure strategy Nash equilibrium for both the throughput and revenue competition game and characterize it.

math.OC↗
arXiv2020

Strategy-Proof Spectrum Allocation among Multiple Operators for Demand Varying Wireless Networks

To address the exponentially increasing data rate demands of end users, necessitates efficient spectrum allocation among co-existing operators in licensed and unlicensed spectrum bands to cater to the temporal and spatial variations of traffic in the wireless network. In this paper, we address the spectrum allocation problem among non-cooperative operators via auctions. The classical Vickrey-Clarke-Groves (VCG) approach provides the framework for a strategy-proof and social welfare maximizing auction at high computational complexity, which makes it infeasible for practical implementation. We propose sealed bid auction mechanisms for spectrum allocation which are computationally tractable and hence applicable for allocating spectrum by performing auctions in short durations as per the dynamic load variations of the network. We establish that the proposed algorithm is strategy-proof for uniform demand. Furthermore, for non-uniform demand we propose an algorithm that satisfies weak strategy-proofness. We also consider non-linear increase in the marginal valuations with demand. Simulation results are presented to exhibit the performance comparison of the proposed algorithms with VCG and other existing mechanisms.

cs.GT↗
arXiv2019

Statistical Economies of Scale in Battery Sharing

The goal of this paper is to shed light on the statistical economies of scale achievable from sharing of storage between renewable generators. We conduct an extensive study using real world wind data from a grid of equispaced wind generators sharing a common battery. We assume each generator is contracted to meet a certain demand profile to a prescribed level of reliability. We find that the statistical diversity in wind generation across different locations yields useful economies of scale once the grid spacing exceeds 200 km. When the grid spacing exceeds 500 km, we find that the economies grow dramatically: The shared battery size becomes insensitive to the number of participating generators. This means that the generators can access a common, shared battery and collectively achieve the same reliability they would have, had each of them had the entire battery to themselves. To provide a rigourous foundation for this remarkable observation, we propose a mathematical model that demonstrates this phenomenon, assuming that the net generation (generation minus demand) processes associated with the generators are statistically independent. The result is derived by characterizing the large deviations exponent of the loss of load probability with increasing battery size, and showing that this exponent is invariant with the number of generators.

eess.SY↗
arXiv2019

Efficiency Fairness Tradeoff in Battery Sharing

The increasing presence of decentralized renewable generation in the power grid has motivated consumers to install batteries to save excess energy for future use. The high price of energy storage calls for a shared storage system, but careful battery management is required so that the battery is operated in a manner that is fair to all and as efficiently as possible. In this paper, we study the tradeoffs between efficiency and fairness in operating a shared battery. We develop a framework based on constrained Markov decision processes to study both regimes, namely, optimizing efficiency under a hard fairness constraint and optimizing fairness under hard efficiency constraint. Our results show that there are fundamental limits to efficiency under fairness and vice-versa, and, in general, the two cannot be achieved simultaneously. We characterize these fundamental limits via absolute bounds on these quantities, and via the notion of price of fairness that we introduce in this paper.

math.OC↗
arXiv2019

The Efficiency of Generalized Nash and Variational Equilibria

Shared-constraint games are noncooperative $N$-player games where players are coupled through a common coupling constraint. It is known that such games admit two kinds of equilibria -- generalized Nash equilibria (GNE) and variational equilibria (VE) -- with two different economic interpretations. We consider such games in the context of resource allocation, where players move simultaneously to decide portions of the resource they can consume under a coupling constraint that the sum of the portions they demand be no more than the capacity of the resource. We clarify the worst case and best case efficiency of these kinds of equilibria over all games in a class. We find that the worst case efficiency of both solution concepts in zero and the best case efficiency is unity. Moreover, we characterize the subclass of games where all VE are efficient and show that even in this subclass but the worst case efficiency of GNE is zero. We finally discuss means by which zero worst case efficiency can be remedied.

cs.GT↗