Resolving Braess’s Paradox in Random Networks

Abstract

Braess’s paradox states that removing a part of a network may improve the players’ latency at equilibrium. In this work, we study the approximability of the best subnetwork problem for the class of random $\mathcal{G}_{n,p}$ instances proven prone to Braess’s paradox by (Roughgarden and Valiant, RSA 2010) and (Chung and Young, WINE 2010). Our main contribution is a polynomial-time approximation-preserving reduction of the best subnetwork problem for such instances to the corresponding problem in a simplified network where all neighbors of s and t are directly connected by 0 latency edges. Building on this, we obtain an approximation scheme that for any constant ε > 0 and with high probability, computes a subnetwork and an ε-Nash flow with maximum latency at most (1 + ε)L ^∗ + ε, where L ^∗ is the equilibrium latency of the best subnetwork. Our approximation scheme runs in polynomial time if the random network has average degree O(poly(ln n)) and the traffic rate is O(poly(ln ln n)), and in quasipolynomial time for average degrees up to o(n) and traffic rates of O(poly(ln n)).

This research was supported by the project Algorithmic Game Theory, co-financed by the European Union (European Social Fund - ESF) and Greek national funds, through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES, investing in knowledge society through the European Social Fund, by the ERC project RIMACO, and by the EU FP7/2007-13 (DG INFSO G4-ICT for Transport) under Grant Agreement no. 288094 (Project eCompass).