# Hypothesis Testing under Subjective Priors and Costs as a Signaling Game

## TL;DR

This paper analyzes binary signaling games with subjective priors and costs, exploring equilibrium existence and properties under different game-theoretic frameworks, and examining robustness to perturbations.

## Contribution

It formulates signaling problems as Bayesian games under Nash and Stackelberg equilibria, deriving conditions for informative equilibria and analyzing robustness to perturbations.

## Key findings

- Informative and non-informative equilibria can exist under Stackelberg and Nash.
- Equilibrium existence is guaranteed in the team setup, always informative.
- Stackelberg equilibria are sensitive to small perturbations, unlike Nash.

## Abstract

Many communication, sensor network, and networked control problems involve agents (decision makers) which have either misaligned objective functions or subjective probabilistic models. In the context of such setups, 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. We show that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg and Nash assumptions, and derive the conditions under which an informative equilibrium exists for the Stackelberg and Nash setups. 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.