Nash and Stackelberg Equilibria for Dynamic Cheap Talk and Signaling Games


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Saritas S. , Yuksel S., Gezici S.

American Control Conference (ACC), Washington, United States Of America, 24 - 26 May 2017, pp.3644-3649 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.23919/acc.2017.7963511
  • City: Washington
  • Country: United States Of America
  • Page Numbers: pp.3644-3649

Abstract

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 multidimensional 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.