Formalizing Opponent Modeling with the Rock, Paper, Scissors Game

In simple dyadic games such as rock, paper, scissors (RPS), people exhibit peculiar sequential dependencies across repeated interactions with a stable opponent. These regularities seem to arise from a mutually adversarial process of trying to outwit their opponent. What underlies this process, and what are its limits? Here, we offer a novel framework for formally describing and quantifying human adversarial reasoning in the rock, paper, scissors game. We first show that this framework enables a precise characterization of the complexity of patterned behaviors that people exhibit themselves, and appear to exploit in others. This combination allows for a quantitative understanding of human opponent modeling abilities. We apply these tools to an experiment in which people played 300 rounds of RPS in stable dyads. We find that although people exhibit very complex move dependencies, they cannot exploit these dependencies in their opponents, indicating a fundamental limitation in people’s capacity for adversarial reasoning. Taken together, the results presented here show how the rock, paper, scissors game allows for precise formalization of human adaptive reasoning abilities.

Recursive Adversarial Reasoning in the Rock, Paper, Scissors Game

In this study, we investigate people’s ability to predict and adapt to the behavior of others in order to make plans of their own, a cornerstone of cooperative and competitive behavior. Participants played 300 rounds of rock, paper, scissors against another human player. We investigate the degree to which participants are able to identify patterns in their opponent’s behavior in order to exploit them in subsequent rounds. We find strong evidence that participants exploit their opponents over the course of 300 rounds, suggesting that people identify dependencies in their opponent’s move choices during the game. Nonetheless, analysis of dependencies across participant move choices reveals that people exhibit a number of regularities in their own moves. Based on these dependencies, we argue that participants are far from optimal in their exploiting, suggesting that there are substantial constraints on people’s ability to identify and adapt to patterned opponent behavior across repeated interactions.