Formalizing Opponent Modeling with the Rock, Paper, Scissors Game

Repeated rock, paper, scissors play reveals limits in adaptive sequential behavior

How do people adapt to others in adversarial settings? Prior work has shown that people often violate rational models of adversarial decision-making in repeated interactions. In particular, in mixed strategy equilibrium (MSE) games, where optimal action selection entails choosing moves randomly, people often do not play randomly, but instead try to outwit their opponents. However, little is known about the adaptive reasoning that underlies these deviations from random behavior. Here, we examine strategic decision-making across repeated rounds of rock, paper, scissors, a well-known MSE game. In experiment 1, participants were paired with bot opponents that exhibited distinct stable move patterns, allowing us to identify the bounds of the complexity of opponent behavior that people can detect and adapt to. In experiment 2, bot opponents instead exploited stable patterns in the human participants' moves, providing a symmetrical bound on the complexity of patterns people can revise in their own behavior. Across both experiments, people exhibited a robust and flexible attention to transition patterns from one move to the next, exploiting these patterns in opponents and modifying them strategically in their own moves. However, their adaptive reasoning showed strong limitations with respect to more sophisticated patterns. Together, results provide a precise and consistent account of the surprisingly limited scope of people's adaptive decision-making in this setting.

Assessing behavioural profiles following neutral, positive and negative feedback

Previous data suggest zero-value, neutral outcomes (draw) are subjectively assigned negative rather than positive valence. The combined observations of faster rather than slower reaction times, subsequent actions defined by shift rather than stay behaviour, reduced flexibility, and, larger rather than smaller deviations from optimal performance following draws all align with the consequences of explicitly negative outcomes such as losses. We further tested the relationships between neutral, positive and negative outcomes by manipulating value salience and observing their behavioural profiles. Despite speeded reaction times and a non-significant bias towards shift behaviour similar to losses when draws were assigned the value of 0 (Experiment 1), the degree of shift behaviour approached an approximation of optimal performance when the draw value was explicitly positive (+1). This was in contrast to when the draw value was explicitly negative (-1), which led to a significant increase in the degree of shift behaviour (Experiment 2). Similar modifications were absent when the same value manipulations were applied to win or lose trials (Experiment 3). Rather than viewing draws as neutral and valence-free outcomes, the processing cascade generated by draws produces a complex behavioural profile containing elements found in response to both explicitly positive and explicitly negative results.