Hierarchical Game Theory for System-Optimal Control: Applications of Reverse Stackelberg Games in Regulating Marketing Channels and Traffic Routing

Abstract

Complex decision-making problems have two common features: 1) they involve agents (firms, drivers, countries) with interdependent payoffs, that is, the action of one agent affects the others' rewards, and 2) they are inherently dynamic, that is, the agents compete or cooperate repeatedly over time, and their actions have an impact on the evolution of the state of the system. An example can be found in road-traffic networks, where a driver affects the other drivers' travel time by selecting a particular route and a particular speed profile. When too many drivers opt for a popular connection at the same time, congestion results. Fisheries provide another, similar example. Overfishing means fewer fish are available for others in the short run, and the long-term sustainability of the fishery is put at risk. These situations illustrate how the lack of coordination between parties in a system may result in a highly suboptimal use of scarce resources. While it is in the parties' common interest that some players act in an individually suboptimal manner, for instance, by taking unpopular routes that are not the shortest in distance, there is no mechanism that guarantees the behavior of the other parties. As a result, all parties act selfishly and face the suboptimal result of a severe traffic jam or a shortage of fish. For an illustration of this dilemma, see "The Wardrop Equilibrium Principles and the Braess Paradox."

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