Cooperation Under Network-Constrained Communication

TL;DR

This paper investigates how network topology and communication delays influence the emergence of cooperation in distributed games with local Prisoner's Dilemma interactions, providing conditions for cooperative equilibrium.

Contribution

It derives a sufficient condition for cooperation based on network diameter and locations, extending existing frameworks to delayed communication scenarios.

Findings

Cooperation depends on network diameter and number of locations.

Extreme cases of communication delay analyzed.

Scale-free networks show sub-linear growth of diameter.

Abstract

In this paper, we study cooperation in distributed games under network-constrained communication. Building on the framework of Monderer and Tennenholtz (1999), we derive a sufficient condition for cooperative equilibrium in settings where communication between agents is delayed by the underlying network topology. Each player deploys an agent at every location, and local interactions follow a Prisoner's Dilemma structure. We derive a sufficient condition that depends on the network diameter and the number of locations, and analyze extreme cases of instantaneous, delayed, and proportionally delayed communication. We also discuss the asymptotic case of scale-free communication networks, in which the network diameter grows sub-linearly in the number of locations. These insights clarify how communication latency and network design jointly determine the emergence of distributed cooperation.