Abstract
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.
Highlights
Subjective randomness or win-stay, loseshift responding would be surprising. This illustrates a critical underlying dynamic in repeated mixed strategy equilibrium (MSE) games: Optimal play depends on the predictability of the opponent
We have argued that behavior in repeated rounds of the rock, paper, scissors game provides a window into how people perform the sort of adaptive, adversarial reasoning that allows them to outwit a stable opponent
We started with the observation that human play in simple cyclic-dominance games, such as matching pennies or rock, paper, scissors, systematically deviates from the mixed strategy Nash Equilibrium of purely random play
Summary
Human conflict and coordination are rooted in the ability to predict the behavior of others and make plans . Our focus is on decision making across many iterated rounds against a stable opponent—often hundreds, rather than the “best of 3” used to resolve household disputes In such laboratory studies of the rock, paper, scissors game, the large number of interactions allow people to detect and adapt to potentially complex patterns in their opponent’s behavior. RPS, like other mixed strategy equilibrium games, is characterized by its Nash Equilibrium solution [27], which dictates random move selection, a strategy which presents unique cognitive challenges for human players For these reasons, a large body of literature has examined human behavior over repeated interactions in the rock, paper, scissors game, motivated by diverse questions about the nature of human learning, sequential behavior, and perceptions of randomness [28,29,30]. We present an analysis of existing results which suggests that the ability to recognize and exploit sequential patterns in RPS is highly constrained, revealing the limits of human adaptive reasoning
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