arXiv subjects

Nirabhra Mandal

Publications and source records attributed to Nirabhra Mandal.

8 recordsLinked to original sources

arXiv2026

Distributionally Robust Nash Equilibrium Seeking with Partial Observations and Distributed Communication

In this work, we study stochastic one-shot games where agents' utilities depend on the collective strategy profiles of other agents as well as on some well-behaved randomness. While each decision-maker is agnostic to the random variable's underlying distribution, they have access to finitely many i.i.d. samples generated from it. We consider two cases: one where samples are shared; and another, more special one, where samples are individually accessible. To hedge against the unknown uncertainty, each agent plays a distributionally robust game and aims to maximize the worst-case expected utility over a Wasserstein ball around the sample average distribution. In this setting, we provide conditions under which the game has a non-empty set of distributionally robust Nash equilibria (DRoNE) and then characterize the closeness of the DRoNE set to the Nash equilibria (NE) of the associated stochastic game. We then propose an inertial, supported, better response, ascending supergradient dynamics ISBRAG that seeks the DRoNE's when the distributionally robust game possesses what we term as amicable supergradients. This forms the basis of a distributed version (d-ISBRAG) where agents estimate others' strategies by means of a dynamic consensus subroutine over a directed communication network. While initially the distributed algorithm works in the case where agents have individual samples, we later extend this to the case of shared observations under certain simplifying assumptions. This involves analyzing a tractable reformulation of the distributionally robust optimization problem and solving it in a distributed manner to compute the required supergradients. Simulations illustrate our results.

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arXiv2025

Behaviorally Heterogeneous Multi-Agent Exploration Using Distributed Task Allocation

We study a problem of multi-agent exploration with behaviorally heterogeneous robots. Each robot maps its surroundings using SLAM and identifies a set of areas of interest (AoIs) or frontiers that are the most informative to explore next. The robots assess the utility of going to a frontier using Behavioral Entropy (BE) and then determine which frontier to go to via a distributed task assignment scheme. We convert the task assignment problem into a non-cooperative game and use a distributed algorithm (d-PBRAG) to converge to the Nash equilibrium (which we show is the optimal task allocation solution). For unknown utility cases, we provide robust bounds using approximate rewards. We test our algorithm (which has less communication cost and fast convergence) in simulation, where we explore the effect of sensing radii, sensing accuracy, and heterogeneity among robotic teams with respect to the time taken to complete exploration and path traveled. We observe that having a team of agents with heterogeneous behaviors is beneficial.

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arXiv2025

Multi-Topic Projected Opinion Dynamics for Resource Allocation

We propose a model of opinion formation on resource allocation among multiple topics by multiple agents, who are subject to hard budget constraints. We define a utility function for each agent and then derive a projected dynamical system model of opinion evolution assuming that each agent myopically seeks to maximize its utility subject to its constraints. Inter-agent coupling arises from an undirected social network, while inter-topic coupling arises from resource constraints. We show that opinions always converge to the equilibrium set. For special networks with very weak antagonistic relations, the opinions converge to a unique equilibrium point. We further show that the underlying opinion formation game is a potential game. We relate the equilibria of the dynamics and the Nash equilibria of the game and characterize the unique Nash equilibrium for networks with no antagonistic relations. Finally, simulations illustrate our findings.

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arXiv2024

Opinion Dynamics for Utility Maximizing Agents: Exploring the Impact of the Resource Penalty

We propose a continuous-time nonlinear model of opinion dynamics with utility-maximizing agents connected via a social influence network. A distinguishing feature of the proposed model is the inclusion of an opinion-dependent resource-penalty term in the utilities, which limits the agents from holding opinions of large magnitude. This model is applicable in scenarios where the opinions pertain to the usage of resources, such as money, time, computational resources etc. Each agent myopically seeks to maximize its utility by revising its opinion in the gradient ascent direction of its utility function, thus leading to the proposed opinion dynamics. We show that, for any arbitrary social influence network, opinions are ultimately bounded. For networks with weak antagonistic relations, we show that there exists a globally exponentially stable equilibrium using contraction theory. We establish conditions for the existence of consensus equilibrium and analyze the relative dominance of the agents at consensus. We also conduct a game-theoretic analysis of the underlying opinion formation game, including on Nash equilibria and on prices of anarchy in terms of satisfaction ratios. Additionally, we also investigate the oscillatory behavior of opinions in a two-agent scenario. Finally, simulations illustrate our findings.

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arXiv2023

Distributed Task Allocation for Self-Interested Agents with Partially Unknown Rewards

This paper provides a novel solution to a task allocation problem, by which a group of agents decides on the assignment of a discrete set of tasks in a distributed manner. In this setting, heterogeneous agents have individual preferences and associated rewards for doing each task; however, these rewards are only known asymptotically. We start by formulating the assignment problem by means of a combinatorial partition game for known rewards, with no constraints on number of tasks per agent. We relax this into a weight game, which together with the former, are shown to contain the optimal task allocation in the corresponding set of Nash Equilibria (NE). We then propose a projected, best-response, ascending gradient dynamics (PBRAG) that converges to a NE in finite time. This forms the basis of a distributed online version that can deal with a converging sequence of rewards by means of an agreement sub-routine. We present simulations that support our results

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arXiv2023

Control of Discrete-Time LTI Systems using Stochastic Ensemble Systems

In this paper, we study the control properties of a new class of stochastic ensemble systems that consists of families of random variables. These random variables provide an increasingly good approximation of an unknown discrete, linear-time invariant (DLTI) system, and can be obtained by a standard, data-driven procedure. Our first result relates the reachability properties of the stochastic ensemble system with that of the limiting DLTI system. We then provide a method to combine the control inputs obtained from the stochastic ensemble systems to compute a control input for the DLTI system. Later, we deal with a particular kind of stochastic ensemble system generated from realizing Bernoulli random variables. For this, we characterize the variance of the computed state and control. We also do the same for a situation where the data is updated sequentially in a streaming fashion. We illustrate the results numerically in various simulation examples.

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arXiv2020

Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part I: Modeling and Convergence Analysis

In this work, we consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is stratified and hence agents opting for the same choice may not get the same payoff. In particular, we assume payoff functions that model diminishing returns, that is, agents in "newer" strata of a node receive a smaller payoff compared to "older" strata. In this first part of two-part work, we model the population dynamics under three choice revision policies, each having varying levels of coordination -- i. no coordination and the agents are selfish, ii. coordination among agents in each node and iii. coordination across the entire population. To model the case with selfish agents, we generalize the Smith dynamics to our setting, where we have a stratified population and network constraints. To model nodal coordination, we allow the fraction of population in a node, as a whole, to take the `best response' to the state of the population in the node's neighborhood. For the case of population-wide coordination, we explore a dynamics where the population evolves according to centralized gradient ascent of the social utility, though constrained by the network. In each case, we show that the dynamics has existence and uniqueness of solutions and also show that the solutions from any initial condition asymptotically converge to the set of Nash equilibria.

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arXiv2020

Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part II: Steady State Analysis

In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on a maximum payoff density parameter of each node under which there exists a unique Nash equilibrium. We then utilize positive correlation properties of the dynamics to reduce the flow graph in order to provide an upper bound on the steady state social utility. Finally we extend the idea behind the sufficient condition for the existence of a unique Nash equilibrium to partition the graph appropriately in order to provide a lower bound on the steady state social utility. We also illustrate interesting cases as well as our results using simulations.

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