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Distributed Equilibrium-Seeking in Target Coverage Games via Self-Configurable Networks under Limited Communication

Jayanth Bhargav, Zirui Xu, Vasileios Tzoumas, Mahsa Ghasemi, Shreyas Sundaram

Abstract

We study a target coverage problem in which a team of sensing agents, operating under limited communication, must collaboratively monitor targets that may be adaptively repositioned by an attacker. We model this interaction as a zero-sum game between the sensing team (known as the defender) and the attacker. However, computing an exact Nash equilibrium (NE) for this game is computationally prohibitive as the action space of the defender grows exponentially with the number of sensors and their possible orientations. Exploiting the submodularity property of the game's utility function, we propose a distributed framework that enables agents to self-configure their communication neighborhoods under bandwidth constraints and collaboratively maximize the target coverage. We establish theoretical guarantees showing that the resulting sensing strategies converge to an approximate NE of the game. To our knowledge, this is the first distributed, communication-aware approach that scales effectively for games with combinatorial action spaces while explicitly incorporating communication constraints. To this end, we leverage the distributed bandit-submodular optimization framework and the notion of Value of Coordination that were introduced in [1]. Through simulations, we show that our approach attains near-optimal game value and higher target coverage compared to baselines.

Distributed Equilibrium-Seeking in Target Coverage Games via Self-Configurable Networks under Limited Communication

Abstract

We study a target coverage problem in which a team of sensing agents, operating under limited communication, must collaboratively monitor targets that may be adaptively repositioned by an attacker. We model this interaction as a zero-sum game between the sensing team (known as the defender) and the attacker. However, computing an exact Nash equilibrium (NE) for this game is computationally prohibitive as the action space of the defender grows exponentially with the number of sensors and their possible orientations. Exploiting the submodularity property of the game's utility function, we propose a distributed framework that enables agents to self-configure their communication neighborhoods under bandwidth constraints and collaboratively maximize the target coverage. We establish theoretical guarantees showing that the resulting sensing strategies converge to an approximate NE of the game. To our knowledge, this is the first distributed, communication-aware approach that scales effectively for games with combinatorial action spaces while explicitly incorporating communication constraints. To this end, we leverage the distributed bandit-submodular optimization framework and the notion of Value of Coordination that were introduced in [1]. Through simulations, we show that our approach attains near-optimal game value and higher target coverage compared to baselines.
Paper Structure (17 sections, 3 theorems, 11 equations, 3 figures, 3 algorithms)

This paper contains 17 sections, 3 theorems, 11 equations, 3 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Performance Guarantees
  3. Anytime Self-Configuration
  4. Problem Formulation
  5. Scalable Equilibrium Approximation
  6. Preliminaries
  7. Main Algorithm
  8. Performance Guarantees
  9. Numerical Evaluation
  10. Convergence to Approximate NE of the Game
  11. Impact of Network Optimization
  12. Conclusion
  13. Theoretical Proofs
  14. Proof of \ref{['th:defender_regret']}
  15. Proof of \ref{['lem:attacker_regret_bound']}
  16. ...and 2 more sections

Key Result

Theorem 1

After running alg:main for $T$ rounds, the defender achieves: where $\kappa_{I}\triangleq \max_{i\in{\@fontswitch\mathcal{N}}}\kappa_{I,i}$, $\bar{\alpha}\triangleq \max_{i\in{\@fontswitch\mathcal{N}}}\alpha_i$, $|\bar{{\@fontswitch\mathcal{V}}}|\triangleq\max_{i\in{\@fontswitch\mathcal{N}}}|{\@fontswitch\mathcal{V}}_i|$, $|\bar{{\@fontswitch\mathcal{M}}}|\

Figures (3)

  • Figure 1: Distributed Target Coverage Game. Team of sensing agents choose communication neighbors and orientations to maximize target coverage. Simultaneously, the attacker selects a target deployment strategy to achieve the least coverage for the sensing agents. The algorithms ActSel, NeiSel, and their interaction framework via the Value of Coordination, follows xu2026self.
  • Figure 2: Payoffs and duality gap. Consider the repeated game dynamics per Algorithm \ref{['alg:main']} between three sensors each with bandwidth constraint $1$ (defender) and an $|Y| = 20$ possible target deployments (attacker). As $T\rightarrow\infty$, the players asymptotically achieve the approximate NE, with the duality gap, i.e., the difference between the players' payoffs, decreasing to its minimum, as shown in \ref{['thm:epsilon_ne']}. Results are averaged over 20 Monte Carlo trials, each with 15000 rounds.
  • Figure 3: Comparison of neighbor selection strategies. Four algorithms are compared under the same action selection strategy ( ActSel) and adversarial environment ( EXP3), differing only in their neighbor selection strategies. Results are averaged over 20 Monte Carlo trials, each with 10000 rounds.

Theorems & Definitions (8)

  • Definition 1: $\epsilon$-Nash Equilibrium ($\epsilon$-NE) bhargav2025sensor
  • Definition 2: Normalized and Non-Decreasing Submodular Set Function fisher1978analysis
  • Definition 3: 2nd-order Submodularity foldes2005submodularity
  • Definition 4: Value of Coordination ( VoC VoC ) xu2026self
  • Definition 5: Curvature conforti1984submodular
  • Theorem 1: Defender's Average Regret Bound
  • Lemma 1: Attacker's Average Regret Bound
  • Theorem 2: Duality Gap