Probabilistic prediction and context tree identification in the Goalkeeper Game
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In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions – left, center or right – to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: 1) the shape of the context tree summarizing the dependencies between present and past directions; 2) the entropy of the stochastic chain used to generate the sequences of events; 3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.
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