Mutually Quadratically Invariant Information Structures in Two-Team Stochastic Dynamic Games

TL;DR

This paper introduces the concept of mutual quadratic invariance (MQI) for two-team stochastic dynamic games, enabling easier computation of equilibrium strategies under certain information structures, with distinctions between zero-sum and nonzero-sum cases.

Contribution

It defines MQI for two-team games, demonstrating its role in simplifying the computation of structured equilibrium strategies in zero-sum scenarios and highlighting limitations in nonzero-sum cases.

Findings

Structured state feedback Nash equilibria can be derived from disturbance strategies in zero-sum games.

MQI facilitates the computation of equilibrium strategies under specific information structures.

Counterexample shows the equivalence does not extend to nonzero-sum games.

Abstract

We formulate a two-team linear quadratic stochas- tic dynamic game featuring two opposing teams each with decentralized information structures. We introduce the concept of mutual quadratic invariance (MQI), which, analogously to quadratic invariance in (single team) decentralized control, defines a class of interacting information structures for the two teams under which optimal linear feedback control strate- gies are easy to compute. We show that, for zero-sum two- team dynamic games, structured state feedback Nash (saddle- point) equilibrium strategies can be computed from equivalent structured disturbance feedforward saddle point equilibrium strategies. However, for nonzero-sum games we show via a counterexample that a similar equivalence fails to hold. The results are illustrated with a simple yet rich numerical example that illustrates the importance of the information structure for dynamic games.