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

Janani S K; Kushagra Gupta; Ufuk Topcu; David Fridovich-Keil

cs.GTMar 19, 2026

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

Authors: Janani S K, Kushagra Gupta, Ufuk Topcu, David Fridovich-Keil

Organizations: Department of Engineering Design, Indian Institute of Technology Madras, Chennai, India · Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX 78712, USA · Department of Aerospace Engineering and the Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, USA

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.

Figures & tables

Panel of Figure 1 — Fig. 1: MPN building blocks across successive time steps for dynamic games with canonical information structures.

Panel of Figure 2 — Fig. 2: MPN building block across successive timesteps for a dynamic game in which agents $i$ and $j$ exhibit a non-canonical interleaved information structure. Additional edges may appear depending on the information relationships with other agents in the game.

Panel of Figure 3 — Fig. 3: MPN for a three-agent, three timestep game with a cyclical information structure: agent 1 observes agent 2, who in turn observes agent 3, who in turn observes agent 1.

Game Theory

Game theory studies how interacting decision-makers choose strategies, form agreements, and shape outcomes under competition and cooperation.

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Learning Dynamic Games for Cooperative Iterative Tasks

Mark Pustilnik, Francesco Borrelli

University of California at Berkeley, USA

Multi-Agent Control Game Theory Cooperative Game Theory Iterative Learning Control

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We consider cooperative and iterative tasks involving multiple agents whose interactions are modeled as a dynamic game with shared constraints. We propose a general learning framework applicable to nonlinear and nonconvex dynamic games that uses previously executed feasible trajectories to construct a sampled joint safe set and player-specific cost-to-go functions. At each time step, the agents jointly select a previously sampled terminal state and a Generalized Nash equilibrium used to reach it. A new solution is adopted only if it satisfies a cooperative acceptance rule agreed upon by the players. The framework accommodates individual non-degradation requirements and selection criteria such as weighted costs and Nash bargaining. We show that the proposed framework guarantees recursive feasibility and characterize conditions under which each player's cost is non-increasing across iterations.

Abstract

Game Theory

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