61 research outputs found
Cores of Cooperative Games in Information Theory
Cores of cooperative games are ubiquitous in information theory, and arise
most frequently in the characterization of fundamental limits in various
scenarios involving multiple users. Examples include classical settings in
network information theory such as Slepian-Wolf source coding and multiple
access channels, classical settings in statistics such as robust hypothesis
testing, and new settings at the intersection of networking and statistics such
as distributed estimation problems for sensor networks. Cooperative game theory
allows one to understand aspects of all of these problems from a fresh and
unifying perspective that treats users as players in a game, sometimes leading
to new insights. At the heart of these analyses are fundamental dualities that
have been long studied in the context of cooperative games; for information
theoretic purposes, these are dualities between information inequalities on the
one hand and properties of rate, capacity or other resource allocation regions
on the other.Comment: 12 pages, published at
http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP
Journal on Wireless Communications and Networking, Special Issue on "Theory
and Applications in Multiuser/Multiterminal Communications", April 200
Submodularity and Its Applications in Wireless Communications
This monograph studies the submodularity in wireless
communications and how to use it to enhance or improve the design
of the optimization algorithms. The work is done in three
different systems.
In a cross-layer adaptive modulation problem, we prove the
submodularity of the dynamic programming (DP), which contributes
to the monotonicity of the optimal transmission policy. The
monotonicity is utilized in a policy iteration algorithm to
relieve the curse of dimensionality of DP. In addition, we show
that the monotonic optimal policy can be determined by a
multivariate minimization problem, which can be solved by a
discrete simultaneous perturbation stochastic approximation
(DSPSA) algorithm. We show that the DSPSA is able to converge to
the optimal policy in real time.
For the adaptive modulation problem in a network-coded two-way
relay channel, a two-player game model is proposed. We prove the
supermodularity of this game, which ensures the existence of pure
strategy Nash equilibria (PSNEs). We apply the Cournot
tatonnement and show that it converges to the extremal, the
largest and smallest, PSNEs within a finite number of iterations.
We derive the sufficient conditions for the extremal PSNEs to be
symmetric and monotonic in the channel signal-to-noise (SNR)
ratio.
Based on the submodularity of the entropy function, we study the
communication for omniscience (CO) problem: how to let all users
obtain all the information in a multiple random source via
communications. In particular, we consider the minimum sum-rate
problem: how to attain omniscience by the minimum total number of
communications. The results cover both asymptotic and
non-asymptotic models where the transmission rates are real and
integral, respectively. We reveal the submodularity of the
minimum sum-rate problem and propose polynomial time algorithms
for solving it. We discuss the significance and applications of
the fundamental partition, the one that gives rise to the minimum
sum-rate in the asymptotic model. We also show how to achieve the
omniscience in a successive manner
The Green Choice: Learning and Influencing Human Decisions on Shared Roads
Autonomous vehicles have the potential to increase the capacity of roads via
platooning, even when human drivers and autonomous vehicles share roads.
However, when users of a road network choose their routes selfishly, the
resulting traffic configuration may be very inefficient. Because of this, we
consider how to influence human decisions so as to decrease congestion on these
roads. We consider a network of parallel roads with two modes of
transportation: (i) human drivers who will choose the quickest route available
to them, and (ii) ride hailing service which provides an array of autonomous
vehicle ride options, each with different prices, to users. In this work, we
seek to design these prices so that when autonomous service users choose from
these options and human drivers selfishly choose their resulting routes, road
usage is maximized and transit delay is minimized. To do so, we formalize a
model of how autonomous service users make choices between routes with
different price/delay values. Developing a preference-based algorithm to learn
the preferences of the users, and using a vehicle flow model related to the
Fundamental Diagram of Traffic, we formulate a planning optimization to
maximize a social objective and demonstrate the benefit of the proposed routing
and learning scheme.Comment: Submitted to CDC 201
A system-theoretic approach to multi-agent models
A system-theoretic model for cooperative settings is presented that unifies and ex-
tends the models of classical cooperative games and coalition formation processes and
their generalizations. The model is based on the notions of system, state and transi-
tion graph. The latter describes changes of a system over time in terms of actions
governed by individuals or groups of individuals. Contrary to classic models, the pre-
sented model is not restricted to acyclic settings and allows the transition graph to have
cycles.
Time-dependent solutions to allocation problems are proposed and discussed. In par-
ticular, Weber’s theory of randomized values is generalized as well as the notion of
semi-values. Convergence assertions are made in some cases, and the concept of the
Cesà ro value of an allocation mechanism is introduced in order to achieve convergence
for a wide range of allocation mechanisms. Quantum allocation mechanisms are de-
fined, which are induced by quantum random walks on the transition graph and it is
shown that they satisfy certain fairness criteria. A concept for Weber sets and two dif-
ferent concepts of cores are proposed in the acyclic case, and it is shown under some
mild assumptions that both cores are subsets of the Weber set.
Moreover, the model of non-cooperative games in extensive form is generalized such
that the presented model achieves a mutual framework for cooperative and non-co-
operative games. A coherency to welfare economics is made and to each allocation
mechanism a social welfare function is proposed
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