Quadratic Signaling Games with Channel Combining Ratio

TL;DR

This paper analyzes quadratic signaling games with noisy channels, deriving equilibrium strategies and costs for both Nash and Stackelberg scenarios, considering multi-stage and single-stage setups with misaligned objectives.

Contribution

It provides explicit characterizations of linear and affine equilibrium strategies in quadratic signaling games with channel noise and source observation, including the combining ratio for the decoder.

Findings

Existence of linear strategies at Stackelberg equilibrium.

Explicit affine equilibria in single-stage Nash games.

Conditions for meaningful transmission by the encoder.

Abstract

In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. For the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message.