Multi-objective road pricing: Game Theoretic and Multistakeholder Approach

Costs associated with traf﬿c externalities such as congestion, air pollution, noise, safety, etcetera are becoming “unbearable‿. The Braess paradox shows that combating congestion by adding infrastructure may not improve traf﬿c conditions, and geographical and/or ﬿nancial constraints may not allow infrastructure expansion. Road pricing presents an alternative to combat the mentioned externalities. The traditional way of road pricing, namely; congestion charging, may create negative bene﬿ts for the society and stakeholders, thus, defeating its main purpose (increasing transportation ef﬿ciency and social welfare). We study a road pricing that encompasses all the mentioned externalities. A meanwhile standard approach to deal with conflicting objectives (externalities) are models from Multi-objective Optimization. This approach assumes that there is one leader stakeholder/decision-maker. But then, if more than one stakeholder participates in the road pricing, the concept of Nash equilibrium (NE) from economics may constitute an alternative model. Using game theoretic approach, we study and extend the single authority road pricing scheme (Stackelberg game) to a pricing scheme with multiple authorities/regions (with likely contradicting objectives). Our model includes users interests in the upper level - giving a promising model that deals with user acceptability of road pricing. We investigate the existence of NE among actors and prove that no pure NE exists in general. Then again, NE may exist under special conditions. Since NE may not exist, and since competition may deteriorate the social welfare, we further design a mechanism that simultaneously induces a pure NE and cooperative behaviour among actors, thus, yielding optimal tolls for the system.