4,501 research outputs found
Dynamic Power Allocation Games in Parallel Multiple Access Channels
We analyze the distributed power allocation problem in parallel multiple
access channels (MAC) by studying an associated non-cooperative game which
admits an exact potential. Even though games of this type have been the subject
of considerable study in the literature, we find that the sufficient conditions
which ensure uniqueness of Nash equilibrium points typically do not hold in
this context. Nonetheless, we show that the parallel MAC game admits a unique
equilibrium almost surely, thus establishing an important class of
counterexamples where these sufficient conditions are not necessary.
Furthermore, if the network's users employ a distributed learning scheme based
on the replicator dynamics, we show that they converge to equilibrium from
almost any initial condition, even though users only have local information at
their disposal.Comment: 18 pages, 4 figures, submitted to Valuetools '1
Distributed Learning Policies for Power Allocation in Multiple Access Channels
We analyze the problem of distributed power allocation for orthogonal
multiple access channels by considering a continuous non-cooperative game whose
strategy space represents the users' distribution of transmission power over
the network's channels. When the channels are static, we find that this game
admits an exact potential function and this allows us to show that it has a
unique equilibrium almost surely. Furthermore, using the game's potential
property, we derive a modified version of the replicator dynamics of
evolutionary game theory which applies to this continuous game, and we show
that if the network's users employ a distributed learning scheme based on these
dynamics, then they converge to equilibrium exponentially quickly. On the other
hand, a major challenge occurs if the channels do not remain static but
fluctuate stochastically over time, following a stationary ergodic process. In
that case, the associated ergodic game still admits a unique equilibrium, but
the learning analysis becomes much more complicated because the replicator
dynamics are no longer deterministic. Nonetheless, by employing results from
the theory of stochastic approximation, we show that users still converge to
the game's unique equilibrium.
Our analysis hinges on a game-theoretical result which is of independent
interest: in finite player games which admit a (possibly nonlinear) convex
potential function, the replicator dynamics (suitably modified to account for
nonlinear payoffs) converge to an eps-neighborhood of an equilibrium at time of
order O(log(1/eps)).Comment: 11 pages, 8 figures. Revised manuscript structure and added more
material and figures for the case of stochastically fluctuating channels.
This version will appear in the IEEE Journal on Selected Areas in
Communication, Special Issue on Game Theory in Wireless Communication
Satisfaction Equilibrium: A General Framework for QoS Provisioning in Self-Configuring Networks
This paper is concerned with the concept of equilibrium and quality of
service (QoS) provisioning in self-configuring wireless networks with
non-cooperative radio devices (RD). In contrast with the Nash equilibrium (NE),
where RDs are interested in selfishly maximizing its QoS, we present a concept
of equilibrium, named satisfaction equilibrium (SE), where RDs are interested
only in guaranteing a minimum QoS. We provide the conditions for the existence
and the uniqueness of the SE. Later, in order to provide an equilibrium
selection framework for the SE, we introduce the concept of effort or cost of
satisfaction, for instance, in terms of transmit power levels, constellation
sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined.
At the ESE, transmitters satisfy their minimum QoS incurring in the lowest
effort. We prove that contrary to the (generalized) NE, at least one ESE always
exists whenever the network is able to simultaneously support the individual
QoS requests. Finally, we provide a fully decentralized algorithm to allow
self-configuring networks to converge to one of the SE relying only on local
information.Comment: Accepted for publication in Globecom 201
An evolutionary advantage for extravagant honesty
A game-theoretic model of handicap signalling over a pair of signalling channels is introduced in order to determine when one channel has an evolutionary advantage over the other. The stability conditions for honest handicap signalling are presented for a single channel and are shown to conform with the results of prior handicap signalling models. Evolutionary simulations are then used to show that, for a two-channel system in which honest signalling is possible on both channels, the channel featuring larger advertisements at equilibrium is favoured by evolution. This result helps to address a significant tension in the handicap principle literature. While the original theory was motivated by the prevalence of extravagant natural signalling, contemporary models have demonstrated that it is the cost associated with deception that stabilises honesty, and that the honest signals exhibited at equilibrium need not be extravagant at all. The current model suggests that while extravagant and wasteful signals are not required to ensure a signalling system's evolutionary stability, extravagant signalling systems may enjoy an advantage in terms of evolutionary attainability
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