Distributed consensus in noncooperative congestion games: An application to road pricing

In this paper, we discuss a repeated noncooperative congestion game in which players have limited information about each other and make their decisions simultaneously. A consensus protocol is introduced to estimate the percentage of players selecting each resource. The underlying network at a given stage is chosen from a possible graph set randomly and independently. We show that the congestion game under investigation has at least one pure Nash equilibrium. In addition, we show that if some sort of inertia is imposed, the almost sure convergence to a pure Nash equilibrium can be ensured. After that, two dynamic pricing strategies are introduced to achieve social optimum and to spread out players´ choices, respectively. Also, we apply these results to a trip timing problem based on the real traffic data in Singapore.