Cooperation Under Network-Constrained Communication
Tommy Mordo, Omer Madmon, Moshe Tennenholtz
TL;DR
This work addresses cooperation in distributed games where communication is constrained by a network. By extending the Monderer–Tennenholtz framework to network-delayed settings, it derives a sufficient condition for cooperative equilibrium that depends on the number of locations $n$ and the network diameter $\tau$, and analyzes regimes from instantaneous to proportional delays. The key result, the bound $b \le c + (c-a)\frac{(n-\tau)(n-\tau-1)}{(2n-\tau)(\tau+1)}$, shows how delays shrink the shadow of the future and can undermine cooperation, with scale-free networks mitigating this effect via short path lengths. The findings offer design guidance for multi-agent protocols and network topologies that sustain cooperation in distributed, latency-prone environments.
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.