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A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium., Competing Interests: The authors have declared that no competing interests exist.

Predicting and modeling human behavior and finding trends within human decision-making processes is a major problem of social science. Rock Paper Scissors (RPS) is the fundamental strategic question in many game theory problems and real-world competitions. Finding the right approach to beat a particular human opponent is challenging. Here we use an AI (artificial intelligence) algorithm based on Markov Models of one fixed memory length (abbreviated as "single AI") to compete against humans in an iterated RPS game. We model and predict human competition behavior by combining many Markov Models with different fixed memory lengths (abbreviated as "multi-AI"), and develop an architecture of multi-AI with changeable parameters to adapt to different competition strategies. We introduce a parameter called "focus length" (a positive number such as 5 or 10) to control the speed and sensitivity for our multi-AI to adapt to the opponent's strategy change. The focus length is the number of previous rounds that the multi-AI should look at when determining which Single-AI has the best performance and should choose to play for the next game. We experimented with 52 different people, each playing 300 rounds continuously against one specific multi-AI model, and demonstrated that our strategy could win against more than 95% of human opponents.

How humans make decisions in non-cooperative strategic interactions is a big question. For the fundamental Rock-Paper-Scissors (RPS) model game system, classic Nash equilibrium (NE) theory predicts that players randomize completely their action choices to avoid being exploited, while evolutionary game theory of bounded rationality in general predicts persistent cyclic motions, especially in finite populations. However as empirical studies have been relatively sparse, it is still a controversial issue as to which theoretical framework is more appropriate to describe decision-making of human subjects. Here we observe population-level persistent cyclic motions in a laboratory experiment of the discrete-time iterated RPS game under the traditional random pairwise-matching protocol. This collective behavior contradicts with the NE theory but is quantitatively explained, without any adjustable parameter, by a microscopic model of win-lose-tie conditional response. Theoretical calculations suggest that if all players adopt the same optimized conditional response strategy, their accumulated payoff will be much higher than the reference value of the NE mixed strategy. Our work demonstrates the feasibility of understanding human competition behaviors from the angle of non-equilibrium statistical physics.

Collective efforts are a trademark of both insect and human societies. They are achieved through relatedness in the former and unknown mechanisms in the latter. The problem of achieving cooperation among non-kin has been described as the 'tragedy of the commons', prophesying the inescapable collapse of many human enterprises. In public goods experiments, initial cooperation usually drops quickly to almost zero. It can be maintained by the opportunity to punish defectors or the need to maintain good reputation. Both schemes require that defectors are identified. Theorists propose that a simple but effective mechanism operates under full anonymity. With optional participation in the public goods game, 'loners' (players who do not join the group), defectors and cooperators will coexist through rock-paper-scissors dynamics. Here we show experimentally that volunteering generates these dynamics in public goods games and that manipulating initial conditions can produce each predicted direction. If, by manipulating displayed decisions, it is pretended that defectors have the highest frequency, loners soon become most frequent, as do cooperators after loners and defectors after cooperators. On average, cooperation is perpetuated at a substantial level.

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.

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory. [ABSTRACT FROM AUTHOR]

Land use configuration in any given landscape is the result of a multi-objective optimization process, which takes into account different ecological, economic, and social factors. In this process, coordinating stakeholders is a key factor to successful spatial land use optimization. Stakeholders need to be modeled as players who have the ability to interact with each other towards their best solution, while considering multiple goals and constraints at the same time. Game theory provides a tool for land use planners to model and analyze such interactions. In order to apply the spatial allocation model and address stakeholder conflicts, an integrated model based on linear programming and game theory was designed in this study. For implementing such model, we conducted an optimal land use allocation process through multi-objective land allocation (MOLA) and linear programming methods. Then, two groups of environmental and land development players were considered to implement the optimization model. The game algorithm was used to select the appropriate constraint so that the result would be acceptable to all stakeholders. The results showed that during the third round of the game, the decision-making process and the optimization of land uses reached the desired Nash Equilibrium state and the conflict between stakeholders was resolved. Ultimately, in order to localize the results, a suitable solution was presented in a GIS environment., (© 2023. The Author(s), under exclusive licence to Springer Nature Switzerland AG.)

