Binary Signaling under Subjective Priors and Costs as a Game

TL;DR

This paper analyzes binary signaling games with subjective priors and costs, exploring how equilibrium solutions vary under different game-theoretic assumptions and the robustness of these equilibria to small changes.

Contribution

It formulates binary signaling as a Bayesian game under Nash and Stackelberg frameworks, analyzing equilibrium existence, properties, and robustness with subjective priors and costs.

Findings

Stackelberg equilibria can be informative or non-informative.

Nash equilibrium may not exist with deterministic policies under certain conditions.

Stackelberg equilibrium is sensitive to small perturbations in priors and costs.

Abstract

Many decentralized and networked control problems involve decision makers which have either misaligned criteria or subjective priors. In the context of such a setup, in this paper we consider binary signaling problems in which the decision makers (the transmitter and the receiver) have subjective priors and/or misaligned objective functions. Depending on the commitment nature of the transmitter to his policies, we formulate the binary signaling problem as a Bayesian game under either Nash or Stackelberg equilibrium concepts and establish equilibrium solutions and their properties. In addition, the effects of subjective priors and costs on Nash and Stackelberg equilibria are analyzed. It is shown that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg assumption, but there always exists an equilibrium. However, apart from the informative and non-informative equilibria cases, under certain conditions, there does not exist a Nash equilibrium when the receiver is restricted to use deterministic policies. For the corresponding team setup, however, an equilibrium typically always exists and is always informative. Furthermore, we investigate the effects of small perturbations in priors and costs on equilibrium values around the team setup (with identical costs and priors), and show that the Stackelberg equilibrium behavior is not robust to small perturbations whereas the Nash equilibrium is.