Partial Controllability in Mean Field Incentive Dynamics

Abstract

Abstract This study proposes a reward-based framework for public transit demand control under partial controllability, where only a subset of users can be directly influenced by incentives. The framework integrates a mean-field model of day-to-day behavioral adjustment with a budget-feasible reverse auction based on congestion externalities. Controllable and uncontrollable users are coupled through aggregate network congestion, while the operator allocates limited rewards using class-level externality weights computed from observed flow states. The proposed mechanism satisfies perday strategy-proofness, individual rationality, and budget feasibility in the induced single-parameter environment. The resulting system is formulated as a feedbackperturbed population dynamic, in which uncontrolled users follow inertial logit revision and controllable users are additionally shifted by auction-induced reallocation. Numerical experiments show that the mechanism reduces peak-period congestion even when the controllable fraction is limited, while also revealing a trade-off between externality-based targeting and budget efficiency under heterogeneous weights.