Chicken Game Research Articles

A complete classification of evolutionary games with environmental feedback

Abstract A tragedy of the commons, in which rational behavior of individuals to maximize their own payoffs depletes common resources, is one of the most important research topics in game theory. To better understand the social dilemma problem, recent studies have developed a theoretical framework of feedback-evolving game where individual behavior affects an environmental (renewable) resource and the environmental resource changes individual payoffs. While previous studies assumed that the frequency of defectors increases (prisoner's dilemma [PD] game) when the environmental resource is abundant to investigate an oscillating tragedy of the commons, it is also possible for other types of game to produce the social dilemma. In this paper, we extend the feedback-evolving game by considering not only PD game, but also the other three game structures when the environmental resource is replete for a reasonably complete classification. The three games are Chicken game where defectors and cooperators coexist through minority advantage, Stag-Hunt (SH) game with minority disadvantage, and Trivial game where the frequency of cooperators increases. In addition, we utilize a dilemma phase plane to visually track (transient) dynamics of game structure changes. We found that an emergent initial condition dependence (i.e. bistability) is pervasive in the feedback-evolving game when the three games are involved. We also showed that persistent oscillation dynamics arise even with Chicken or SH games in replete environments. Our generalized analysis will be an important step to further extend the theoretical framework of feedback-evolving game to various game situations with environmental feedback.

Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects.

Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.

Asymmetric Adaption in Social Learning: Understanding the Dilemma of Competition and Cooperation.

The constant challenge in social interactions involves making informed decisions in the face of competitive and cooperative dilemmas. The decision-making process can be influenced by various factors present in the social context. According to the behavior-pattern-categorization framework of information acquisition, potential biases may develop at all stages of decision-making as information about social context is progressively entered and integrated. In this study, employing the Chicken Game, we investigated the influence of varying information levels within the behavior-pattern-categorization framework (i.e., competitiveness of behavior choice, uncertainty of behavior pattern, and sociality of category) on decision-making in the dilemma of competition and cooperation. Combined with reinforcement learning models, our findings from three experiments showed that participants exhibited basic complementary behavior, becoming less competitive against highly competitive opponents and vice versa. Notably, individuals exhibited varying adaptation rates to different levels of opponent competitiveness and fluctuations. Specifically, participants adapted slower to highly competitive opponents and faster to cooperative opponents. This asymmetric adaptation in social learning is related to the rate at which various levels of information are updated. The current study disentangles the different levels of information acquisition and highlights the asymmetric processing that can occur during the updating of information within each level.

Quantum Chicken game under fluctuating quantum field

In this paper, we study the quantum Chicken game under fluctuating massless scalar field subjected to a reflecting boundary. The noisy scheme of quantum Chicken game affected by fluctuating scalar field is constructed. Then we analyze the influences of vacuum fluctuation, two-atom separation and boundary on the game payoff and Nash equilibrium. It is shown that for different strategy profiles, vacuum fluctuation, two-atom distance and atom-boundary distance have different influences on game payoffs. Vacuum fluctuation and two-atom distance may produce positive or negative effects on game payoffs dependent on the specific strategies. It is found that boundary can effectively promote the game payoffs corresponding to those strategy profiles with which payoffs are degraded by vacuum fluctuation. Furthermore, Nash equilibrium of the game is broken under the influence of fluctuating quantum field, but the game symmetry does not change. For long-time evolution, ([Formula: see text]) and ([Formula: see text]) turn into new Nash equilibria. The results would be helpful for understanding and conducting quantum Chicken game in an open quantum system.

Neural correlates of static and dynamic social decision-making in real-time sibling interactions.

