1,705 research outputs found
Constrained Cost-Coupled Stochastic Games with Independent State Processes
We consider a non-cooperative constrained stochastic games with N players
with the following special structure. With each player there is an associated
controlled Markov chain. The transition probabilities of the i-th Markov chain
depend only on the state and actions of controller i. The information structure
that we consider is such that each player knows the state of its own MDP and
its own actions. It does not know the states of, and the actions taken by other
players. Finally, each player wishes to minimize a time-average cost function,
and has constraints over other time-avrage cost functions. Both the cost that
is minimized as well as those defining the constraints depend on the state and
actions of all players. We study in this paper the existence of a Nash
equilirium. Examples in power control in wireless communications are given.Comment: 7 pages, submitted in september 2006 to Operations Research Letter
Player aggregation in the traveling inspector model
We consider a model of dynamic inspection/surveillance of
a number of facilities in different geographical locations. The inspector in
this process travels from one facility to another and performs an
inspection at each facility he visits. His aim is to devise an inspection/
travel schedule which minimizes the losses to society (or to his employer)
resulting both from undetected violations of the regulations and from the
costs of the policing operation. This model is formulated as a non-cooperative,
single-controller, stochastic game. The existence of stationary Nash
equilibria is established as a consequence of aggregating all the inspectees
into a single “aggregated inspectee”. It is shown that such player
aggregation causes no loss of generality under very mild assumptions. A
notion of an “optimal Nash equilibrium” for the inspector is introduced
and proven to be well-defined in this context. The issue of the inspector’s
power to “enforce” such an equilibrium is also discussed
Modeling and Control of Rare Segments in BitTorrent with Epidemic Dynamics
Despite its existing incentives for leecher cooperation, BitTorrent file
sharing fundamentally relies on the presence of seeder peers. Seeder peers
essentially operate outside the BitTorrent incentives, with two caveats: slow
downlinks lead to increased numbers of "temporary" seeders (who left their
console, but will terminate their seeder role when they return), and the
copyright liability boon that file segmentation offers for permanent seeders.
Using a simple epidemic model for a two-segment BitTorrent swarm, we focus on
the BitTorrent rule to disseminate the (locally) rarest segments first. With
our model, we show that the rarest-segment first rule minimizes transition time
to seeder (complete file acquisition) and equalizes the segment populations in
steady-state. We discuss how alternative dissemination rules may {\em
beneficially increase} file acquisition times causing leechers to remain in the
system longer (particularly as temporary seeders). The result is that leechers
are further enticed to cooperate. This eliminates the threat of extinction of
rare segments which is prevented by the needed presence of permanent seeders.
Our model allows us to study the corresponding trade-offs between performance
improvement, load on permanent seeders, and content availability, which we
leave for future work. Finally, interpreting the two-segment model as one
involving a rare segment and a "lumped" segment representing the rest, we study
a model that jointly considers control of rare segments and different uplinks
causing "choking," where high-uplink peers will not engage in certain
transactions with low-uplink peers.Comment: 18 pages, 6 figures, A shorter version of this paper that did not
include the N-segment lumped model was presented in May 2011 at IEEE ICC,
Kyot
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