530 research outputs found
Joint strategy fictitious play with inertia for potential games
We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion
High country river processes : a technical discussion of results from research on the Kowai River system, Springfield, Canterbury
A sub-catchment (Torlesse Stream) of the Kowai River, Canterbury, has been the site of an interdisciplinary study of the relationships between erosion and stream sedimentation (Hayward 1975). It was logical to extend the stream sediment investigation of that study (Hayward 1978) into the Kowai system proper in order to establish changes in the nature and distribution of the stream sediments with distance downstream.
The sediment sampling study, comprising Part I of Paper A in this volume, analyses the changes in size, distribution, form and rock type of the river gravels from ahead water mountain stream to the wide braided river beds of the middle reaches of the Kowai River. Part 2 of Paper A discusses the possible implications for the management that these sediment studies have for this and other similar river systems. It is believed that if thought necessary it is possible to design a river training programme to guide the river towards a more manageable pattern.
Paper B of this volume compares the results of the present river gravel survey with those from a sedimentological analysis of fluvio-glacial outwash gravels deposited several thousand years ago within the lower reaches of the Kowai system. This comparative study is used to indicate differences in the hydrologic environment prevailing at their respective times of deposition, and aids in our understanding of the processes at work in hill and high country rivers today.
Both Papers A and B relate to the Kowai River system, but the authors wish to emphasise that the findings from these studies are believed to have application to other similar gravel bed river systems
Efficient Model Learning for Human-Robot Collaborative Tasks
We present a framework for learning human user models from joint-action
demonstrations that enables the robot to compute a robust policy for a
collaborative task with a human. The learning takes place completely
automatically, without any human intervention. First, we describe the
clustering of demonstrated action sequences into different human types using an
unsupervised learning algorithm. These demonstrated sequences are also used by
the robot to learn a reward function that is representative for each type,
through the employment of an inverse reinforcement learning algorithm. The
learned model is then used as part of a Mixed Observability Markov Decision
Process formulation, wherein the human type is a partially observable variable.
With this framework, we can infer, either offline or online, the human type of
a new user that was not included in the training set, and can compute a policy
for the robot that will be aligned to the preference of this new user and will
be robust to deviations of the human actions from prior demonstrations. Finally
we validate the approach using data collected in human subject experiments, and
conduct proof-of-concept demonstrations in which a person performs a
collaborative task with a small industrial robot
Flows and Decompositions of Games: Harmonic and Potential Games
In this paper we introduce a novel flow representation for finite games in
strategic form. This representation allows us to develop a canonical direct sum
decomposition of an arbitrary game into three components, which we refer to as
the potential, harmonic and nonstrategic components. We analyze natural classes
of games that are induced by this decomposition, and in particular, focus on
games with no harmonic component and games with no potential component. We show
that the first class corresponds to the well-known potential games. We refer to
the second class of games as harmonic games, and study the structural and
equilibrium properties of this new class of games. Intuitively, the potential
component of a game captures interactions that can equivalently be represented
as a common interest game, while the harmonic part represents the conflicts
between the interests of the players. We make this intuition precise, by
studying the properties of these two classes, and show that indeed they have
quite distinct and remarkable characteristics. For instance, while finite
potential games always have pure Nash equilibria, harmonic games generically
never do. Moreover, we show that the nonstrategic component does not affect the
equilibria of a game, but plays a fundamental role in their efficiency
properties, thus decoupling the location of equilibria and their payoff-related
properties. Exploiting the properties of the decomposition framework, we obtain
explicit expressions for the projections of games onto the subspaces of
potential and harmonic games. This enables an extension of the properties of
potential and harmonic games to "nearby" games. We exemplify this point by
showing that the set of approximate equilibria of an arbitrary game can be
characterized through the equilibria of its projection onto the set of
potential games
Tunneling and the Band Structure of Chaotic Systems
We compute the dispersion laws of chaotic periodic systems using the
semiclassical periodic orbit theory to approximate the trace of the powers of
the evolution operator. Aside from the usual real trajectories, we also include
complex orbits. These turn out to be fundamental for a proper description of
the band structure since they incorporate conduction processes through
tunneling mechanisms. The results obtained, illustrated with the kicked-Harper
model, are in excellent agreement with numerical simulations, even in the
extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax
Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
To treat the spectral statistics of quantum maps and flows that are fully
chaotic classically, we use the rigorous Riemann-Siegel lookalike available for
the spectral determinant of unitary time evolution operators . Concentrating
on dynamics without time reversal invariance we get the exact two-point
correlator of the spectral density for finite dimension of the matrix
representative of , as phenomenologically given by random matrix theory. In
the limit the correlator of the Gaussian unitary ensemble is
recovered. Previously conjectured cancellations of contributions of
pseudo-orbits with periods beyond half the Heisenberg time are shown to be
implied by the Riemann-Siegel lookalike
Path Defense in Dynamic Defender-Attacker Blotto Games (dDAB) with Limited Information
We consider a path guarding problem in dynamic Defender-Attacker Blotto games
(dDAB), where a team of robots must defend a path in a graph against
adversarial agents. Multi-robot systems are particularly well suited to this
application, as recent work has shown the effectiveness of these systems in
related areas such as perimeter defense and surveillance. When designing a
defender policy that guarantees the defense of a path, information about the
adversary and the environment can be helpful and may reduce the number of
resources required by the defender to achieve a sufficient level of security.
