1,626 research outputs found
Learning an Unknown Network State in Routing Games
We study learning dynamics induced by myopic travelers who repeatedly play a
routing game on a transportation network with an unknown state. The state
impacts cost functions of one or more edges of the network. In each stage,
travelers choose their routes according to Wardrop equilibrium based on public
belief of the state. This belief is broadcast by an information system that
observes the edge loads and realized costs on the used edges, and performs a
Bayesian update to the prior stage's belief. We show that the sequence of
public beliefs and edge load vectors generated by the repeated play converge
almost surely. In any rest point, travelers have no incentive to deviate from
the chosen routes and accurately learn the true costs on the used edges.
However, the costs on edges that are not used may not be accurately learned.
Thus, learning can be incomplete in that the edge load vectors at rest point
and complete information equilibrium can be different. We present some
conditions for complete learning and illustrate situations when such an outcome
is not guaranteed
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
Value of Information in Bayesian Routing Games
We study a routing game in an environment with multiple heterogeneous
information systems and an uncertain state that affects edge costs of a
congested network. Each information system sends a noisy signal about the state
to its subscribed traveler population. Travelers make route choices based on
their private beliefs about the state and other populations' signals. The
question then arises, "How does the presence of asymmetric and incomplete
information affect the travelers' equilibrium route choices and costs?'' We
develop a systematic approach to characterize the equilibrium structure, and
determine the effect of population sizes on the relative value of information
(i.e. difference in expected traveler costs) between any two populations. This
effect can be evaluated using a population-specific size threshold. One
population enjoys a strictly positive value of information in comparison to the
other if and only if its size is below the corresponding threshold. We also
consider the situation when travelers may choose an information system based on
its value, and characterize the set of equilibrium adoption rates delineating
the sizes of subscribed traveler populations. The resulting routing strategies
are such that all travelers face an identical expected cost and no traveler has
the incentive to change her subscription
- …