CS364A: Algorithmic Game Theory Lecture #19: Pure Nash Equilibria and PLS-Completeness

1 The Big Picture We now have an impressive list of tractability results — polynomial-time algorithms and quickly converging learning dynamics — for several equilibrium concepts in several classes of games. Such tractability results, especially via reasonably natural learning processes, lend credibility to the predictive power of these equilibrium concepts. See also Figure 1. [Lecture 17] In general games, no-(external)-regret dynamics converges quickly to an approximate coarse correlated equilibrium (CCE). [Lecture 18] In general games, no-swap-regret dynamics converges quickly to an approximate correlated equilibrium (CE). PNE MNE CE CCE tractable in symmetric routing/congestion games tractable in 2-player 0-sum games tractable in general Figure 1: The hierarchy of solution concepts.