Roberto Cominetti

On the Price of Anarchy of Highly Congested Nonatomic Network Games

We consider nonatomic network games with one source and one destination. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we show that, under suitable conditions, the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case. The counterexamples occur in very simple parallel graphs.

Sharp convergence rates for averaged nonexpansive maps

We establish sharp estimates for the convergence rate of the Kranosel’skiĭ–Mann fixed point iteration in general normed spaces, and we use them to show that the optimal constant of asymptotic regularity is exactly

Price of Anarchy for Highly Congested Routing Games in Parallel Networks

1/sqrt pi

Long Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

1/π. To this end we consider a nested family of optimal transport problems that provide a recursive bound for the distance between the iterates. We show that these bounds are tight by building a nonexpansive map T: [0, 1]N → [0, 1]N that attains them with equality, settling a conjecture by Baillon and Bruck. The recursive bounds are in turn reinterpreted as absorption probabilities for an underlying Markov chain which is used to establish the tightness of the constant

The common-line problem in congested transit networks

1/sqrt pi

The Buck-Passing Game.

1/π.