4,071 research outputs found
Equilibria of Channel Selection Games in Parallel Multiple Access Channels
International audienceIn this paper, the parallel multiple access channel (MAC) is studied under the assumption that transmitters maximize their individual spectral efficiency by selfishly tuning their power allocation policy. Two particular scenarios are studied: (a) transmitters are allowed to use all the available channels; and (b) transmitters are constrained to use a single channel. Both scenarios are modeled by one-shot games and the corresponding sets of Nash equilibria (NE) are fully characterized under the assumption that the receiver treads the multiple access interference as noise. In both cases, the set of NE is non-empty. In the case in which transmitters use a single channel, an upper bound of the cardinality of the NE set is provided in terms of the number of transmitters and number of channels. In particular, it is shown that in fully loaded networks, the sum spectral efficiency at the NE in scenario (a) is at most equal to the sum spectral efficiency at the NE in scenario (b). A formal proof of this observation, known in general as a Braess Paradox, is provided in the case of 2 transmitters and 2 channels. In general scenarios, we conjecture that the same effect holds as long as the network is kept fully loaded, as shown by numerical examples. Moreover, the price of anarchy and the price of stability in both games is also studied. Interestingly, under certain conditions on the channel gains, Pareto optimality can be achieved at some NE if and only if the number of channels equals or exceeds the number of transmitters. Finally, simulations are presented to verify the theoretical results
On the Fictitious Play and Channel Selection Games
Considering the interaction through mutual interference of the different
radio devices, the channel selection (CS) problem in decentralized parallel
multiple access channels can be modeled by strategic-form games. Here, we show
that the CS problem is a potential game (PG) and thus the fictitious play (FP)
converges to a Nash equilibrium (NE) either in pure or mixed strategies. Using
a 2-player 2-channel game, it is shown that convergence in mixed strategies
might lead to cycles of action profiles which lead to individual spectral
efficiencies (SE) which are worse than the SE at the worst NE in mixed and pure
strategies. Finally, exploiting the fact that the CS problem is a PG and an
aggregation game, we present a method to implement FP with local information
and minimum feedback.Comment: In proc. of the IEEE Latin-American Conference on Communications
(LATINCOM), Bogota, Colombia, September, 201
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
On the Nash Equilibria in Decentralized Parallel Interference Channels
In this paper, the 2-dimensional decentralized parallel interference channel
(IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static
game. Each transmitter is assumed to be a fully rational entity with complete
information on the game, aiming to maximize its own individual spectral
efficiency by tuning its own power allocation (PA) vector. Two scenarios are
analysed. First, we consider that transmitters can split their transmit power
between both dimensions (PA game). Second, we consider that each transmitter is
limited to use only one dimension (channel selection CS game). In the first
scenario, the game might have either one or three NE in pure strategies (PS).
However, two or infinitely many NE in PS might also be observed with zero
probability. In the second scenario, there always exists either one or two NE
in PS. We show that in both games there always exists a non-zero probability of
observing more than one NE. More interestingly, using Monte-Carlo simulations,
we show that the highest and lowest network spectral efficiency at any of the
NE in the CS game are always higher than the ones in the PA.Comment: 6 pages, 4 figures, presented in ICCC Kyoto 201
A Comprehensive Survey of Potential Game Approaches to Wireless Networks
Potential games form a class of non-cooperative games where unilateral
improvement dynamics are guaranteed to converge in many practical cases. The
potential game approach has been applied to a wide range of wireless network
problems, particularly to a variety of channel assignment problems. In this
paper, the properties of potential games are introduced, and games in wireless
networks that have been proven to be potential games are comprehensively
discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on
Communications, vol. E98-B, no. 9, Sept. 201
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
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