Title : A game theoretic approach to optimal containment policies under uncertainty of Individuals compliance
Abstract:
At the onset of a pandemic, when no effective medicine or vaccine is available, governments implement non-pharmaceutical interventions to control the outbreak. The effectiveness of these policies depends on individuals' compliance, which is inherently uncertain, necessitating an optimal decision-making approach. This paper proposes a robust control framework that integrates H∞-optimal control and cooperative differential games (CDG) to design adaptive, individual-centered containment strategies. By modeling pandemic dynamics as a nonlinear stochastic system and incorporating control inputs to capture individual adherence and response variability, we derive a feedback law that minimizes worst-case policy outcomes. Our approach combines H2/H∞ control, ensuring optimal performance while maintaining robustness against uncertainties. Additionally, adaptive dynamic programming (ADP) is employed to obtain Pareto-optimal strategies within a cooperative game framework, while a non-cooperative differential game (NCDG) formulation ensures Nash equilibrium under adverse conditions. This integrated framework provides a robust and adaptive approach to designing containment policies that balance effectiveness and resilience in uncertain compliance environments.
