Balancing Asymptotic and Transient Efficiency Guarantees in Set Covering Games

TL;DR

This paper investigates the transient efficiency of game-theoretic algorithms in set covering games, revealing a trade-off between short-term and long-term guarantees and proposing optimal utility designs for better transient performance.

Contribution

It characterizes the optimal utility design for transient efficiency and explores the Pareto frontier between transient and asymptotic guarantees in set covering games.

Findings

Optimal utility design maximizes transient efficiency.

Existence of a trade-off between transient and asymptotic guarantees.

Asymptotically optimal designs can perform poorly in the transient.

Abstract

Game theoretic approaches have gained traction as robust methodologies for designing distributed local algorithms that induce a desired overall system configuration in multi-agent settings. However, much of the emphasis in these approaches is on providing asymptotic guarantees on the performance of a network of agents, and there is a gap in the study of efficiency guarantees along transients of these distributed algorithms. Therefore, in this paper, we study the transient efficiency guarantees of a natural game-theoretic algorithm in the class of set covering games, which have been used to model a variety of applications. Our main results characterize the optimal utility design that maximizes the guaranteed efficiency along the transient of the natural dynamics. Furthermore, we characterize the Pareto-optimal frontier with regards to guaranteed efficiency in the transient and the asymptote under a class of game-theoretic designs. Surprisingly, we show that there exists an extreme trade-off between the long-term and short-term guarantees in that an asymptotically optimal game-theoretic design can perform arbitrarily bad in the transient.