Behavioural Isomorphism, Cognitive Economy and Recursive Thought in Non-Transitive Game Strategy

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.

Exploring the role of mutual prediction in inter-brain synchronization during competitive interactions: an fNIRS hyperscanning investigation

Mutual prediction is crucial for understanding the mediation of bodily actions in social interactions. Despite this importance, limited studies have investigated neurobehavioral patterns under the mutual prediction hypothesis in natural competitive scenarios. To address this gap, our study employed functional near-infrared spectroscopy hyperscanning to examine the dynamics of real-time rock-paper-scissors games using a computerized paradigm with 54 participants. Firstly, our results revealed activations in the right inferior frontal gyrus, bilateral dorsolateral prefrontal cortex, and bilateral frontopolar cortex, each displaying distinct temporal profiles indicative of diverse cognitive processes during the task. Subsequently, a task-related increase in inter-brain synchrony was explicitly identified in the right dorsolateral prefrontal cortex, which supported the mutual prediction hypothesis across the two brains. Moreover, our investigation uncovered a close association between the coherence value in the right dorsolateral prefrontal cortex and the dynamic predictive performances of dyads using inter-subject representational similarity analysis. Finally, heightened inter-brain synchrony values were observed in the right dorsolateral prefrontal cortex before a draw compared to a no-draw scenario in the second block, suggesting that cross-brain signal patterns could be reflected in behavioral responses during competition. In summary, these findings provided initial support for expanding the understanding of cognitive processes underpinning natural competitive engagements.

Breaking the bonds of reinforcement: Effects of trial outcome, rule consistency and rule complexity against exploitable and unexploitable opponents

In two experiments, we used the simple zero-sum game Rock, Paper and Scissors to study the common reinforcement-based rules of repeating choices after winning (win-stay) and shifting from previous choice options after losing (lose-shift). Participants played the game against both computer opponents who could not be exploited and computer opponents who could be exploited by making choices that would at times conflict with reinforcement. Against unexploitable opponents, participants achieved an approximation of random behavior, contrary to previous research commonly finding reinforcement biases. Against exploitable opponents, the participants learned to exploit the opponent regardless of whether optimal choices conflicted with reinforcement or not. The data suggest that learning a rule that allows one to exploit was largely determined by the outcome of the previous trial.

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.

Rock-Paper-Scissors Play: Beyond the Win-Stay/Lose-Change Strategy

This research studied the strategies that players use in sequential adversarial games. We took the Rock-Paper-Scissors (RPS) game as an example and ran players in two experiments. The first experiment involved two humans, who played the RPS together for 100 times. Importantly, our payoff design in the RPS allowed us to differentiate between participants who used a random strategy from those who used a Nash strategy. We found that participants did not play in agreement with the Nash strategy, but rather, their behavior was closer to random. Moreover, the analyses of the participants’ sequential actions indicated heterogeneous cycle-based behaviors: some participants’ actions were independent of their past outcomes, some followed a well-known win-stay/lose-change strategy, and others exhibited the win-change/lose-stay behavior. To understand the sequential patterns of outcome-dependent actions, we designed probabilistic computer algorithms involving specific change actions (i.e., to downgrade or upgrade according to the immediate past outcome): the Win-Downgrade/Lose-Stay (WDLS) or Win-Stay/Lose-Upgrade (WSLU) strategies. Experiment 2 used these strategies against a human player. Our findings show that participants followed a win-stay strategy against the WDLS algorithm and a lose-change strategy against the WSLU algorithm, while they had difficulty in using an upgrade/downgrade direction, suggesting humans’ limited ability to detect and counter the actions of the algorithm. Taken together, our two experiments showed a large diversity of sequential strategies, where the win-stay/lose-change strategy did not describe the majority of human players’ dynamic behaviors in this adversarial situation.

Variability in competitive decision-making speed and quality against exploiting and exploitative opponents

A presumption in previous work has been that sub-optimality in competitive performance following loss is the result of a reduction in decision-making time (i.e., post-error speeding). The main goal of this paper is to test the relationship between decision-making speed and quality, with the hypothesis that slowing down decision-making should increase the likelihood of successful performance in cases where a model of opponent domination can be implemented. Across Experiments 1–3, the speed and quality of competitive decision-making was examined in a zero-sum game as a function of the nature of the opponent (unexploitable, exploiting, exploitable). Performance was also examined against the nature of a credit (or token) system used as a within-experimental manipulation (no credit, fixed credit, variable credit). To compliment reaction time variation as a function of outcome, both the fixed credit and variable credit conditions were designed to slow down decision-making, relative to a no credit condition where the game could be played in quick succession and without interruption. The data confirmed that (a) self-imposed reductions in processing time following losses (post-error speeding) were causal factors in determining poorer-quality behaviour, (b) the expression of lose-shift was less flexible than the expression of win-stay, and, (c) the use of a variable credit system may enhance the perceived control participants have against exploitable opponents. Future work should seek to disentangle temporal delay and response interruption as determinants of decision-making quality against numerous styles of opponency.

Switching Competitors Reduces Win-Stay but Not Lose-Shift Behaviour: The Role of Outcome-Action Association Strength on Reinforcement Learning

Predictability is a hallmark of poor-quality decision-making during competition. One source of predictability is the strong association between current outcome and future action, as dictated by the reinforcement learning principles of win–stay and lose–shift. We tested the idea that predictability could be reduced during competition by weakening the associations between outcome and action. To do this, participants completed a competitive zero-sum game in which the opponent from the current trial was either replayed (opponent repeat) thereby strengthening the association, or, replaced (opponent change) by a different competitor thereby weakening the association. We observed that win–stay behavior was reduced during opponent change trials but lose–shiftbehavior remained reliably predictable. Consistent with the group data, the number of individuals who exhibited predictable behavior following wins decreased for opponent change relative to opponent repeat trials. Our data show that future actions are more under internal control following positive relative to negative outcomes, and that externally breaking the bonds between outcome and action via opponent association also allows us to become less prone to exploitation.

Behavioural and neural limits in competitive decision making: The roles of outcome, opponency and observation

To understand the boundaries we set for ourselves in terms of environmental responsibility during competition, we examined a neural index of outcome valence (feedback-related negativity; FRN) in relation to an early index of visual attention (N1), a later index of motivational significance (P3), and, eventual behaviour. In Experiment 1 (n = 36), participants either were (play) or were not (observe) responsible for action selection. In Experiment 2 (n = 36), opponents additionally either could (exploitable) or could not (unexploitable) be beaten. Various failures in reinforcement learning expression were revealed including large-scale approximations of random behaviour. Against unexploitable opponents, N1 determined the extent to which negative and positive outcomes were perceived as distinct categories by FRN. Against exploitable opponents, FRN determined the extent to which P3 generated neural gain for future events. Differential activation of the N1 - FRN - P3 processing chain provides a framework for understanding the behavioural dynamism observed during competitive decision making.