Title: Semantic-Guided Hierarchical Stackelberg Games for Multi-Agent Coordination with Fuzzy Constraints
Primary area: optimization
Keywords: Stackelberg game optimization, large language models, semantic-embedded optimization, lunar rover energy management, hierarchical game theory, bounded rationality, multi-agent coordination, mission-critical systems

Abstract: Multi-agent coordination under complex constraints remains a fundamental challenge in distributed optimization, particularly when real-world problems involve constraints that practitioners describe informally. While humans intuitively understand and balance such requirements across multiple decision-makers, automated systems demand precise mathematical formulations that may not exist or may lose essential context in translation. We propose a framework where distributed agents learn to interpret and satisfy semantic constraints through collective intelligence rather than explicit programming. The key insight is that natural language constraints often encode contextual priorities that vary with system state, which we capture by treating constraints as adaptive geometric structures whose shape depends on operational context. When an operator specifies "maintain reasonable reserves," the meaning of "reasonable" naturally differs during peak versus off-peak periods, and our framework learns these contextual variations through language model guidance. To coordinate multiple agents under such fluid constraints, we structure the problem as a hierarchical game where semantic understanding at the system level guides local agent decisions without imposing rigid rules, allowing emergent coordination through game-theoretic interactions. The framework remains computationally tractable by recognizing that different aspects of coordination occur at different timescales, with fast local adjustments separated from slower global consensus formation through singular perturbation decomposition. Empirical evaluation on a multi-agent resource allocation task demonstrates that semantic-aware coordination achieves 89.2% efficiency compared to 82.7-86.4% for traditional methods while successfully handling requirements that resist mathematical formalization.