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool. In our game-theoretical framework, the state is playing against a pathogen by introducing non-pharmaceutical interventions to fulfil its socio-political goals, such as guaranteeing hospital care to all needed patients, keeping the country functioning, while the applied social restrictions should be as soft as possible. With the inclusion of activity and economic sector dependent transmission rate, optimal control of lockdowns and health care capacity management is calculated. We identify the presence and length of a pre-symptomatic infectious stage of the disease to have the greatest effect on the probability to cause a pandemic. Here we show that contrary to intuition, the state should not strive for the great expansion of its health care capacities even if its goal is to provide care for all requiring it and minimize the cost of lockdowns., (© 2022. The Author(s).)

Real-life room-escape games are ludic activities in which participants enter a room in order to get out of it only after solving some riddles. In this paper, we explain a Room Escape teaching experience developed in the Engineering School at Universitat Autònoma de Barcelona. The goal of this activity is to increase student's motivation and to improve their learning on two courses of the second year in the "Computer Engineering degree: Computer Networks and Information and Security". [Paper presented at the International Conference on University Teaching and Innovation (CIDUI): Learning and Teaching Innovation Impacts (9th, Bellaterra, Barcelona, Spain, Jul 5-7 2016.)]

A compelling body of evidence indicates that observing a task-irrelevant action makes the execution of that action more likely. However, it remains unclear whether this ‘automatic imitation’ effect is indeed automatic or whether the imitative action is voluntary. The present study tested the automaticity of automatic imitation by asking whether it occurs in a strategic context where it reduces payoffs. Participants were required to play rock–paper–scissors, with the aim of achieving as many wins as possible, while either one or both players were blindfolded. While the frequency of draws in the blind–blind condition was precisely that expected at chance, the frequency of draws in the blind–sighted condition was significantly elevated. Specifically, the execution of either a rock or scissors gesture by the blind player was predictive of an imitative response by the sighted player. That automatic imitation emerges in a context where imitation reduces payoffs accords with its ‘automatic’ description, and implies that these effects are more akin to involuntary than to voluntary actions. These data represent the first evidence of automatic imitation in a strategic context, and challenge the abstraction from physical aspects of social interaction typical in economic and game theory. [ABSTRACT FROM AUTHOR]

The article presents the actuarial artificial intelligence in playing the rock-paper-scissors game. Topics discussed include an overview of the rock-paper-scissors game, an outline of its different strategies, the definition of its variables, its basics, the reset of its probabilities, and the flexibility of its probabilities.

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. [ABSTRACT FROM AUTHOR]

The article discusses the result of an experimental study which shows that people do not follow the optimal strategy in practice and suggests two strategies for defeating human opponents in rock-paper-scissors (RPS). The study found that the probability of repeating a game on the next trial is well above one-third, while the strategy of always playing the symbol is assessed to be an effective strategy in defeating the symbol that the other player has previously played. The study also observed that the wins of each competition have increased by 26.4%, while the losses are decreased by 9.51%.

The paper studies product bundling in a duopoly supply chain network under the influence of different power-balance structures, bundling decisions and advertising efforts on total supply chain profit. Mathematical models comprising two manufacturers and a single retailer are developed to capture the impact of bundling policy and advertisement strategy under three power-balance structures, namely Manufacturer Stackelberg, Retailer Stackelberg and Vertical Nash. Following game theory models and numerical examples, the study found that the total profit of the supply chain is undifferentiated under the manufacturer Stackelberg and Vertical Nash case in the manufacturer bundling and retailer bundling strategies. However, total supply chain profit under manufacturer bundling strongly dominates under retailer bundling in Retailer Stackelberg and Vertical Nash, and remains valid under multiple settings of market size, price elasticity and advertising elasticity. It is also found that manufacturer bundling is significantly affected by advertising effort compared to retailer bundling. The study contributes to the literature interfacing supply chain and marketing by studying bundling policy and advertising strategy simultaneously for homogenous products, under various power-balance structures and price competition. [ABSTRACT FROM AUTHOR]

Abstract: Two players of Rock-Paper-Scissors are modeled as adaptive agents which use a reinforcement learning algorithm and exhibit chaotic behavior in terms of trajectories of probability in mixed strategies space. This paper demonstrates that an external super-agent can exploit the behavior of the other players to predict favorable moments to play against one of the other players the symbol suggested by a sub-optimal strategy. This third agent does not affect the learning process of the other two players, whose only goal is to beat each other. The choice of the best moment to play is based on a threshold associated with the Local Lyapunov Exponent or the Entropy, each computed by using the time series of symbols played by one of the other players. A method for automatically adapting such a threshold is presented and evaluated. The results show that these techniques can be used effectively by a super-agent in a game involving adaptive agents that exhibit collective chaotic behavior. [Copyright &y& Elsevier]