Linear Quadratic Games with Costly Measurements

TL;DR

This paper analyzes a stochastic linear quadratic two-player game where players decide when to establish costly measurements via a switching communication link, balancing improved estimation against switching costs.

Contribution

It introduces a framework for solving a two-player game with costly measurements by decoupling control and switching strategies through dynamic programming.

Findings

Optimal subgame perfect equilibrium strategies are derived.

The problem reduces to solving two separate dynamic programming problems.

The approach provides a systematic way to handle measurement costs in game settings.

Abstract

In this work we consider a stochastic linear quadratic two-player game. The state measurements are observed through a switched noiseless communication link. Each player incurs a finite cost every time the link is established to get measurements. Along with the usual control action, each player is equipped with a switching action to control the communication link. The measurements help to improve the estimate and hence reduce the quadratic cost but at the same time the cost is increased due to switching. We study the subgame perfect equilibrium control and switching strategies for the players. We show that the problem can be solved in a two-step process by solving two dynamic programming problems. The first step corresponds to solving a dynamic programming for the control strategy and the second step solves another dynamic programming for the switching strategy