Characterizing the Convergence of Game Dynamics via Potentialness
Résumé
Understanding the convergence landscape of multi-agent learning is a fundamental problem of great practical relevance in many applications of artificial intelligence and machine learn- ing. While it is known that learning dynamics converge to Nash equilibrium in potential games, the behavior of dynamics in many important classes of games that do not admit a potential is poorly understood. To measure how “close” a game is to being potential, we consider a distance function, that we call “potentialness”, and which relies on a strategic decomposition of games introduced by Candogan et al. (2011). We introduce a numerical framework enabling the computation of this metric, which we use to calculate the degree of “potentialness” in generic matrix games, as well as (non-generic) games that are important in economic applications, namely auctions and contests. Understanding learning in the lat- ter games has become increasingly important due to the wide-spread automation of bidding and pricing with no-regret learning algorithms. We empirically show that potentialness decreases and concentrates with an increasing number of agents or actions; in addition, po- tentialness turns out to be a good predictor for the existence of pure Nash equilibria and the convergence of no-regret learning algorithms in matrix games. In particular, we observe that potentialness is very low for complete-information models of the all-pay auction where no pure Nash equilibrium exists, and much higher for Tullock contests, first-, and second-price auctions, explaining the success of learning in the latter. In the incomplete-information version of the all-pay auction, a pure Bayes-Nash equilibrium exists and it can be learned with gradient-based algorithms. Potentialness nicely characterizes these differences to the complete-information version.
Domaines
| Origine | Fichiers éditeurs autorisés sur une archive ouverte |
|---|---|
| Licence |