Strategic Heterogeneity: Welfare Gains from Secession and Immigration

2026-08-06

AI Summary

This study investigates the impact of endogenous population segregation on social welfare in large anonymous games, focusing on strategic heterogeneity between conformists and anti-conformists. By constructing a continuum-player binary-action model, it demonstrates that under costless segregation, any mixed-strategy Nash equilibrium can be Pareto-improved through jurisdictional partitioning. The analysis integrates techniques from continuum games, equilibrium characterization, Pareto optimization, and concavification to solve a Bayesian persuasion problem, establishing a mathematical isomorphism between optimal jurisdiction design and Bayesian persuasion. The key contributions include proving that segregation systematically mitigates coordination failures and enhances both individual and aggregate welfare, and providing structural conditions for stability under unilateral group migration.

Abstract

This paper investigates the strategic and welfare properties of endogenous population partitioning (secession) within large-population anonymous games featuring strategic heterogeneity. We consider a continuum-player framework with a binary action space where players are categorized either as fol- lowers, who experience positive network externalities from conformity, or as contrarians, who seek distinctiveness via anti-conformism. We fully characterize the set of Nash equilibria and establish con- ditions under which costless secession yields structural Pareto improvements. We demonstrate that in any strategically mixed society, every mixed-strategy Nash equilibrium admits a Pareto-improving se- cession. With finitely many types, secession systematically mitigates coordination frictions, enhancing both individual payoffs and aggregate utility. Furthermore, we characterize social planner configura- tions optimizing weighted aggregate utility, establishing a formal mathematical isomorphism between optimal jurisdictional design and the theory of Bayesian persuasion solved via concavification. Finally, we derive the structural conditions governing migration stability when subgroups can unilaterally re- locate across distinct societies.

Problem

• strategic heterogeneity
• secession
• welfare gains
• coordination frictions
• population partitioning

Innovation

• strategic heterogeneity
• endogenous secession
• Pareto improvement
• Bayesian persuasion
• migration stability