ANALYTICAL MODELING OF STATE-CONTINGENT DRIVING DECISIONS UNDER DAILY ROAD-USE QUOTAS

This study develops a state-contingent equilibrium model for daily road-use quotas with heterogeneous trip urgency. Commuters, who learn their travel state (urgent or regular) at the start of the day, choose probabilistic driving strategies under a daily quota set ex ante by the regulator based on state occurrence probabilities. The model is formulated as a non-atomic congestion game and characterized via the Beckmann potential, yielding a unique equilibrium. Analytical results reveal three behavioral regimes determined by two quota thresholds: (i) small-quota, where only urgent trips drive and the shadow price is high; (ii) medium-quota, where both trip types are active and marginal net benefits equalized; and (iii) large-quota, where the cap is non-binding and both states operate at unconstrained optima. A calibrated example quantifies the thresholds and shows how quota ratio changes reshape driving probabilities and scarcity values.