The paper develops a two‑population evolutionary game‑theoretic model in which members of two cultural groups are repeatedly matched to play a coordination game with an arbitrary number of actions. Each group faces a cultural constraint that limits its feasible action set (Xk ⊆ X) and enjoys a cultural payoff (δ{kx}) for each permissible action. Payoffs consist of a coordination benefit θk when both players choose the same action plus the cultural payoff. The model studies how these constraints affect the emergence of social conventions. The authors define compatibility (XA ∩ XB ≠ ∅), alignment, and misalignment of cultures, and show that when cultures are compatible but misaligned, the system can converge to a miscoordinated equilibrium (M) where each group plays its own cultural ideal, even though any coordinated outcome Pareto‑dominates miscoordination. Using a noisy best‑response revision protocol (Kandori‑Mailath‑Rob/Young), they analyze stochastic stability as the error rate ε → 0. They prove (Proposition 1) that the deterministic best‑response dynamics converge to coordination if cultures are aligned, to miscoordination if they are incompatible, and to either outcome depending on initial conditions when cultures are compatible but misaligned. They then establish (Proposition 2) that miscoordination is the unique stochastically stable class if it is strictly risk‑dominant, i.e., if the sum of scaled cultural biases D{Ax}+D_{Bx}>1 for every mutually permissible action. When payoffs are simple (cultural payoffs uniform across permissible actions), strict risk dominance is also necessary. The paper applies the framework to identity‑based conflict, modeling exclusive (ethnic/religious) versus inclusive identities. It shows that exclusive identities persist when the cultural bias β exceeds a critical threshold proportional to wealth, implying that poorer and more unequal societies are more prone to persistent miscoordination. Finally, the authors relax the error structure to allow unconstrained mistakes (players may randomly select any action, even culturally forbidden ones). Under this extension, a weaker condition (9) suffices for miscoordination to be stochastically stable, demonstrating that occasional violations of cultural constraints can actually reinforce miscoordination. The paper situates its contributions relative to the literature on stochastic stability, coordination games, cultural economics, and identity conflict, highlighting that the identified miscoordination arises without any ingroup‑outgroup trade‑off and persists even when coordination is Pareto‑superior.
Topics
Cultural Constraints as Action‑Set Restrictions
Introduces the core modeling assumption that each cultural group k can only choose actions from a subset X_k of the global action set X, and defines cultural payoffs δ_{kx} and the non‑degeneracy condition (ND).
Compatibility, Alignment, and Misalignment of Cultures
Defines when cultures are compatible (non‑empty intersection of feasible sets), aligned (cultural ideals intersect feasible sets), and misaligned (cultural ideals lie outside the other group's feasible set), setting the stage for coordination versus miscoordination analysis.
Best‑Response Dynamics and Deterministic Convergence (Proposition 1)
Analyzes the unperturbed (ε=0) noisy best‑response process, showing almost‑sure convergence to coordination if cultures are aligned, to miscoordination if incompatible, and to either outcome depending on initial conditions when compatible but misaligned.
Stochastic Stability, Risk Dominance, and Miscoordination (Proposition 2)
Uses the Young (1993) tree‑surgery method to prove that miscoordination M is uniquely stochastically stable when it strictly risk‑dominates all coordinated equilibria (condition D_{Ax}+D_{Bx}>1). When payoffs are simple, this condition is also necessary.
Half‑Dominance vs. Strict Risk Dominance
Compares the derived strict risk‑dominance condition to the stronger half‑dominance concept, showing that the former is sufficient and weaker, thus expanding the parameter region where miscoordination persists.
Application to Identity‑Based Conflict
Maps the abstract model to a setting with exclusive (ethnic/religious) and inclusive identities, derives the critical cultural bias β̄ = w/4, and predicts that poorer or more unequal societies are more likely to sustain exclusive identities.
Unconstrained Errors and Strengthened Miscoordination (Proposition 4)
Extends the error structure to allow random selection from the full action set, derives a weaker sufficient condition (9) for stochastic stability of miscoordination, and demonstrates that occasional cultural violations can reinforce miscoordination.
Literature Positioning and Contributions
Places the work within the broader research on stochastic stability in coordination games, cultural economics, and identity conflict, emphasizing the novelty of miscoordination arising without ingroup‑outgroup trade‑offs and the methodological contribution of graph‑theoretic proofs for asymmetric multi‑action games.