Search Results (15)

In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players. Full article

The Central Asian Orogenic Belt (CAOB) is the world’s largest accretionary orogenic belt, and its formation is related to the closure of the Paleo-Asian Ocean (PAO). However, the closure time and style of the PAO remain controversial. To address these issues, this paper presents zircon U-Pb dating, whole-rock geochemistry and zircon Lu-Hf isotope analyses of the volcanic rocks in the Faku-Kaiyuan area on the northern margin of the North China Craton. The results show that the Bachagou andesites formed in the Early Permian (287 ± 2 Ma), while the Chaijialing andesites and dacites formed in the Late Permian (253.3 ± 3.7 Ma) and Middle Triassic (244.3 ± 1.3 Ma), respectively. The Bachagou andesites and Chaijialing andesites are enriched in LILEs and LREEs and depleted in HFSEs and HREEs, indicating that they formed in the active continental margins. The Chaijialing dacites show similar geochemical signatures to adakite and formed in a syn-collisional setting. Geochemistry and isotopic analysis indicates that the Bachagou andesites were derived from a partial melting of the mantle wedge that was metasomatized by subduction fluids. The Chaijialing andesites were generated from a metasomatized mantle by slab-derived and sediment fluids. The Chaijialing dacites formed by a partial melting of thickened lower crust. Combined with previous research results, we can conclude that the Eastern PAO closed by a scissor-like movement from west to east during the Late Permian–Middle Triassic. Full article

Evidence shows that diversity and spatial distributions of biological communities are largely driven by the race of living organisms in their adaptation to chemicals synthesized by their neighbors. In this report, the emergence of mathematical models on pure spatial self-organization induced by biochemical suppression (allelopathy) and competition between species were investigated through numerical analysis. For both random and patched initial spatial distributions of species, we demonstrate that warfare survivors are self-organized on the landscape in Turing-like patterns driven by diffusive instabilities of allelochemicals. These patterns are simple; either all species coexist at low diffusion rates or are massively extinct, except for a few at high diffusivities, but they are complex and biodiversity-sustained at intermediate diffusion rates. “Defensive alliances” and ecotones seem to be basic mechanisms that sustain great biodiversity in our hybrid cellular automata model. Moreover, species coexistence and extinction exhibit multi-stationarity. Full article

In this study, we investigated the human capacity to generate randomness in decision-making processes using the rock-paper-scissors (RPS) game. The randomness of the time series was evaluated using the time-series data of RPS moves made by 500 subjects who played 50 consecutive RPS games. The indices used for evaluation were the Lempel–Ziv complexity and a determinism index obtained from a recurrence plot, and these indicators represent the complexity and determinism of the time series, respectively. The acquired human RPS time-series data were compared to a pseudorandom RPS sequence generated by the Mersenne Twister and the RPS time series generated by the RPS game’s strategy learned using the human RPS time series acquired via genetic programming. The results exhibited clear differences in randomness among the pseudorandom number series, the human-generated series, and the AI-generated series. Full article

In this paper, we quantify the non-transitivity in chess using human game data. Specifically, we perform non-transitivity quantification in two ways—Nash clustering and counting the number of rock–paper–scissor cycles—on over one billion matches from the Lichess and FICS databases. Our findings indicate that the strategy space of real-world chess strategies has a spinning top geometry and that there exists a strong connection between the degree of non-transitivity and the progression of a chess player’s rating. Particularly, high degrees of non-transitivity tend to prevent human players from making progress in their Elo ratings. We also investigate the implications of non-transitivity for population-based training methods. By considering fixed-memory fictitious play as a proxy, we conclude that maintaining large and diverse populations of strategies is imperative to training effective AI agents for solving chess. Full article

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. Full article

When we play competitive games, the opponents that we face act as predictors of the outcome of the game. For instance, if you are an average chess player and you face a Grandmaster, you anticipate a loss. Framed in a reinforcement learning perspective, our opponents can be thought of as predictors of rewards and punishments. The present study investigates whether facing an opponent would be processed as a reward or punishment depending on the level of difficulty the opponent poses. Participants played Rock, Paper, Scissors against three computer opponents while electroencephalographic (EEG) data was recorded. In a key manipulation, one opponent (HARD) was programmed to win most often, another (EASY) was made to lose most often, and the third (AVERAGE) had equiprobable outcomes of wins, losses, and ties. Through practice, participants learned to anticipate the relative challenge of a game based on the opponent they were facing that round. An analysis of our EEG data revealed that winning outcomes elicited a reward positivity relative to losing outcomes. Interestingly, our analysis of the predictive cues (i.e., the opponents’ faces) demonstrated that attentional engagement (P3a) was contextually sensitive to anticipated game difficulty. As such, our results for the predictive cue are contrary to what one might expect for a reinforcement model associated with predicted reward, but rather demonstrate that the neural response to the predictive cue was encoding the level of engagement with the opponent as opposed to value relative to the anticipated outcome. Full article

