Sequential public signaling in routing games with feedback information

It is known that in traffic systems, less information can lead to better social welfare. This paper studies how to sequentially reveal traffic information to drivers to minimize social cost. We model this game as a multi-stage Stackelberg game between a designer, who sends public messages about traffic situation to drivers, and drivers, who can help improve the designer's observations. This paper studies the belief systems and the optimal strategies of both players, shows that drivers have a stationary optimal strategy, and provides a recursive formula to compute the designer's optimal strategy. Our simulation results indicate that feedback information from drivers help reduce total social cost and refine their own belief. In some cases, the designer broadcasts confusing information such that more drivers choose the congested path, which leads to more accurate future observation of the designer. In this way, the designer gains better future social welfare by sacrificing a little current social welfare.