General two-population logit equilibrium selection

Characterize stochastic equilibrium selection for asymmetric two-population coordination games under risk-sensitive logit dynamics beyond the super-dominant regime.

Background

The paper analyzes two-population asymmetric coordination games with heterogeneous entropic risk parameters. It establishes results for best response with mutations and proves robustness under risk-sensitive logit dynamics when a super-dominant equilibrium exists. However, the two-dimensional state space makes logit transition costs dependent on both the state and the path, preventing the paper from providing a general characterization outside the super-dominant case.

References

Although BRM remains tractable, transition costs under logit dynamics are state- and path-dependent, requiring a genuinely two-dimensional analysis. We characterize stochastic selection under super-dominance, while the general risk-sensitive two-population logit case remains open.

— Entropic Risk-Sensitive Evolutionary Learning and Equilibrium Selection in Coordination Games  (2609.08677 - Mohammadi et al., 8 Sep 2026) in Section 5, Extension: Two-Population Asymmetric Setting

Several directions remain open. First, our analysis focused on homogeneous risk attitudes within each population. Relaxing this assumption and allowing risk sensitivity to vary across agents or over time could provide a broader understanding of how risk preferences can shape the long-run equilibrium selection.

— Entropic Risk-Sensitive Evolutionary Learning and Equilibrium Selection in Coordination Games  (2609.08677 - Mohammadi et al., 8 Sep 2026) in Section 8, Concluding Remarks

Second, we studied entropic risk sensitivity because it provided a natural and analytically tractable way to incorporate payoff uncertainty into evolutionary learning. Other risk-sensitive criteria may induce different effective payoff comparisons and, consequently, different stochastic-stability patterns, which are worth further investigation.

— Entropic Risk-Sensitive Evolutionary Learning and Equilibrium Selection in Coordination Games  (2609.08677 - Mohammadi et al., 8 Sep 2026) in Section 8, Concluding Remarks

Finally, the present analysis focused on coordination-game environments. Extending the framework to richer population structures and other payoff structures may further illustrate how risk attitudes can shape the collective behaviors in multi-agent interactions.

— Entropic Risk-Sensitive Evolutionary Learning and Equilibrium Selection in Coordination Games  (2609.08677 - Mohammadi et al., 8 Sep 2026) in Section 8, Concluding Remarks