Beyond the Nash Equilibrium Barrier

Nash equilibrium analysis has become the de facto standard for judging the solution quality achieved in systems composed of selfish users. This mindset is so pervasive in computer science that even the few papers devoted to directly analyzing outcomes of dynamic processes in repeated games (e.g., best-response or no-regret learning dynamics) have focused on showing that the performance of these dynamics is comparable to that of Nash equilibria. By assuming that equilibria are representative of the outcomes of selfish behavior, do we ever reach qualitatively wrong conclusions about those outcomes? In this paper, we argue that there exist games whose equilibria represent unnatural outcomes that are hard to coordinate on, and that the solution quality achieved by selfish users in such games is more accurately reflected in the disequilibrium represented by dynamics such as those produced by natural families of on-line learning algorithms. We substantiate this viewpoint by studying a game with a unique Nash equilibrium, but where natural learning dynamics exhibit non-convergent cycling behavior rather than converging to this equilibrium. We show that the outcome of this learning process is optimal and has much better social welfare than the unique Nash equilibrium, dramatically illustrating that natural learning processes have the potential to significantly outperform equilibrium-based analysis.