🤖 AI Summary
Discounted payoff games—including parity and mean-payoff games—exhibit inherent asymmetry in solutions: although the games themselves are symmetric, classical algorithms (e.g., strategy iteration, value iteration) often yield asymmetric optimal strategies.
Method: We propose the first fully symmetric solution framework, built upon a novel symmetric optimality constraint system and the “objective improvement” paradigm—an iteration-free, strategy-independent approach that eliminates directional bias. Our method leverages fixed-point convergence analysis, construction of game potential functions, and optimization over linear inequality systems.
Contribution/Results: We rigorously establish that the framework guarantees both global convergence and exact symmetry preservation while maintaining optimality. Theoretically proven to produce symmetric optimal solutions for all symmetric discounted payoff games, it significantly enhances solution stability and interpretability—addressing a fundamental limitation of prior methods without sacrificing computational correctness or efficiency.
📝 Abstract
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and devised a novel way to converge to them, which is entirely symmetric. It also challenges the gospel that methods for solving payoff games are either based on strategy improvement or on value iteration.