Generating Dominant Strategies for Continuous Two-Player Zero-Sum Games

Abstract

Motivated by the synthesis of controllers from high-level temporal specifications, we present two algorithms to compute dominant strategies for continuous two-player zero-sum games based on the Counter-Example Guided Inductive Synthesis (CEGIS) paradigm. In CEGIS, we iteratively propose candidate dominant strategies and find counterexamples. For scalability, past work has constrained the number of counterexamples used to generate new candidates, which leads to oscillations and incompleteness, even in very simple examples. The first algorithm combines Satisfiability Modulo Theory (SMT) solving with optimization to efficiently implement CEGIS. The second abstracts previously refuted strategies, while maintaining a finite counterexample set. We characterize sufficient conditions for soundness and termination, and show that both algorithms are sound and terminate. Additionally, the second approach can be made complete to within an arbitrary factor. We conclude by comparing across different variants of CEGIS.