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

A team of researchers has published a novel game theory model that explains how AI agents or strategic entities form networks to maximize their influence. In the paper "A Network Formation Game for Katz Centrality Maximization: A Resource Allocation Perspective," authors Balaji R, Prashil Wankhede, and Pavankumar Tallapragada frame network formation as a strategic game. Each agent has a constrained budget of resources to allocate for forming weighted connections (edges) with others in a predefined underlying topology. The agent's utility or payoff is defined by its Katz centrality, a well-known network measure that quantifies influence by considering both direct and indirect connections through the network.

The researchers analyze the Nash equilibria of this game—states where no agent can unilaterally improve its influence. They demonstrate that a simple, sequential best-response dynamics (BRD) process, where agents iteratively adjust their connections, reliably converges to these equilibrium networks under mild assumptions. A key finding is that for complete underlying networks, an agent's equilibrium influence (Katz centrality) becomes directly proportional to its resource budget. For more general topologies where agents have self-loops, the equilibria naturally form hierarchical network structures, with influence concentrated according to resource allocation.

This work, submitted to the 2026 IEEE Conference on Decision and Control, moves beyond descriptive analysis to provide a prescriptive, computational framework. It formally models the trade-off agents face between investing resources to build connections and the resulting positional power within a network. The simulations included validate the theoretical findings, showing how these strategic interactions shape the emergent social or organizational structure.