Browsing by Subject "Multi dimensional"

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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
On multi-dimensional and noisy quadratic signaling games and affine equilibria
(IEEE, 2015-07) Sarıtaş, Serkan; Yüksel, Serdar; Gezici, Sinan
This study investigates extensions of the quadratic cheap talk and signaling game problem, which has been introduced in the economics literature. Two main contributions of this study are the extension of Crawford and Sobel's cheap talk formulation to multi-dimensional sources, and the extension to noisy channel setups as a signaling game problem. We show that, in the presence of misalignment, the quantized nature of all equilibrium policies holds for any scalar random source. It is shown that for multi-dimensional setups, unlike the scalar case, 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 power term scaled by a multiplier. Conditions for the existence of affine equilibrium policies as well as general informative equilibria are presented for both the scalar and multi-dimensional setups. © 2015 American Automatic Control Council.