Optimal transportation with traffic congestion and Wardrop equilibria

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant taking into account congestion. This leads to an optimization problem posed on a set of probability measures on a suitable paths space. We establish existence of minimizers and give a characterization. As an application, we obtain existence and variational characterization of equilibria of Wardrop type in a continuous space setting

Matroids are Immune to Braess Paradox

The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper we consider general nonatomic congestion games and give a characterization of the maximal combinatorial property of strategy spaces for which Braess paradox does not occur. In a nutshell, bases of matroids are exactly this maximal structure. We prove our characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest.Comment: 21 page

Models and applications of Optimal Transport in Economics, Traffic and Urban Planning

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with Monge-Kantorovich theory and PDEs. Then, two models for urban planning are introduced. The last section is devoted to two problems from economics and their translation in the language of optimal transport

US Highway Privatization and Heterogeneous Preferences

Abstract: We assess the welfare effects of highway privatization accounting for government’s behavior in setting the sale price, firms’ strategic behavior in setting tolls in various competitive environments, and motorists’ heterogeneous preferences for speedy and reliable travel. We conclude motorists can benefit from privatization if they are able to negotiate aggressively with a private provider to obtain tolls and service that align with their varying preferences. Surprisingly, motorists are likely to be better off negotiating with a monopolist than with duopoly providers or under public-private competition. Toll regulation may be counterproductive because it would treat motorists as homogeneous. Revised June 2009.Security Breach Costs; Financial Distress; Insurance; Resource Allocation.

Wardrop Equilibrium in Discrete-Time Selfish Routing with Time-Varying Bounded Delays

This paper presents a multi-commodity, discrete- time, distributed and non-cooperative routing algorithm, which is proved to converge to an equilibrium in the presence of heterogeneous, unknown, time-varying but bounded delays. Under mild assumptions on the latency functions which describe the cost associated to the network paths, two algorithms are proposed: the former assumes that each commodity relies only on measurements of the latencies associated to its own paths; the latter assumes that each commodity has (at least indirectly) access to the measures of the latencies of all the network paths. Both algorithms are proven to drive the system state to an invariant set which approximates and contains the Wardrop equilibrium, defined as a network state in which no traffic flow over the network paths can improve its routing unilaterally, with the latter achieving a better reconstruction of the Wardrop equilibrium. Numerical simulations show the effectiveness of the proposed approach