Demand management policies aim to shift individual behavior toward sustainable choices (e.g., goods, transport modes). Personalized incentive policies tailor subsidies to agents' needs and constraints, but personalization also exposes the regulator to agents' strategic manipulative behavior. The extent to which agents can profitably manipulate such policies remains poorly understood, which limits their applicability. This paper establishes analytically the conditions under which manipulation benefits the agent. We formalize a Stackelberg game in which an agent may simulate a different profile to extract higher incentives from a regulator. Previous work typically assumes that the regulator would instantaneously classify agents into the simulated user profile. In contrast, we explicitly model the regulator's process of learning the agent profile, based on observed past behavior. This makes manipulation harder, since it forces the agent to consistently behave according to a simulated profile, thus renouncing following their true preferences. Manipulative agents thus incur a Cost of Manipulation, which has typically been neglected. By accounting for it, we get a counterintuitive finding: although classification uncertainty reduces personalization accuracy, it may benefit the regulator by deterring manipulation. We establish an upper bound on the agent's gain from manipulation, which becomes stricter as profiles become harder to distinguish for the regulator. Simulations on the London Passenger Mode Choice dataset illustrate this deterrence effect. The framework can therefore be used to stress-test the robustness of personalized incentive policies before deployment.

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