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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

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.

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

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.
Paper Structure (13 sections, 16 equations, 3 figures)

This paper contains 13 sections, 16 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. On Mathematical Program Networks (MPNs)
  4. On Dynamic Noncooperative Games
  5. Open-Loop Nash Equilibria in Dynamic Games
  6. Feedback Nash Equilibria in Dynamic Games
  7. Formulating Interleaved Information Games as MPNs
  8. MPNs for open-loop games
  9. MPNs for feedback games
  10. MPNs for arbitrarily interleaved information
  11. Finding Nash Equilibria in Interleaved Information Games
  12. Illustrative Example
  13. Conclusion

Figures (3)

  • Figure 1: MPN building blocks across successive time steps for dynamic games with canonical information structures.
  • Figure 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.
  • Figure 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.

Theorems & Definitions (2)

  • Definition 1: Equilibrium of an MPN
  • Remark 1