In traditional game theory tasks, social decision-making is centered on the prediction of the intentions (i.e., mentalizing) of strangers or manipulated responses. In contrast, real-life scenarios often involve familiar individuals in dynamic environments. Further research is needed to explore neural correlates of social decision-making with changes in the available information and environmental settings. This study collected fMRI hyperscanning data (N = 100, 46 same-sex pairs were analyzed) to investigate sibling pairs engaging in an iterated Chicken Game task within a competitive context, including two decision-making phases. In the static phase, participants chose between turning (cooperate) and continuing (defect) in a fixed time window. Participants could estimate the probability of different events based on their priors (previous outcomes and representation of other's intentions) and report their decision plan. The dynamic phase mirrored real-world interactions in which information is continuously changing (replicated within a virtual environment). Individuals had to simultaneously update their beliefs, monitor the actions of the other, and adjust their decisions. Our findings revealed substantial choice consistency between the two phases and evidence for shared neural correlates in mentalizing-related brain regions, including the prefrontal cortex, temporoparietal junction (TPJ), and precuneus. Specific neural correlates were associated with each phase; increased activation of areas associated with action planning and outcome evaluation were found in the static compared with the dynamic phase. Using the opposite contrast, dynamic decision-making showed higher activation in regions related to predicting and monitoring other's actions, including the anterior cingulate cortex and insula. Cooperation (turning), compared with defection (continuing), showed increased activation in mentalizing-related regions only in the static phase, while defection, relative to cooperation, exhibited higher activation in areas associated with conflict monitoring and risk processing in the dynamic phase. Men were less cooperative and had greater TPJ activation. Sibling competitive relationship did not predict competitive behavior but showed a tendency to predict brain activity during dynamic decision-making. Only individual brain activation results are included here, and no interbrain analyses are reported. These neural correlates emphasize the significance of considering varying levels of information available and environmental settings when delving into the intricacies of mentalizing during social decision-making among familiar individuals.

THE PROBLEM OF MODEL ADEQUACY IN THE APPLICATION OF GAME THEORY IN INTERNATIONAL RELATIONS

The article considers the use of game theory in international relations and the risks associated with it. An analysis is made of the possibility of reflecting the same real situations using different game models with different connotations. The concept of the adequacy of the model in relation to the situation is considered, as well as the necessary logical stage of proving this adequacy and the risk of manipulative influence in the absence of such proof. Attention is paid to the phenomenon of the model itself and its relation to the real object of modeling.The opinion is argued about the need to prove the similarity before using the analogy as an argument for attempts to persuade on the basis of this similarity. The mechanism of manipulation is considered in which, by skipping the discussion of the adequacy of the model, it is automatically considered adequate, so the author of the model can impose his own forecasts on the consumer of information regarding the development of events, as well as his own subjective vision of the positivity of the results.As an example, two well-known problems in game theory are considered, actively used for modeling international relations: the Prisoner's Dilemma and the Chicken game. An example of modeling the same hypothetical situation using both games and differences in subjective perception of the same results, which are manifested in the choice of which of these games to use, is given. The opinion is given that although both games can be very useful in the field of international relations, when consuming information which incorporates these and other games, it is necessary to carefully check not only the author's forecasts regarding the development of events, but also the assessment of the positivity of the results in the model.

Risk-dominant Equilibrium in Chicken and Stag-hunt Games with Different Dilemma Strengths

Objective: This study investigates how the strength of risk-averting and gamble-intending dilemmas can affect the risk-dominant equilibrium in chicken and stag-hunt games. The focus is on deriving conditions under which the risk-dominant equilibrium can maximize group benefit. Methods: Basic concepts of game theory were used to determine the Nash equilibria of each game.The Harsanyi-Selten theory was applied to determine the risk-dominant equilibrium. By manipulating the parameters related to risk-averting and gamble-intending dilemmas, different game scenarios are sim-ulated to observe the resulting equilibria. Results: The study found that for a given strength of the risk-averting dilemma, the risk-dominant equilibrium in the chicken game continuously shifts towards mutual cooperation as the strength of the gamble-intending dilemma decreases. In the SH game, the degree of cooperation of the risk-dominant equilibrium for a given strength of the gamble-intending dilemma decreases with increasing strength of the risk-averting dilemma and takes the discrete values: 1, 0.5 and 0. The results show the importance of understanding individual risk preferences to predict strategic decisions and equilibrium outcomes in these game settings. Conclusion: The risk-dominant equilibrium in chicken and stag-hunt games depends on the relative strength of the risk-averting and gamble-intending dilemmas. By taking these factors into account, researchers and policy makers can better predict the likely outcomes of strategic interactions in scenarios with conflicting interests and different risk tolerances. The risk-dominant equilibrium can provide reasonable solutions to real-world conflict situations, such as the Iran-Iraq conflict over shared oil and gas resources.

