dc.title: Strategic decision making for multi-agent interaction : a study in game theory and optimization dc.description.abstract: Autonomous robots increasingly operate in environments shared with other agents, including humans, teleoperated machinery, and other autonomous robots. In these scenarios, safe and effective decision-making requires strategic reasoning about the intentions, capabilities, and likely behaviors of others. This dissertation proposes game-theoretic, data-driven, and optimization-based methods for multi-agent trajectory planning and inference in such settings, with contributions spanning three interconnected areas: defining and solving for game equilibria, inverse games and inference, and data-driven behavior modeling. Two unifying themes connect these areas: modeling novel forms of uncertainty in multi-agent interactions, and maintaining computational tractability while doing so. In the first part of this thesis, we address dynamic games with hierarchical information structures by introducing SILQGames (Chapter 2) and mixed-hierarchy games (Chapter 3). In the second part, we develop methods for inferring strategic properties from observed interactions, including leadership roles (Stackelberg leadership filter, Chapter 4) and agents' beliefs about one another's objectives (level-2 games and level-2 inverse games, Chapter 5). In the third part, we define a data-driven representation of human-like behavior and use it to project nominal trajectories into learned sets of naturalistic motions (Chapter 6). Finally, in Chapter 7, we describe open problems and propose directions for improving strategic autonomous planning. Together, these contributions provide a suite of computational tools for multi-agent autonomy, spanning model-based game-theoretic reasoning to data-driven behavior learning, with applications to autonomous driving and multi-robot coordination.