Problem
Research questions and friction points this paper is trying to address.
network formation
Katz centrality
resource allocation
strategic game
Nash equilibrium
A Network Formation Game for Katz Centrality Maximization: A Resource Allocation Perspective
🤖 AI Summary
This study addresses how strategic agents allocate limited resources to weight their outgoing edges under topological constraints in order to maximize their own Katz centrality. The problem is formulated for the first time as a resource-constrained network formation game. Through Nash equilibrium analysis, sequential best-response dynamics (BRD), and graph-theoretic arguments, the authors establish that BRD converges to an equilibrium under mild assumptions. In complete graphs, equilibrium centrality is shown to be proportional to individual budgets, while in general graphs with self-loops, equilibrium networks exhibit a hierarchical structure. These theoretical findings are corroborated by simulations, revealing quantitative relationships between budget allocation and centrality as well as structural regularities in emergent network formation.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
network formation game
Katz centrality
resource allocation
Nash equilibrium
best-response dynamics
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