On the dynamics of coordinated hierarchies: Economic growth versus poverty traps

We study development traps generated by payoff-mediated coordination between an institutional layer and a private-sector layer. The leading interpretation is the transition from informality to formal-sector participation: institutional effort raises the return to formalisation, while formal participation raises the fiscal, compliance, and legitimacy returns to institutional effort. The paper develops this mechanism through nested continuous-time replicator models. The one-population benchmark gives the familiar critical-mass and hysteresis result. The two-role follower model shows how a scalar threshold becomes a stable saddle branch. The main contribution is a leader–follower phase-plane analysis: we derive local stability conditions for joint poverty, joint prosperity, and decoupled regimes; give sufficient global conditions under which the stable manifold of an interior saddle is the basin boundary; and prove a comparison result showing that payoff-improving reforms weakly expand the basin of joint prosperity. A multi-role extension records local rare-deviation stability and monotone nullcline shifts, without claiming a complete global classification in four dimensions. The analysis implies that unilateral policy interventions do not fail by definition; they fail when the induced state remains in the basin of the low-activity equilibrium.