Extend competing-model analysis to endogenous misspecified learning

Extend the competing-model analysis in Supplemental Appendix Section S.6 from exogenous correctly specified environments to endogenous learning environments with misspecified models.

Background

Supplemental Appendix Section S.6 analyzes an agent who switches between two models and establishes persistence results only for correctly specified exogenous environments. The persistence comparison is governed by the models' learning coefficients.

The authors explicitly leave unresolved the extension of this analysis to settings in which actions affect observations and the models are misspecified.

References

Several extensions remain open. First, one could define and study singular equilibria in games with multiple players and with mixed actions. Second, Supplemental Appendix \ref{supp:competing} only considers the exogenous and correctly specified setting, so one could extend it to the endogenous and misspecified setting.

— Singular Equilibrium and Selection of Narratives  (2610.11615 - Jin, 8 Oct 2026) in Section 6, Concluding Remarks; Supplemental Appendix, Section S.6 (Competing Narratives)