Learning in Games I
summary
Argues that repeated play with simple belief updates — fictitious play — is analyzed by replacing discontinuous best responses with smooth ones and applying stochastic approximation to map the discrete stochastic process to a continuous best‑response dynamic. Shows convergence to Nash when that Nash is a global attractor, proves 2×2 games cannot sustain cycles, and proves smoothed fictitious play satisfies no-regret (universal consistency). Notes cycles or recency effects can break these results, and heterogeneous asynchronous play converges under sufficient mixing.
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