Nash and Stackelberg equilibria for dynamic cheap talk and signaling games
Author
Sarıtaş, Serkan
Yüksel, S.
Gezici, Sinan
Date
2017Source Title
Proceedings of the American Control Conference, IEEE 2017
Print ISSN
0743-1619
Publisher
IEEE
Pages
3644 - 3649
Language
English
Type
Conference PaperItem Usage Stats
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Show full item recordAbstract
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.
Keywords
Bayesian networksBayesian formulation
Gaussian channels
Invariant subspace
Multi dimensional
Multi-dimensional case
Nash equilibria
Signaling game
Stackelberg equilibrium
Game theory