In recent years, there has been enormous public interest in autonomous vehicles (AV), with more than 80 billion dollars invested in self-driving car technology. However, for the foreseeable future, self-driving cars will interact with human driven vehicles and other human road users, such as pedestrians and cyclists. Therefore, in order to ensure safe operation of AVs, there is need for computational models of humans traffic behaviour that can be used for testing and verification of autonomous vehicles. Game theoretic models of human driving behaviour is a promising computational tool that can be used in many phases of AV development. However, traditional game theoretic models are typically built around the idea of rationality, i.e., selection of the most optimal action based on individual preferences. In reality, not only is it hard to infer diverse human preferences from observational data, but real-world traffic shows that humans rarely choose the most optimal action that a computational model suggests. Through the lens of behavioural game theory, my thesis bridges the gap between observational naturalistic behaviour and game theory to create models of traffic behaviour that can have versatile applications in AV development, including testing, verification, and motion planning.

The first part of the thesis makes a set of methodological contributions towards creating models of traffic behaviour from naturalistic datasets using behavioural game theory. In the second part, the thesis demonstrates practical uses of models for safety validation of autonomous vehicle planners. At each step, the models are built around the behaviour of boundedly rational agents and demonstrate multiple ways of modelling suboptimal behaviour, with suboptimality being considered from the perspective of a game designer.

Although there has been an increasing interest in the use of game theoretic models for AV, it is not clear which solution concepts align well with naturalistic driving behaviour. Based on the structure of a hierarchical game, the thesis first presents various design choices that can be used in the construction of a game, along with the solution concepts from behavioural game theory that can be applied to solve such games. These choices result in thirty behaviour models, which are evaluated based on their model fit and predictive accuracy on naturalistic data. The results provide practical guidance for practitioners for the construction of traffic behaviour models.

Driving is a multi-objective task, and humans aggregate objectives of safety and progress in a context and individual specific manner. It is challenging to infer the parameters of multiobjective utility aggregation solely from observations because of a number of unobserved variables. Based on the concept of rationalisability, the thesis develops algorithms for estimating multiobjective aggregation parameters for two aggregation methods, weighted and satisficing aggregation, and also when the underlying model of reasoning consists of both strategic and nonstrategic reasoners. Experiments conducted in three different datasets provide interesting insights into how road users aggregate these objectives, as well as the situational dependence of the aggregation process.

In the final methodological contribution, the thesis addresses two key challenges of building traffic behaviour models using dynamic games;​ model instability and model uncertainty. Model instability arises when a class of boundedly rational agents who follow elementary nonstrategic models of behaviour have no reason to adhere to elementary models over time in the game. The thesis addresses this problem by developing a nonstrategic yet sophisticated finite-state transducer-based model of level-0 behaviour within the level-k framework. Model uncertainty arises when agents are free to follow any model of reasoning as is often the case in naturalistic data. This problem is addressed by developing a generalised cognitive hierarchy model consisting of three layers, nonstrategic, strategic, and robust. Each layer can hold multiple behaviour models, and the chapter develops solutions for heterogeneous models based on the consistency of beliefs over observations. Simulation experiments demonstrate that a robust layer model is an appropriate choice for an AV behaviour planner.

Building on the game theoretic models, the second part of the thesis demonstrates the application of the models by developing novel safety validation methodologies for testing AV planners. The first application is an automated generation of interpretable variations of lane change behaviour based on Quantal Best Response model. The proposed model is shown to be effective for generating both rare-event situations and to replicate the typical behaviour distribution observed in naturalistic data. The second application is safety validation of strategic planners in situations of dynamic occlusion. Using the concept of hypergames, in which different agents have different views of the game, the thesis develops a new safety surrogate metric, dynamic occlusion risk (DOR), that can be used to evaluate the risk associated with each action in situations of dynamic occlusion. The thesis concludes with a taxonomy of strategic interactions that maps complex design specific strategies in a game to a simpler taxonomy of traffic interactions. Regulations around what strategies an AV should execute in traffic can be developed over the simpler taxonomy, and a process of automated mapping can protect the proprietary design decisions of an AV manufacturer.