In this work, we characterize the necessary and sufficient number of assets
needed to guarantee the defense of a shortest path between two nodes in dDAB
games when the defender can only detect assets within -hops of a shortest
path. By characterizing the relationship between sensing horizon and required
resources, we show that increasing the sensing capability of the defender
greatly reduces the number of defender assets needed to defend the path
Quantum Chaotic Dynamics and Random Polynomials
We investigate the distribution of roots of polynomials of high degree with
random coefficients which, among others, appear naturally in the context of
"quantum chaotic dynamics". It is shown that under quite general conditions
their roots tend to concentrate near the unit circle in the complex plane. In
order to further increase this tendency, we study in detail the particular case
of self-inversive random polynomials and show that for them a finite portion of
all roots lies exactly on the unit circle. Correlation functions of these roots
are also computed analytically, and compared to the correlations of eigenvalues
of random matrices. The problem of ergodicity of chaotic wave-functions is also
considered. For that purpose we introduce a family of random polynomials whose
roots spread uniformly over phase space. While these results are consistent
with random matrix theory predictions, they provide a new and different insight
into the problem of quantum ergodicity. Special attention is devoted all over
the paper to the role of symmetries in the distribution of roots of random
polynomials.Comment: 33 pages, Latex, 6 Figures not included (a copy of them can be
requested at [email protected]); to appear in Journal of Statistical
Physic
The Asymptotic distribution of circles in the orbits of Kleinian groups
Let P be a locally finite circle packing in the plane invariant under a
non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When
Gamma is geometrically finite, we construct an explicit Borel measure on the
plane which describes the asymptotic distribution of small circles in P,
assuming that either the critical exponent of Gamma is strictly bigger than 1
or P does not contain an infinite bouquet of tangent circles glued at a
parabolic fixed point of Gamma. Our construction also works for P invariant
under a geometrically infinite group Gamma, provided Gamma admits a finite
Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite.
Some concrete circle packings to which our result applies include Apollonian
circle packings, Sierpinski curves,
Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat
A Lovelock black hole bestiary
We revisit the study of (A)dS black holes in Lovelock theories. We present a
new tool that allows to attack this problem in full generality. In analyzing
maximally symmetric Lovelock black holes with non-planar horizon topologies
many distinctive and interesting features are observed. Among them, the
existence of maximally symmetric vacua do not supporting black holes in vast
regions of the space of gravitational couplings, multi-horizon black holes, and
branches of solutions that suggest the existence of a rich diagram of phase
transitions. The appearance of naked singularities seems unavoidable in some
cases, raising the question about the fate of the cosmic censorship conjecture
in these theories. There is a preferred branch of solutions for planar black
holes, as well as non-planar black holes with high enough mass or temperature.
Our study clarifies the role of all branches of solutions, including
asymptotically dS black holes, and whether they should be considered when
studying these theories in the context of AdS/CFT.Comment: 40 pages, 16 figures; v2: references added and minor amendments; v3:
title changed to improve its accuracy and general reorganization of the
results to ameliorate their presentatio
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