331 research outputs found
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
Emergence of Equilibria from Individual Strategies in Online Content Diffusion
Social scientists have observed that human behavior in society can often be
modeled as corresponding to a threshold type policy. A new behavior would
propagate by a procedure in which an individual adopts the new behavior if the
fraction of his neighbors or friends having adopted the new behavior exceeds
some threshold. In this paper we study the question of whether the emergence of
threshold policies may be modeled as a result of some rational process which
would describe the behavior of non-cooperative rational members of some social
network. We focus on situations in which individuals take the decision whether
to access or not some content, based on the number of views that the content
has. Our analysis aims at understanding not only the behavior of individuals,
but also the way in which information about the quality of a given content can
be deduced from view counts when only part of the viewers that access the
content are informed about its quality. In this paper we present a game
formulation for the behavior of individuals using a meanfield model: the number
of individuals is approximated by a continuum of atomless players and for which
the Wardrop equilibrium is the solution concept. We derive conditions on the
problem's parameters that result indeed in the emergence of threshold
equilibria policies. But we also identify some parameters in which other
structures are obtained for the equilibrium behavior of individuals
A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks
In this paper we propose a LWR-like model for traffic flow on networks which
allows one to track several groups of drivers, each of them being characterized
only by their destination in the network. The path actually followed to reach
the destination is not assigned a priori, and can be chosen by the drivers
during the journey, taking decisions at junctions.
The model is then used to describe three possible behaviors of drivers,
associated to three different ways to solve the route choice problem: 1.
Drivers ignore the presence of the other vehicles; 2. Drivers react to the
current distribution of traffic, but they do not forecast what will happen at
later times; 3. Drivers take into account the current and future distribution
of vehicles. Notice that, in the latter case, we enter the field of
differential games, and, if a solution exists, it likely represents a global
equilibrium among drivers.
Numerical simulations highlight the differences between the three behaviors
and suggest the existence of multiple Wardrop equilibria
Unilateral Altruism in Network Routing Games with Atomic Players
We study a routing game in which one of the players unilaterally acts
altruistically by taking into consideration the latency cost of other players
as well as his own. By not playing selfishly, a player can not only improve the
other players' equilibrium utility but also improve his own equilibrium
utility. To quantify the effect, we define a metric called the Value of
Unilateral Altruism (VoU) to be the ratio of the equilibrium utility of the
altruistic user to the equilibrium utility he would have received in Nash
equilibrium if he were selfish. We show by example that the VoU, in a game with
nonlinear latency functions and atomic players, can be arbitrarily large. Since
the Nash equilibrium social welfare of this example is arbitrarily far from
social optimum, this example also has a Price of Anarchy (PoA) that is
unbounded. The example is driven by there being a small number of players since
the same example with non-atomic players yields a Nash equilibrium that is
fully efficient
Nash and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
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