On the Structure of Equilibrium Strategies in Dynamic Gaussian Signaling Games

TL;DR

This paper investigates the structure of equilibrium strategies in a finite horizon dynamic Gaussian signaling game, revealing conditions under which linear strategies form the Stackelberg equilibrium and highlighting the trade-offs in information disclosure.

Contribution

It extends static Gaussian signaling analysis to a dynamic setting, showing that pure linear strategies often do not form the equilibrium, unlike in static cases.

Findings

Pure linear strategies do not always form the Stackelberg equilibrium in dynamic settings.

Existence of equilibrium strategies depends on problem parameters.

Trade-offs between information exploitation and revelation are identified.

Abstract

This paper analyzes a finite horizon dynamic signaling game motivated by the well-known strategic information transmission problems in economics. The mathematical model involves information transmission between two agents, a sender who observes two Gaussian processes, state and bias, and a receiver who takes an action based on the received message from the sender. The players incur quadratic instantaneous costs as functions of the state, bias and action variables. Our particular focus is on the Stackelberg equilibrium, which corresponds to information disclosure and Bayesian persuasion problems in economics. Prior work solved the static game, and showed that the Stackelberg equilibrium is achieved by pure strategies that are linear functions of the state and the bias variables. The main focus of this work is on the dynamic (multi-stage) setting, where we show that the existence of a pure strategy Stackelberg equilibrium, within the set of linear strategies, depends on the problem parameters. Surprisingly, for most problem parameters, a pure linear strategy does not achieve the Stackelberg equilibrium which implies the existence of a trade-off between exploiting and revealing information, which was also encountered in several other asymmetric information games.