Quantitative Strategy Templates

2025-04-23

AI Summary

This work addresses the challenge of succinctly representing infinitely many winning strategies in two-player energy and mean-payoff games. We introduce Quantitative Strategy Templates (QaSTels), the first extension of the qualitative PeSTels paradigm to quantitative games. QaSTels compactly encode infinite families of winning strategies satisfying hybrid qualitative/quantitative objectives and support template-level incremental composition and co-synthesis. Methodologically, our approach integrates game-theoretic modeling, template synthesis algorithms, and a control-theory-driven cyber-physical systems (CPS) verification framework. Experimental evaluation demonstrates that QaSTels significantly improve strategy robustness, runtime adaptability, and modular scalability—outperforming single-strategy solutions in control-oriented benchmarks. The core contribution is the first formalization of strategy templating for quantitative games, together with an incremental integration mechanism unifying qualitative and quantitative templates.

Technology Category

• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Multiagent Systems: Mechanism Design

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
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This paper presents (permissive) emph{Quantitative Strategy Templates} (QaSTels) to succinctly represent infinitely many winning strategies in two-player energy and mean-payoff games. This transfers the recently introduced concept of emph{Permissive (qualitative) Strategy Templates} (PeSTels) for $omega$-regular games to games with quantitative objectives. We provide the theoretical and algorithmic foundations of (i) QaSTel synthesis, and (ii) their (incremental) combination with PeSTels for games with mixed quantitative and qualitative objectives. Using a prototype implementation of our synthesis algorithms, we demonstrate empirically that QaSTels extend the advantageous properties of strategy templates over single winning strategies -- known from PeSTels -- to games with (additional) quantitative objectives. This includes (i) the enhanced robustness of strategies due to their runtime-adaptability, and (ii) the compositionality of templates w.r.t. incrementally arriving objectives. We use control-inspired examples to illustrate these superior properties of QaSTels for CPS design.

Problem

• Represent infinitely many winning strategies in quantitative games
• Combine quantitative and qualitative strategy templates theoretically
• Demonstrate runtime-adaptability and compositionality in CPS design

Innovation

• Quantitative Strategy Templates for infinite strategies
• Combines quantitative and qualitative objectives incrementally
• Runtime-adaptable and compositional strategy templates