3,696 research outputs found
Quadratic Multi-Dimensional Signaling Games and Affine Equilibria
This paper studies the decentralized quadratic cheap talk and signaling game
problems when an encoder and a decoder, viewed as two decision makers, have
misaligned objective functions. The main contributions of this study are the
extension of Crawford and Sobel's cheap talk formulation to multi-dimensional
sources and to noisy channel setups. We consider both (simultaneous) Nash
equilibria and (sequential) Stackelberg equilibria. We show that for arbitrary
scalar sources, in the presence of misalignment, the quantized nature of all
equilibrium policies holds for Nash equilibria in the sense that all Nash
equilibria are equivalent to those achieved by quantized encoder policies. On
the other hand, all Stackelberg equilibria policies are fully informative. For
multi-dimensional setups, unlike the scalar case, Nash equilibrium policies may
be of non-quantized nature, and even linear. In the noisy setup, a Gaussian
source is to be transmitted over an additive Gaussian channel. The goals of the
encoder and the decoder are misaligned by a bias term and encoder's cost also
includes a penalty term on signal power. Conditions for the existence of affine
Nash equilibria as well as general informative equilibria are presented. For
the noisy setup, the only Stackelberg equilibrium is the linear equilibrium
when the variables are scalar. Our findings provide further conditions on when
affine policies may be optimal in decentralized multi-criteria control problems
and lead to conditions for the presence of active information transmission in
strategic environments.Comment: 15 pages, 4 figure
Some notions of decentralization and coordination in large-scale dynamic systems
Some notions of decentralization and coordination in the control of large-scale dynamic systems are discussed. Decentralization and coordination have always been important concepts in the study of large systems. Roughly speaking decentralization is the process of dividing a large problem into subproblems so that it can be handled more easily. Coordination is the manipulation of the subproblem so that the original problem is solved. The various types of decentralization and coordination that have been used to control dynamic systems are discussed. The emphasis was to distinguish between on-line and off-line operations to understand the results available by indicating the aspects of the problem which are decentralized
Optimal Control for LQG Systems on Graphs---Part I: Structural Results
In this two-part paper, we identify a broad class of decentralized
output-feedback LQG systems for which the optimal control strategies have a
simple intuitive estimation structure and can be computed efficiently. Roughly,
we consider the class of systems for which the coupling of dynamics among
subsystems and the inter-controller communication is characterized by the same
directed graph. Furthermore, this graph is assumed to be a multitree, that is,
its transitive reduction can have at most one directed path connecting each
pair of nodes. In this first part, we derive sufficient statistics that may be
used to aggregate each controller's growing available information. Each
controller must estimate the states of the subsystems that it affects (its
descendants) as well as the subsystems that it observes (its ancestors). The
optimal control action for a controller is a linear function of the estimate it
computes as well as the estimates computed by all of its ancestors. Moreover,
these state estimates may be updated recursively, much like a Kalman filter
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