The added value of perceived values: Partner's perceived values predict own behaviour in interdependent interactions

AbstractPersonal values have been widely recognized as important determinants of individuals’ behaviour. But can behaviour be shaped by the values one attributes to others? Focusing on interdependent interactions, this research integrates literature on personal values and the role of expectations in social dilemmas to investigate the overlooked effect of value perceptions on people's choices. In Study 1, players in a prisoner's dilemma (a game capturing cooperation vs. competition) who were informed that their partner prioritized self‐transcendence values tended to cooperate more than players informed that the partner prioritized self‐enhancement values. In Study 2, players in the same game who assumed their partner was higher in self‐transcendence values and lower in self‐enhancement values were more likely to opt for the cooperative choice. In Study 3, players in a chicken game (a game capturing risk‐taking vs. risk‐avoidance) who assumed their partner was higher in conservation values and lower in openness‐to‐change values were more likely to opt for the riskier choice in the game. Study 4 indicated that the effect of perceived values on behaviour is mediated by assumptions regarding the partner's choice. Perceived values of the other side predicted behaviour beyond the perceiver's own values. We discuss the relationships between own and perceived values and our contributions to the values literature and conflict research.

Online Assessment of Social Cognition in a Population of Gamers and Gamblers: Results of the eSMILE Study

The purpose of the eSMILE study was to explore social cognition (SC) in the two behavioural addictions (BAs) included in international classifications: gaming disorder and gambling disorder. In these disorders, cognitive functioning is involved in the development and maintenance of addiction. Nevertheless, SC have received less attention than other cognitive functions. The eSMILE study was conducted online and included 105 participants (gamers and gamblers). This study included: the Penn emotion recognition task, the Condensed and Revised Multifaced Empathy Test, the Interpersonal Reactivity Index, the Chicken Game, social metacognition questions, and the Toronto Alexithymia Scale. We analysed the relationships among SC measures, addiction levels, and behaviour frequency. For gamers, we showed that the higher their level of addiction was, the lower their self-confidence following the identification of basic emotions, although the more frequently they played, the better their performance on this task. Additionally, we found lower performance on the identification of more complex emotions by gamblers, which seems to be the result of their levels of addiction rather than the frequency of their gambling behaviour. This study contributes to our understanding of the cognitive processes underlying BAs. Additionally, working on SC abilities may be an additional management mode for BAs that could be added to existing treatments.

Joint Probabilities Approach to Quantum Games with Noise.

A joint probability formalism for quantum games with noise is proposed, inspired by the formalism of non-factorizable probabilities that connects the joint probabilities to quantum games with noise. Using this connection, we show that the joint probabilities are non-factorizable; thus, noise does not generically destroy entanglement. This formalism was applied to the Prisoner's Dilemma, the Chicken Game, and the Battle of the Sexes, where noise is coupled through a single parameter μ. We find that for all the games except for the Battle of the Sexes, the Nash inequalities are maintained up to a threshold value of the noise. Beyond the threshold value, the inequalities no longer hold for quantum and classical strategies. For the Battle of the sexes, the Nash inequalities always hold, no matter the noise strength. This is due to the symmetry and anti-symmetry of the parameters that determine the joint probabilities for that game. Finally, we propose a new correlation measure for the games with classical and quantum strategies, where we obtain that the incorporation of noise, when we have quantum strategies, does not affect entanglement, but classical strategies result in behavior that approximates quantum games with quantum strategies without the need to saturate the system with the maximum value of noise. In this manner, these correlations can be understood as entanglement for our game approach.

The role of dominance in sibling relationships: differences in interactive cooperative and competitive behavior

Siblings strongly influence each other in their social development and are a major source of support and conflict. Yet, studies are mostly observational, and little is known about how adult sibling relationships influence social behavior. Previous tasks exploring dynamically adjusting social interactions have limitations in the level of interactivity and naturalism of the interaction. To address these limitations, we created a cooperative tetris puzzle-solving task and an interactive version of the chicken game task. We validated these two tasks to study cooperative and competitive behavior in real-time interactions (N = 56). Based on a dominance questionnaire (DoPL), sibling pairs were clustered into pairs that were both low in dominance (n = 7), both high in dominance (n = 8), or one low and one high in dominance (n = 13). Consistent with our hypothesis, there were significantly more mutual defections, less use of turn-taking strategies, and a non-significant trend for reduced success in solving tetris puzzles together among high dominance pairs compared to both other pair types. High dominant pairs also had higher Machiavellian and hypercompetitiveness traits and more apathetic sibling relationships. Both tasks constitute powerful and reliable tools to study personality and relationship influences on real and natural social interactions by demonstrating the different cooperative and competitive dynamics between siblings.

