Convergence rates of random-order best-response dynamics in public good games on networks

TL;DR

This paper analyzes how quickly random-order best-response dynamics converge in networked public good games, revealing structural factors that influence slow convergence and identifying phenomena causing delays.

Contribution

It provides a formal analysis of convergence rates in network games with linear best responses, highlighting structural graph properties affecting dynamics.

Findings

Certain network structures lead to slower convergence.

Inactive nodes can delay overall convergence.

Graph spectral properties are insufficient to predict convergence speed.

Abstract

We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow convergence. One of the key such phenomena is convergence to stable strategy profiles in parts of the network neighboring sets of nodes which remain inactive until the dynamics is close to converging and then switch to activity, initiating convergence to profiles with a new set of active agents and possibly leading to another iteration of such behavior. We identify structural properties of graphs which make such phenomena more likely. These properties go beyond the spectrum of a graph, which we demonstrate analyzing convergence rates on co-spectral mates.