Repeated-Game Convergence Laboratory

CSCE 631 · Module 3 (Regret Minimization, L7–L9). Two learners repeatedly play a small normal-form game under full-information, expected-payoff dynamics. Watch marginal averages, the joint empirical distribution, regret, and equilibrium gaps.

Configure Game Row learner Column learner Seed Initialization Planned horizon (MWU η)

Disclosed: the "lecture perturbation" preset uses the seed to generate a small, reproducible non-uniform starting point so the dynamics are not trivially stationary. This is not the deck's uniform initialization.

Control (round cap T = 100,000) Round T = 0 Speed

Strategies (current • average • trail)

Row player

Column player

Joint empirical play vs. product of marginals

The left matrix is the joint empirical distribution p^T(a) = T⁻¹∑_t∏_i x^t_{i,a_i}. CCE and CE are properties of this joint object — not of the product of marginals on the right. Their L₁ distance measures temporal correlation.

Joint p^T

Product x̄ ȳ^T

L₁ distance ||p^T − x̄ȳ^T||₁ = 0

Convergence diagnostics

Zero-sum game: the duality gap (sum exploitability) of the average strategies is shown; it should fall as averages converge.

Strategies (current • average • trail)

Joint empirical play vs. product of marginals

Convergence diagnostics

Numeric summary (accessible fallback)