Resource-Aware Protocols for Network Cost-Sharing Games

TL;DR

This paper investigates resource-aware decentralized protocols for network cost-sharing games, achieving near-optimal price of anarchy bounds in various network structures and cost function settings, with some fundamental limitations identified.

Contribution

It introduces new cost-sharing protocols with improved PoA bounds for concave and convex cost functions in specific network classes, and establishes lower bounds on PoA performance.

Findings

PoA of 2+ε for symmetric DAG games with concave costs

PoA of 1+ε for series-parallel graphs with concave costs

Lower bound of Ω(√n) for multicast games without overcharging

Abstract

We study the extent to which decentralized cost-sharing protocols can achieve good price of anarchy (PoA) bounds in network cost-sharing games with $n$ agents. We focus on the model of resource-aware protocols, where the designer has prior access to the network structure and can also increase the total cost of an edge(overcharging), and we study classes of games with concave or convex cost functions. We first consider concave cost functions and our main result is a cost-sharing protocol for symmetric games on directed acyclic graphs that achieves a PoA of $2+\varepsilon$ for some arbitrary small positive $\varepsilon$, which improves to $1+\varepsilon$ for games with at least two players. We also achieve a PoA of 1 for series-parallel graphs and show that no protocol can achieve a PoA better than $\Omega(\sqrt{n})$ for multicast games. We then also consider convex cost functions and prove analogous results for series-parallel networks and multicast games, as well as a lower bound of $\Omega(n)$ for the PoA on directed acyclic graphs without the use of overcharging.