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. Full article

With the rapid development of the autonomous world, local decision making between devices is becoming important. This article provides a new paradigm (Rock-Paper-Scissors-Hammer: RPSH) that can reduce the number of conflicts or decision draws and thus increase the throughput of autonomous devices while reducing the kept number of records or transactions. The paradigm requires a sealed envelope protocol and sequential message passing between both parties to decide unanimously a winner between the two participants without a third-party mediation. The message passing proposes a detailed record in a blockchain-like format that is not corruptible and is verifiable for conflict resolution. A simulated IoT environment is created to show the advantage of the proposed protocol and it shows significant reduction in mean efforts due to the elimination of draws or undecided situations. Autonomous devices, such as cars, need to maintain meticulous, lightweight, but blockchain-like record keeping for insurance settlements or conflict resolutions; that archival data size is significantly reduced by the RPSH protocol. Full article

To explore whether the brain contains pattern differences in the rock–paper–scissors (RPS) imagery task, this paper attempts to classify this task using fNIRS and deep learning. In this study, we designed an RPS task with a total duration of 25 min and 40 s, and recruited 22 volunteers for the experiment. We used the fNIRS acquisition device (FOIRE-3000) to record the cerebral neural activities of these participants in the RPS task. The time series classification (TSC) algorithm was introduced into the time-domain fNIRS signal classification. Experiments show that CNN-based TSC methods can achieve 97% accuracy in RPS classification. CNN-based TSC method is suitable for the classification of fNIRS signals in RPS motor imagery tasks, and may find new application directions for the development of brain–computer interfaces (BCI). Full article

The human brain carries out cognitive control for the inhibition of habitual behaviors by suppressing some familiar but inappropriate behaviors instead of engaging specific goal-directed behavior flexibly in a given situation. To examine the characteristics of neural dynamics related to such inhibition of habitual behaviors, we used a modified rock–paper–scissors (RPS) task that consisted of a basic, a lose-, and a win-conditioned game. Spectral and phase synchrony analyses were conducted to examine the acquired electroencephalogram signals across the entire brain during all RPS tasks. Temporal variations in frontal theta power activities were directly in line with the stream of RPS procedures in accordance with the task conditions. The lose-conditioned RPS task gave rise to increases in the local frontal power and global phase-synchronized pairs of theta oscillations. The activation of the global phase-synchronized network preceded the activation of frontal theta power. These results demonstrate that the frontal regions play a pivotal role in the inhibition of habitual behaviors—stereotyped and ingrained stimulus–response mappings that have been established over time. This study suggests that frontal theta oscillations may be engaged during the cognitive inhibition of habitual behaviors and that these oscillations characterize the degree of cognitive load required to inhibit habitual behaviors. Full article

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. Full article

Game spaces in which an organism must repeatedly compete with an opponent for mutually exclusive outcomes are critical methodologies for understanding decision-making under pressure. In the non-transitive game rock, paper, scissors (RPS), the only technique that guarantees the lack of exploitation is to perform randomly in accordance with mixed-strategy. However, such behavior is thought to be outside bounded rationality and so decision-making can become deterministic, predictable, and ultimately exploitable. This review identifies similarities across economics, neuroscience, nonlinear dynamics, human, and animal cognition literatures, and provides a taxonomy of RPS strategy. RPS strategies are discussed in terms of (a) whether the relevant computations require sensitivity to item frequency, the cyclic relationships between responses, or the outcome of the previous trial, and (b) whether the strategy is framed around the self or other. The negative implication of this taxonomy is that despite the differences in cognitive economy and recursive thought, many of the identified strategies are behaviorally isomorphic. This makes it difficult to infer strategy from behavior. The positive implication is that this isomorphism can be used as a novel design feature in furthering our understanding of the attribution, agency, and acquisition of strategy in RPS and other game spaces. Full article

We make use of data from a Facebook application where hundreds of thousands of people played a simultaneous move, zero-sum game—rock-paper-scissors—with varying information to analyze whether play in strategic settings is consistent with extant theories. We report three main insights. First, we observe that most people employ strategies consistent with Nash, at least some of the time. Second, however, players strategically use information on previous play of their opponents, a non-Nash equilibrium behavior; they are more likely to do so when the expected payoffs for such actions increase. Third, experience matters: players with more experience use information on their opponents more effectively than less experienced players, and are more likely to win as a result. We also explore the degree to which the deviations from Nash predictions are consistent with various non-equilibrium models. We analyze both a level-k framework and an adapted quantal response model. The naive version of each these strategies—where players maximize the probability of winning without considering the probability of losing—does better than the standard formulation. While one set of people use strategies that resemble quantal response, there is another group of people who employ strategies that are close to $k_1$; for naive strategies the latter group is much larger. Full article

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system’s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed. Full article