Dynamic Signaling Games with Quadratic Criteria under Nash and Stackelberg Equilibria

Abstract

This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader-follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further conditions the equilibria for all time stages must be quantized. In contrast, the Stackelberg equilibria are always fully revealing. In the multi-stage 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 Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be non-linear for multi-dimensional sources. We obtain an explicit recursion for optimal linear encoding policies for multi-dimensional sources, and derive conditions under which Stackelberg equilibria are informative.

17 pages

References in corpus (6)

• Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness
• Information-Theoretic Approach to Strategic Communication as a Hierarchical Game
• Quadratic Multi-Dimensional Signaling Games and Affine Equilibria
• Crawford-Sobel meet Lloyd-Max on the grid
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Cited by in corpus (5)

• On the Number of Bins in Equilibria for Signaling Games
• Hypothesis Testing under Subjective Priors and Costs as a Signaling Game
• Strategic Communication with Side Information at the Decoder
• Quadratic Signaling Games with Channel Combining Ratio
• Signaling Games for Log-Concave Distributions: Number of Bins and Properties of Equilibria