A Game-theoretic and Algorithmic Study of the Toll Rates of Hong Kong Road Tunnels
The cross-harbor tunnels system is an epitome of the whole congested Hong Kong transportation situation. Hong Kong has three cross-harbor tunnels. The Cross Harbor Tunnel is connected to the most complete transportation network and has the lowest toll rate. The Eastern Harbor Crossing (EHC) has the second lowest toll rate while the Western Harbor Crossing (WHC) has the highest toll rate. According to the Legislative Council of Hong Kong, the transportation demand of the CHT and the EHC during the peak hours on weekdays has exceeded their designed capacity of 77% and 38% respectively, while the WHC faces a demand of 90% of the designed capacity (Legislative Council of Hong Kong, 2017).
This project aims at alliviating the congestion problem of the three tunnels in Hong Kong by modeling this problem as a congestion game in the field of game theory. By proper pricing system, the the WHS can lighten the congestion of the CHT and the EHC by accepting part of their traffic flow.
Different models of the tunnel system according to the complexity of the system will be built. For each driver, I assume he or she have the same cost functions for each tunnel C(x) and the driver will choose the tunnel with the least cost. The cost function is assumed to be mainly determined by the time used by the driver and the toll rates of each tunnel.
After modeling, I will try to prove the existence of the Nash equilibrium of each model, which means that the solution exists. Then I will try to figure out the price minimizing the total waiting time caused by the congestion by figuring out the minimum value of the functions provided by the model.
Assistant professor of Computer Science at the University of Hong Kong
Year 4 student of Computer Science at the University of Hong Kong