Probability Antimatching

Abstract

We present a conceptual inversion of probability matching called ``probability antimatching.'' Where probability matching describes a decision strategy of stimulus pursuit, probability antimatching describes an analogous decision strategy of stimulus avoidance. We present three behavioural studies where participants played a computer game of hide-and-seek. Participants played hide-and-seek against a simulated computer opponent that selected rooms for hiding/seeking according to a given probability distribution. Seeking trials replicate traditional probability matching. Hiding trials demonstrate probability antimatching. In Study 1, we formally present our methodology of expressing participant seeking and hiding behaviour as a linear combination of Euclidean vectors. Participant seeking strategies, $\vec{s}$, are well-represented by a linear combination of the optimal maximizing strategy, $\vec{x}$, and the probability matching strategy, $\vec{m}$. Participant hiding strategies, $\vec{h}$, are equally well-represented by a linear combination of the optimal minimizing strategy, $\vec{n}$, and the probability antimatching strategy, $\vec{a}$. We define $\vec{a}$ as a vector reflection of $\vec{m}$ over the uniform distribution vector, $\vec{u}$. This operation is denoted $\vec{a} = refl_{\vec{u}}(\vec{m}) = 2\vec{u} - \vec{m}$. In Study 2, we replicate the findings of Study 1 using data collected online. In Study 3, we demonstrate that our conceptualization of probability antimatching extends to probability distributions that have non-unique optimal hiding/seeking strategies and distributions that have invalid reflections (that result in negative probability values). Across our three studies, we find that hiding/seeking strategies are influenced by the number of rooms presented during hide-and-seek, corresponding to the dimensionality of the underlying probability distributions. However, the direction of this effect fails to replicate across our studies.