Signaling equilibria for dynamic LQG games with asymmetric information

TL;DR

This paper analyzes signaling equilibria in finite horizon dynamic LQG games with asymmetric information, providing a backward-forward algorithm to compute perfect Bayesian equilibria involving linear strategies and Gaussian beliefs.

Contribution

It introduces a novel backward-forward algorithm to compute signaling equilibria in dynamic LQG games with asymmetric information, linking strategies and beliefs explicitly.

Findings

Strategies linear in private types form PBE under certain conditions

Future beliefs are influenced by equilibrium strategies, confirming signaling behavior

Algorithm reduces equilibrium computation to algebraic matrix equations and Kalman filters

Abstract

We consider a finite horizon dynamic game with two players who observe their types privately and take actions, which are publicly observed. Players' types evolve as independent, controlled linear Gaussian processes and players incur quadratic instantaneous costs. This forms a dynamic linear quadratic Gaussian (LQG) game with asymmetric information. We show that under certain conditions, players' strategies that are linear in their private types, together with Gaussian beliefs form a perfect Bayesian equilibrium (PBE) of the game. Furthermore, it is shown that this is a signaling equilibrium due to the fact that future beliefs on players' types are affected by the equilibrium strategies. We provide a backward-forward algorithm to find the PBE. Each step of the backward algorithm reduces to solving an algebraic matrix equation for every possible realization of the state estimate covariance matrix. The forward algorithm consists of Kalman filter recursions, where state estimate covariance matrices depend on equilibrium strategies.