social stability and oucome.mecanisim design

We develop a dynamical systems framework for collective convergence under private incentives, adversarial perturbations, and structural constraints. Modeling society as a continuous-time projected dynamical system, we represent aggregate behavior as the superposition of private utility gradients, adversarial drift, and a corrective social welfare feedback term. A viability constraint set ensures sustainability and feasibility of trajectories. We prove that if corrective feedback strength exceeds the combined misalignment and adversarial forces, the welfare deficit decays exponentially and the system converges to the constrained social optimum. The framework formalizes tragedy-of-the-commons dynamics and provides Lyapunov-based conditions under which institutional mechanisms stabilize collective outcomes. This approach bridges evolutionary game dynamics, mechanism design, and viability theory, offering a control-theoretic perspective on social stability under adversarial pressure.