Passivity Tools for Hybrid Learning Rules in Large Populations

Large populations of strategic agents may combine continuous adaptation, pairwise comparison, and discontinuous best-response behavior. This work extends system-theoretic passivity tools to analyze those hybrid learning dynamics within a common framework.

Why it matters

Many learning rules do not fit a single canonical model. A passivity characterization for their combinations creates a modular route to studying equilibrium stability without rebuilding the analysis for every new hybrid rule.

Key contributions

• Generalizes delta-passivity to include discontinuous learning rules.
• Establishes passivity for broad convex cones of hybrid learning dynamics.
• Derives stronger results for the two-strategy setting.
• Illustrates the stability framework through numerical examples.