A Sensitivity Analysis of the Price of Anarchy in Nonatomic Congestion Games

Abstract

The price of anarchy (PoA) is a standard measure to quantify the inefficiency of equilibria in nonatomic congestion games. Most publications have focused on worst-case bounds for the PoA. Only a few have analyzed the sensitivity of the PoA against changes of the demands or cost functions, although that is crucial for empirical computations of the PoA. We analyze the sensitivity of the PoA with respect to (w.r.t.) simultaneous changes of demands and cost functions. The key to this analysis is a metric for the distance between two games that defines a topological metric space consisting of all games with the same combinatorial structure. The PoA is then a locally pointwise Hölder continuous function of the demands and cost functions, and we analyze the Hölder exponent for different classes of cost functions. We also apply our approach to the convergence analysis of the PoA when the total demand tends to zero or infinity. Our results further develop the recent seminal work on the sensitivity of the PoA w.r.t. changes of only the demands under special conditions. Funding: This work was supported by the Science Foundation of Anhui Science and Technology Department [Grant 1908085QF262]; Science Foundation of the Anhui Education Department [Grant KJ2019A0834]; National Science Foundation of China [Grants 61906062, 72271085]; Talent Foundation of Hefei University [Grant 1819RC29].