Signaling games in networked systems
Author
Sarıtaş, Serkan
Advisor
Gezici, Sinan
Date
2018-08Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
We investigate decentralized quadratic cheap talk and signaling game problems
when the decision makers (an encoder and a decoder) have misaligned objective
functions. We first extend the classical results of Crawford and Sobel on
cheap talk to multi-dimensional sources and noisy channel setups, as well as to
dynamic (multi-stage) settings. Under each setup, we investigate the equilibria
of both Nash (simultaneous-move) and Stackelberg (leader-follower) games. We
show that for scalar cheap talk, the quantized nature of Nash equilibrium policies
holds for arbitrary sources; whereas Nash equilibria may be of non-quantized
nature, and even linear for multi-dimensional setups. All Stackelberg equilibria
policies are fully informative, unlike the Nash setup. For noisy signaling games, a
Gauss-Markov source is to be transmitted over a memoryless additive Gaussian
channel. Here, conditions for the existence of a ne equilibria, as well as informative
equilibria are presented, and a dynamic programming formulation is obtained
for linear equilibria. For all setups, conditions under which equilibria are noninformative
are derived through information theoretic bounds. We then provide
a different construction for signaling games in view of the presence of inconsistent
priors among multiple decision makers, where we focus on binary signaling
problems. Here, equilibria are analyzed, a characterization on when informative
equilibria exist, and robustness and continuity properties to misalignment are
presented under Nash and Stackelberg criteria. Lastly, we provide an analysis on
the number of bins at equilibria for the quadratic cheap talk problem under the
Gaussian and exponential source assumptions.
Our findings reveal drastic differences in signaling behavior under team and
game setups and yield a comprehensive analysis on the value of information;
i.e., for the decision makers, whether there is an incentive for information hiding,
or not, which have practical consequences in networked control applications.
Furthermore, we provide conditions on when a ne policies may be optimal in
decentralized multi-criteria control problems and for the presence of active information
transmission even in strategic environments. The results also highlight
that even when the decision makers have the same objective, presence of inconsistent
priors among the decision makers may lead to a lack of robustness in
equilibrium behavior.
Keywords
Networked Control SystemsGame Theory
Signaling Games
Cheap Talk
Quantization
Hypothesis Testing
Inconsistent Priors
Information Theory