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Decentralized air traffic management systems offer a scalable alternative to centralized control, but often assume high levels of cooperation. In practice, such assumptions frequently break down since agents, each representing an airspace sector, may operate independently and prioritize local objectives. We address the problem of sector overload in decentralized air traffic management by proposing a regulated decentralized protocol that models self-interested behaviors based on best response dynamics. Each agent adjusts the departure times of its assigned flights to reduce its own congestion, without requiring centralized joint optimization. A tunable cooperativeness factor models the degree to which each agent accounts for overload in other sectors, while a minimal admissibility rule prevents local updates from creating new overloads. We show that this regulatory restriction is sufficient to guarantee finite-time convergence of best response dynamics to a pure Nash equilibrium under partial cooperation. In addition, we identify a sufficient condition under which an overload-free solution corresponds to a global minimizer of the potential function. Numerical experiments using one month of European flight data demonstrate that the proposed algorithm substantially reduces overload even with only minimal cooperation, achieving performance close to a centralized global mixed-integer optimizer and exceeding a centralized first-come-first-served baseline while requiring substantially less computation than centralized optimization. We further evaluate departure delay and fairness to quantify the operational cost of overload mitigation.