Optimal Utility Design of Greedy Algorithms in Resource Allocation Games

TL;DR

This paper investigates how to design agent utility functions in resource-allocation games to optimize short-term system performance, revealing that transient guarantees can be nearly as good as long-term ones and exploring trade-offs in utility design.

Contribution

It introduces a method for designing agent utilities to achieve near-optimal transient efficiency in resource-allocation games, bridging the gap between short-term and long-term performance.

Findings

Transient performance guarantees are close to asymptotic guarantees.

Utility design can balance between transient and asymptotic efficiency.

Trade-offs exist when optimizing for both short-term and long-term outcomes.

Abstract

Designing distributed algorithms for multi-agent problems is vital for many emerging application domains, and game-theoretic approaches are emerging as a useful paradigm to design such algorithms. However, much of the emphasis of the game-theoretic approach is on the study of equilibrium behavior, whereas transient behavior is often less explored. Therefore, in this paper we study the transient efficiency guarantees of best response processes in the context of resource-allocation games, which are used to model a variety of engineering applications. Specifically, the main focus of the paper is on designing utility functions of agents to induce optimal short-term system-level behavior under a best-response process. Interestingly, the resulting transient performance guarantees are relatively close to the optimal asymptotic performance guarantees. Furthermore, we characterize a trade-off that results when optimizing for both asymptotic and transient efficiency through various utility designs.