Best Response Sequences and Tradeoffs in Submodular Resource Allocation Games

TL;DR

This paper investigates the short-term efficiency of best response dynamics in submodular resource allocation games, revealing that transient performance can be nearly as good as long-term guarantees and exploring trade-offs in utility design.

Contribution

It provides the first analysis of transient efficiency guarantees in submodular resource allocation games, highlighting near-optimal short-term behavior and trade-offs with long-term performance.

Findings

Transient guarantees are close to asymptotic guarantees.

Optimal short-term behavior can be characterized mathematically.

Trade-offs exist between transient and long-term efficiency.

Abstract

Deriving competitive, distributed solutions to multi-agent problems is crucial for many developing application domains; Game theory has emerged as a useful framework to design such algorithms. However, much of the attention within this framework is on the study of equilibrium behavior, whereas transient behavior is often ignored. Therefore, in this paper we study the transient efficiency guarantees of best response processes in the context of submodular resource allocation games, which find application in various engineering contexts. Specifically the main focus of this paper is on characterizing the optimal short-term system-level behavior under the best-response process. Interestingly, the resulting transient performance guarantees are relatively close to the optimal asymptotic performance guarantees. Furthermore, we characterize the trade-offs that result when optimizing for both asymptotic and transient efficiency through various utility designs.