Multilayer mean field differential games in multi-agent systems and an application in intelligent transportation

In this thesis, we describe the results we have obtained on linear-quadratic hierarchical Mean Field Stackelberg differential games with open-loop information structure. We name this new class of games as Mean Field (MF) Multilayer Stackelberg Games (MSG). The model that we have developed consists of three levels of decision making. There is a leader at the top, sub-leaders are at the intermediate level, and followers are at the lowest level. In this structure, Stackelberg Game is played between the leader, sub-leaders and followers in turn. Firstly the leader plays with the sub-leaders and then sub-leaders play with their followers. Consequently, the leader can control the followers not directly, but only through the sub-leaders. The followers are weakly coupled through a Mean Field term, affecting their individual costs. The main novelty in this thesis is to extend the Mean Field Game to multi layer framework. Theoretically, Mean Field Equilibrium arises in the infinite population limit. In our approach, instead of computing the exact Stackelberg equilibrium, the Mean Field equilibrium policies are obtained with the assumption of infinite population. When the population size is sufficiently large, the resulting policy can be regarded as an approximate Stackelberg equilibrium by the law of large numbers, therefore we apply this resulting policy to the original problem in the finite population case. The performance of the developed method is evaluated by a numerical example. In the second part of the thesis, we adapt and apply the developed methodolgy to Intelligent Transportation Systems (ITS) for future Smart Cities. So, another important novelty of the thesis is to apply The Mean Field Game Theory to Automated Highway System (AHS), in order to minimize both total consumed energy and travel time. In this model, there is a Control Center which acts as a leader, Road Links in the intermediate level act as sub-leaders and finally Vehicles are followers. The Control Center, Road Links and Vehicles which are in consecutive layers play Mean Field (MF) Multilayer Stackelberg Games (MSG). Although, the Control Center cannot manipulate the Vehicles directly, it imposes its strategy through the Road Links in the intermediary layer. The Vehicles of each Road Link are weakly coupled through a Mean Field term, which affects their individual cost functions. In order to implement this algorithm to ITS, we have developed our highly realistic simulation environment, Istanbul Technical University City Transportation Simulation (ITUCiTSim) program. The effectiveness of the proposed method is justified by simulations performed in ITUCiTSim.