Theoretical comparison of logit and replicator dynamics

Establish a complete theoretical comparison of convergence and nonconvergence behavior for the coupled SIS epidemic model under bounded-rationality logit learning and replicator learning dynamics.

Background

The paper provides one numerical example in which trajectories under replicator dynamics fail to converge, while trajectories under bounded-rationality logit dynamics converge to an equilibrium. This example demonstrates a possible qualitative distinction between the two learning protocols but does not establish general conditions for such behavior.

The unresolved problem is to develop a complete theoretical analysis identifying when convergence, oscillation, or other asymptotic behavior occurs under the two alternative behavioral dynamics.

References

In this work, we have illustrated one example in which trajectories under replicator dynamics fail to converge, whereas, those under bounded rationality converge. A complete theoretical analysis on this comparison remains an interesting problem.

— SIS Epidemic Containment under Game-theoretic Rational Learning  (2610.03173 - Maitra et al., 2 Oct 2026) in Section 7, “Conclusions and Future Work”