Uncertainty in Multi-Commodity Routing Networks: When does it help?

We study the equilibrium behavior in a multi-commodity selfish routing game with many types of uncertain users where each user over- or under-estimates their congestion costs by a multiplicative factor. Surprisingly, we find that uncertainties in different directions have qualitatively distinct impacts on equilibria. Namely, contrary to the usual notion that uncertainty increases inefficiencies, network congestion actually decreases when users over-estimate their costs. On the other hand, under-estimation of costs leads to increased congestion. We apply these results to urban transportation networks, where drivers have different estimates about the cost of congestion. In light of the dynamic pricing policies aimed at tackling congestion, our results indicate that users' perception of these prices can significantly impact the policy's efficacy, and "caution in the face of uncertainty" leads to favorable network conditions.Comment: Currently under revie

Information Design in Large Anonymous Games

We consider anonymous Bayesian cost games with a large number of players, i.e., games where each player aims at minimizing a cost function that depends on the action chosen by the player, the distribution of the other players' actions and an unknown parameter. We study the nonatomic limit versions of these games. In particular, we introduce the concepts of correlated and Bayes correlated Wardrop equilibria, which extend the concepts of correlated and Bayes correlated equilibria to nonatomic games. We prove that (Bayes) correlated Wardrop equilibria are indeed limits of action flow distributions induced by (Bayes) correlated equilibria of the game with a large finite set of small players. For nonatomic games with complete information admitting a convex potential, we show that the set of correlated Wardrop equilibria is the set of probability distributions over Wardrop equilibria. Then, we study how to implement optimal Bayes correlated Wardrop equilibria and show that in games with a convex potential, every Bayes correlated Wardrop equilibrium can be fully implemented.Comment: 53 page

Information Design for Congested Social Services: Optimal Need-Based Persuasion

We study the effectiveness of information design in reducing congestion in social services catering to users with varied levels of need. In the absence of price discrimination and centralized admission, the provider relies on sharing information about wait times to improve welfare. We consider a stylized model with heterogeneous users who differ in their private outside options: low-need users have an acceptable outside option to the social service, whereas high-need users have no viable outside option. Upon arrival, a user decides to wait for the service by joining an unobservable first-come-first-serve queue, or leave and seek her outside option. To reduce congestion and improve social outcomes, the service provider seeks to persuade more low-need users to avail their outside option, and thus better serve high-need users. We characterize the Pareto-optimal signaling mechanisms and compare their welfare outcomes against several benchmarks. We show that if either type is the overwhelming majority of the population, information design does not provide improvement over sharing full information or no information. On the other hand, when the population is a mixture of the two types, information design not only Pareto dominates full-information and no-information mechanisms, in some regimes it also achieves the same welfare as the "first-best", i.e., the Pareto-optimal centralized admission policy with knowledge of users' types.Comment: Accepted for publication in the 21st ACM Conference on Economics and Computation (EC'20). 40 pages, 6 figure

Optimal information in Bayesian routing games

We study optimal information provision in transportation networks when users are strategic and the network state is uncertain. An omniscient planner observes the network state and discloses information to the users with the goal of minimizing the expected travel time at the user equilibrium. Public signal policies, including full-information disclosure, are known to be inefficient in achieving optimality. For this reason, we focus on private signals and restrict without loss of generality the analysis to signals that coincide with path recommendations that satisfy obedience constraints, namely users have no incentive in deviating from the received recommendation according to their posterior belief. We first formulate the general problem and analyze its properties for arbitrary network topologies and delay functions. Then, we consider the case of two parallel links with affine delay functions, and provide sufficient conditions under which optimality can be achieved by information design. Interestingly, we observe that the system benefits from uncertainty, namely it is easier for the planner to achieve optimality when the variance of the uncertain parameters is large. We then provide an example where optimality can be achieved even if the sufficient conditions for optimality are not met.Comment: 8 pages, 3 figures. Full version of accepted paper for the 2023 62th IEEE Conference on Decision and Control (CDC