Science Advances

Supplementary Materials

This PDF file includes:

  • Section S1. Details of the simulation protocol
  • Section S2. Best reply structure and mixed strategy NE
  • Section S3. Further evidence on the predictive power of the best reply structure
  • Section S4. Ensemble of games constrained by a potential function
  • Section S5. Analytical calculations on the best reply structure with uncorrelated payoffs
  • Fig. S1. Instances of simulation runs of the Bush-Mosteller reinforcement learning algorithm with N = 20.
  • Fig. S2. Instances of simulation runs of fictitious play with N = 20.
  • Fig. S3. Effect of negative payoff correlation on fictitious play for some values of N and Γ.
  • Fig. S4. Instances of simulation runs of replicator dynamics with N = 20.
  • Fig. S5. Instances of simulation runs of EWA with N = 20.
  • Fig. S6. Instances of simulation runs of EWA and EWA with noise with N = 20.
  • Fig. S7. Mixed strategy NE classified in relation to the best reply structure.
  • Fig. S8. Test for how well the best reply structure predicts nonconvergence with N = 5, instead of N = 20 as in the main paper.
  • Fig. S9. Test for how well the best reply structure predicts nonconvergence with N = 50, instead of N = 20 as in the main paper.
  • Fig. S10. Frequency of convergence to mixed strategy NE for N = 20.
  • Fig. S11. Correlation matrix of the co-occurrence of nonconvergence for the six learning algorithms.
  • Fig. S12. How the share of best reply cycles predicts convergence as perfect potential games are approached.
  • Fig. S13. Exhaustive account of best reply configurations with the same best reply vector.
  • Fig. S14. Payoff matrix with N = 11 that is used to illustrate the calculation of the frequency of the best reply vectors.
  • Fig. S15. Frequency of k-cycles, ρ(N, k), as a function of the number of actions N.
  • References (5562)

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