Interleaved Information Structures in Dynamic Games: A General Framework with Application to the Linear-Quadratic Case

TL;DR

This paper introduces a systematic framework for modeling and solving dynamic games with complex interleaved information structures, extending beyond traditional feedback and open-loop paradigms, with a focus on linear-quadratic cases.

Contribution

It develops a novel method to model arbitrary interleaved information structures as Mathematical Program Networks and derives Riccati-like equations for Nash equilibria in LQ games.

Findings

Framework successfully models complex information dependencies.

Systematic derivation of Riccati-like equations for Nash equilibria.

Illustrative example demonstrates applicability to cyclic information structures.

Abstract

A fundamental problem in noncooperative dynamic game theory is the computation of Nash equilibria under different information structures, which specify the information available to each agent during decision-making. Prior work has extensively studied equilibrium solutions for two canonical information structures: feedback, where agents observe the current state at each time, and open-loop, where agents only observe the initial state. However, these paradigms are often too restrictive to capture realistic settings exhibiting interleaved information structures, in which each agent observes only a subset of other agents at every timestep. To date, there is no systematic framework for modeling and solving dynamic games under arbitrary interleaved information structures. To this end, we make two main contributions. First, we introduce a method to model deterministic dynamic games with arbitrary interleaved information structures as Mathematical Program Networks (MPNs), where the network structure encodes the informational dependencies between agents. Second, for linear-quadratic (LQ) dynamic games, we leverage the MPN formulation to develop a systematic procedure for deriving Riccati-like equations that characterize Nash equilibria. Finally, we illustrate our approach through an example involving three agents exhibiting a cyclic information structure.