Multiple interaction strategies in networks related to graph spectra and dominant sets

Abstract

An interaction network is a collection of agents with pairwise connections described by an graph. Our objective is to maximize the payoff of the agents simultaneously. In the classical strategic complements or substitutes setup, the objective function has a linear and a quadratic part, and maximized under linear constraints.

To address this task, we use quadratic objective functions on linear or quadratic constraints. We will show how existing results of combinatorial graph theory and spectral clustering can be used to solve the optimization problems, where solutions are closely related to dominant sets or spectral clusters. Our primary focus is on the graph and show how certain model parameters can be built into the edge-weight matrix to get a new objective, thus modifying the interactions between the agents.