Browsing by Subject "Bayesian formulation"

Now showing 1 - 3 of 3

Open Access
Dynamic signaling games under Nash and Stackelberg equilibria
(IEEE, 2016) Sarıtaş, Serkan; Yüksel, Serdar; Gezici, Sinan
In this study, dynamic and repeated quadratic cheap talk and signaling game problems are investigated. These involve encoder and decoders with mismatched performance objectives, where the encoder has a bias term in the quadratic cost functional. We consider both Nash equilibria and Stackelberg equilibria as our solution concepts, under a perfect Bayesian formulation. These two lead to drastically different characteristics for the equilibria. For the cheap talk problem under Nash equilibria, we show that fully revealing equilibria cannot exist and the final state equilibria have to be quantized for a large class of source models; whereas, for the Stackelberg case, the equilibria must be fully revealing regardless of the source model. In the dynamic signaling game where the transmission of a Gaussian source over a Gaussian channel is considered, the equilibrium policies are always linear for scalar sources under Stackelberg equilibria, and affine policies constitute an invariant subspace under best response maps for Nash equilibria.
Open Access
Nash and Stackelberg equilibria for dynamic cheap talk and signaling games
(IEEE, 2017) Sarıtaş, Serkan; Yüksel, S.; Gezici, Sinan
Simultaneous (Nash) and sequential (Stackelberg) equilibria of two-player dynamic quadratic cheap talk and signaling game problems are investigated under a perfect Bayesian formulation. For the dynamic scalar and multi-dimensional cheap talk, the Nash equilibrium cannot be fully revealing whereas the Stackelberg equilibrium is always fully revealing. Further, the final state Nash equilibria have to be essentially quantized when the source is scalar and has a density, and non-revealing for the multi-dimensional case. In the dynamic signaling game where the transmission of a Gauss-Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for both scalar and multi-dimensional sources under Nash equilibria; however, the Stackelberg equilibrium policies are always linear for scalar sources but may be non-linear for multi-dimensional sources. Further, under the Stackelberg setup, the conditions under which the equilibrium is non-informative are derived for scalar sources.
Open Access
Sequential sensor installation for wiener disorder detection
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2016) Dayanik, S.; Sezer, S. O.
We consider a centralized multisensor online quickest disorder detection problem where the observation from each sensor is a Wiener process gaining a constant drift at a common unobservable disorder time. The objective is to detect the disorder time as quickly as possible with small probability of false alarms. Unlike the earlier work on multisensor change detection problems, we assume that the observer can apply a sequential sensor installation policy. At any time before a disorder alarm is raised, the observer can install new sensors to collect additional signals. The sensors are statistically identical, and there is a fixed installation cost per sensor. We propose a Bayesian formulation of the problem. We identify an optimal policy consisting of a sequential sensor installation strategy and an alarm time, which minimize a linear Bayes risk of detection delay, false alarm, and new sensor installations. We also provide a numerical algorithm and illustrate it on examples. Our numerical examples show that significant reduction in the Bayes risk can be attained compared to the case where we apply a static sensor policy only. In some examples, the optimal sequential sensor installation policy starts with 30% less number of sensors than the optimal static sensor installation policy and the total percentage savings reach to 12%.