arXiv subjects

Prashil Wankhede

Publications and source records attributed to Prashil Wankhede.

3 recordsLinked to original sources

arXiv2026

A Network Formation Game for Katz Centrality Maximization: A Resource Allocation Perspective

In this paper, we study a network formation game in which agents seek to maximize their influence by allocating constrained resources to choose connections with other agents. In particular, we use Katz centrality to model agents' influence in the network. Allocations are restricted to neighbors in a given unweighted network encoding topological constraints. The allocations by an agent correspond to the weights of its outgoing edges. Such allocation by all agents thereby induces a network. This models a strategic-form game in which agents' utilities are given by their Katz centralities. We characterize the Nash equilibrium networks of this game and analyze their properties. We propose a sequential best-response dynamics (BRD) to model the network formation process. We show that it converges to the set of Nash equilibria under very mild assumptions. For complete underlying topologies, we show that Katz centralities are proportional to agents' budgets at Nash equilibria. For general underlying topologies in which each agent has a self-loop, we show that hierarchical networks form at Nash equilibria. Finally, simulations illustrate our findings.

cs.GT↗

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.

eess.SY↗

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.

eess.SY↗