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

2026-03-18

AI Summary

This study addresses the challenge of computing Nash equilibria in noncooperative dynamic games under arbitrary staggered information structures, moving beyond the conventional limitations of feedback and open-loop information patterns. The work proposes a general modeling and solution framework by formulating deterministic dynamic games as Mathematical Programming Networks (MPNs), which explicitly encode inter-agent informational dependencies. In the linear-quadratic (LQ) setting, the approach yields a Riccati-type equation that characterizes the Nash equilibrium. As the first analytical framework applicable to arbitrary staggered information structures in dynamic games, its efficacy is demonstrated through a three-player cyclic information structure example.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Imperfect Information
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

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.

Problem

• dynamic games
• interleaved information structures
• Nash equilibria
• information structure
• noncooperative games

Innovation

• Interleaved Information Structures
• Mathematical Program Networks
• Dynamic Games
• Linear-Quadratic
• Nash Equilibrium