Non-parametric Bayesian inference of strategies in repeated games

Inferring underlying cooperative and competitive strategies from human behaviour in repeated games is important for accurately characterizing human behaviour and understanding how people reason strategically. Finite automata, a bounded model of computation, have been extensively used to compactly represent strategies for these games and are a standard tool in game theoretic analyses. However, inference over these strategies in repeated games is challenging since the number of possible strategies grows exponentially with the number of repetitions yet behavioural data are often sparse and noisy. As a result, previous approaches start by specifying a finite hypothesis space of automata that does not allow for flexibility. This limitation hinders the discovery of novel strategies that may be used by humans but are not anticipated a priori by current theory. Here we present a new probabilistic model for strategy inference in repeated games by exploiting non‐parametric Bayesian modelling. With simulated data, we show that the model is effective at inferring the true strategy rapidly and from limited data, which leads to accurate predictions of future behaviour. When applied to experimental data of human behaviour in a repeated prisoner's dilemma, we uncover strategies of varying complexity and diversity.