Learning in Games
Fictitious play and regret matching convergence
Run fictitious play and regret matching algorithms. Watch empirical frequencies converge to Nash equilibrium in zero-sum games, and observe the characteristic cycling and spiraling patterns.
| Heads | Tails | |
|---|---|---|
| Heads | 1, -1 | -1, 1 |
| Tails | -1, 1 | 1, -1 |
Final p(Heads): 0.537Final q(Heads): 0.493Nash: p*=0.500, q*=0.500
Strategy Probabilities Over Time
p (Row plays Heads)q (Col plays Heads)
Strategy Space Trajectory
Fictitious play converges to Nash in zero-sum games. Regret matching converges to the set of correlated equilibria. The hollow circle marks the mixed Nash equilibrium.