Effect of warning signs on the epidemic spreading of the COVID-19 pandemic

Early warning signs of the outbreak of pandemic disease become a high profile from the beginning and they remind more susceptible individuals to keep social distance on social occasions. However, these signs have no way to the Susceptible–Infected–Recovered (SIR) models which have been concerned by medical scientists. Warning signs imply the risk level of the pandemic disease evaluated by the government. The response of susceptible population ([Formula: see text]-population) to the warning signs is represented by a chicken game. In order to get a better payoff, the more beneficial behavior of the [Formula: see text]-population may be induced in the autonomous society based on the SIR model. We emphasize that participants can choose their strategies whether to follow the health rules or not without coercion in the chicken game while the warning signs released by the policy makers can encourage [Formula: see text]-population to choose beneficial behavior, instead of purely following the healthy rules or not. The agile policy helps [Formula: see text]-population to make a choice on the basis of risk interests but without losing to protect themselves in a serious pandemic situation. Comparing the classic SIR model with our signal-SIR model, the serious pandemic signal released by the policy makers and the disease awareness to it together play an important role in the outbreak period of the pandemic disease.

Managing strategic inventory under retailer competition

Besides carrying the operational inventory, retailers may invest in the strategic inventory for obtaining the discount of future wholesale price, although this behavior can induce the holding cost. In this paper, we adopt a game theoretical method to check the role of strategic inventory under the retailer-to-retailer competition. The impact of strategic inventory on a two-tier supply chain model is investigated under the retailer competition. A supplier sells products to customers through two competing retailers who may choose to carry the strategic inventory in a two-period setting. The results indicate that the retailer-to-retailer competition may affect the decisions of supply chain parties about the strategic inventory and pricing as follows. First, the competition weakens the incentives of retailers in holding the strategic inventory. Second, the lower inventory holding expense would still stimulate retailers to hold the strategic inventory for more profits. Third, facing two competing and asymmetric retailers, the prisoner's dilemma and chicken game equilibrium may occur between the two retailers when the inventory holding cost is intermediate under the uniform wholesale price strategy. However, under the differentiated wholesale price strategy, the prisoner's dilemma and chicken game equilibrium can be eliminated. For similar operational styles including store styles and locations, retailers can break through the dilemma by simultaneously holding the strategic inventory, and can obtain more profits from carrying strategic inventory under differentiated wholesale price strategy. Therefore, the differentiated wholesale price strategy can promote the two retailers to cooperate with each other and can benefit all parties.

Applying Game Theory Models to Inpatient Medicine: Opportunities to Improve Care.

Inpatient hospital costs have been increasing exponentially in the United States. Part of this increase is attributed to over and undertreatment, leading to higher costs and potential patient harm. Research improving clinician-patient interactions can help minimize and optimize the costs. Game theory has the ability improve clinician-patient interaction by modeling outcomes. Using variations of game theory, the bad doctor bad patient stigma can reframed to incentives. We believe the use of different models (prisoner dilemma, centipede game, assurance game, and chicken game) can outline the challenges faced during common inpatient scenarios, including end of life conversations and aggressive procedures. Applying game theory to multiple inpatient scenarios may also assist with analysis during morbidity and mortality conferences and quality improvement projects.

Procedural fairness facilitates cooperative behavior by enhancing cooperative expectations

AbstractTwo experiments were conducted to explore whether and why procedural fairness may promote cooperation. In both experiments, participants first took part in a task in which they were connected to an allocator who then either selected a fair or an unfair procedure for allocating outcomes between them. After this manipulation of procedural fairness, participants performed a second task in which we studied their cooperation in a chicken game. In Experiment 1, participants were informed that their opponent in the chicken game was the same person who had previously selected the fair (vs. unfair) procedure. In Experiment 2, participants learned that their opponent in the chicken game had not been involved in the selection of the prior procedure. Both studies showed that having experienced a fair (vs. unfair) procedure facilitated subsequent cooperation in the chicken game. Mediation analyses suggest that this positive effect was explained by the finding that the prior experience of procedural fairness induced participants to expect higher levels of cooperation from their opponent, even when this opponent was not involved in the prior experience of procedural fairness.

