Bayesian Nonparametric Models Characterize Instantaneous Strategies in a Competitive Dynamic Game

Previous approaches to investigating strategic social interaction in game theory have predominantly used games with clearly-defined turns and limited choices. However, most real-world social behaviors involve dynamic, coevolving decisions by interacting agents, which pose challenges for creating tractable models of behavior. Here, using a competitive game in which human participants control the dynamics of an on-screen avatar against either another human or a computer opponent, we show that it is possible to quantify the dynamic coupling between agents using nonparametric models. We use Gaussian Processes to model the joint distributions of players' actions and identities (human or computer) as a function of game state. Borrowing from a reinforcement learning framework, we successfully approximated both the policy and the value functions used by each human player in this competitive context. This approach offers a natural set of metrics for facilitating analysis at multiple timescales and suggests new classes of tractable paradigms for assessing human behavior.