Population games, stable games, and passivity

Stable games [1] have the attractive property of admitting global convergence to equilibria under many learning dynamics. We show that stable games can be formulated as passive input-output systems. This observation enables us to identify passivity of a learning dynamic as a sufficient condition for global convergence in stable games. Notably, dynamics satisfying our condition need not exhibit positive correlation between the payoffs and their directions of motion. Our condition is satisfied by the dynamics known to exhibit global convergence in stable games. We give a decision-theoretic interpretation for passive learning dynamics that mirrors the interpretation of stable games as strategic environments exhibiting self-defeating externalities. Lastly, we exploit the flexibility of the passivity condition to study the impact of applying various forecasting heuristics to the payoffs used in the learning process.