On the empirical relevance of correlated equilibrium

Absent coordinating signals from an exogenous benevolent agent, can an efficient correlated equilibrium emerge? Theoretical work in adaptive dynamics suggests a positive answer, which we test in a laboratory experiment. In the well-known Chicken game, we observe time average play that is close to the asymmetric pure Nash equilibrium in some treatments, and in other treatments we observe collusive play. In a game resembling rock-paper-scissors or matching pennies, we observe time average play close to a correlated equilibrium that is more efficient than the unique Nash equilibrium. Estimates and simulations of adaptive dynamics capture much of the observed heterogeneity across player pairs as well as dynamic regularities.

The chicken game jako model eksplanacyjno-prognostyczny w polityce

“CHICKEN GAME” AS AN EXPLANATORY AND PROGNOSTIC MODEL IN POLITICS
 The main aim of the article is to present one of the game theory models: chicken game. This model is highly valuable in the processes of analysis and forecasting of the behavior of political decision-makers. Chicken game combines the basic assumptions for game theory based on a rational model and elements of optimizing the results of political games through psychological influence, resisting blackmail, and intimidation of other players. The widespread use of such tactics and strategies justifies a closer and in-depth analysis of this model.

Discriminability of single-trial EEG during decision-making of cooperation or aggression: a study based on machine learning

Decision-making is a very important cognitive process in our daily life. There has been increasing interest in the discriminability of single-trial electroencephalogram (EEG) during decision-making. In this study, we designed a machine learning based framework to explore the discriminability of single-trial EEG corresponding to different decisions. For each subject, the framework split the decision-making trials into two parts, trained a feature model and a classifier on the first part, and evaluated the discriminability on the second part using the feature model and classifier. A proposed algorithm and five existing algorithms were applied to fulfill the feature models, and the algorithm Linear Discriminative Analysis (LDA) was used to implement the classifiers. We recruited 21 subjects to participate in Chicken Game (CG) experiments. The results show that there exists the discriminability of single-trial EEG between the cooperation and aggression decisions during the CG experiments, with the classification accuray of 75% (±6%), and the discriminability is mainly from the EEG information below 40 Hz. The further analysis indicates that the contributions of different brain regions to the discriminability are consistent with the existing knowledge on the cognitive mechanism of decision-making, confirming the reliability of the conclusions. This study exhibits that it is feasible to apply machine learning methods to EEG analysis of decision-making cognitive process.

To make or to buy from a common supplier? Strategic considerations and welfare consequences

AbstractConsider two downstream firms that each can either produce an input in‐house or purchase it from an upstream supplier. We show that depending on the difference between the supplier's and the downstream firms' in‐house production costs, outsourcing by both firms could help them achieve a Pareto improvement or leave them trapped in a prisoner's dilemma. Furthermore, we find that two downstream firms may play a chicken game in which each makes a sourcing decision different from its rival if the input supplier is not as efficient as in the previous cases. The welfare implications of various sourcing outcomes are explored.

Research on Cobot Action Decision-Making Method Based on Intuitionistic Fuzzy Set and Game Theory

The bounded rational properties of humans in human-robot collaboration (HRC) is a fundamental reason for collisions in proximity HRC. As HRC scenarios in manufacturing become increasingly popular, robot action decision-making needs to consider such properties of humans. In previous studies, humans are usually considered as rational agents whose behaviors are predictable and planned, but humans are susceptible to distractions caused by external disturbances, and different cognitive processes of the task can produce unpredictable behaviors. To better simulate human bounded rational behavior, based on an intuitionistic fuzzy (IF) multi-attribute decision algorithm, we propose a cobot action decision-making method that integrates human intention, safety, and efficiency, to produce a human-like decision. The proposed decision-making method integrates the bounded rational behavior of humans and establishes the IF set of human action intention for efficiency and comfort using cumulative prospect theory(CPT) and IF set. The proposed method lights on the human decision-making mechanism for proximity HRC actions. We use IF set to calculate the score and accuracy values of two Nash equilibria of a static chicken game, which can predict human action intentions with collision risk and provide optimal action decisions for the robot simultaneously. We generated 10,000 sets of data using the Monte Carlo method and validated the effectiveness of our proposed method by comparing it with MDP and POMDP methods. The results showed that the decision-making method could effectively perform the task of making action decisions for the robot. Simulation experiments and Turing test results show that our proposed method can predict a human’s subjective action decision intention in a situation with potential collision risk with 87.53% accuracy. At the same time, the experimental participants believe that the robot can get 4.83 out of 5 satisfaction points for an action decision.