The role of facial cues in signalling cooperativeness is limited and nuanced.

Humans display a remarkable tendency to cooperate with strangers; however, identifying prospective cooperation partners accurately before entering any new relationship is essential to mitigate the risk of being exploited. Visual appearance, as inferrable, for example, from facial images on job portals and dating sites, may serve as a potential signal of cooperativeness. This experimental study examines whether static images enable the correct detection of an individual's propensity to cooperate. Participants first played the Prisoner's Dilemma (PD) game, a standard cooperation task. Subsequently, they were asked to predict the cooperativeness of participants from a prior PD study relying solely on their static facial photographs. While our main results indicate only marginal accuracy improvements over random guessing, a more detailed analysis reveals that participants were more successful at identifying cooperative tendencies similar to their own. Despite no detectable main effect in our primary treatment variations (time pressure versus time delay), participants exhibited increased accuracy in identifying male cooperators under time pressure. These findings point towards a limited yet nuanced role of static facial images in predicting cooperativeness, advancing our understanding of non-behavioral cues in cooperative interactions.

Behavioural strategies in simultaneous and alternating prisoner's dilemma games with/without voluntary participation.

The Prisoner's Dilemma is one of the most classic formats for exploring the principle of direct reciprocity. Although numerous theoretical and experimental studies have been conducted, little attention has been paid to the divergence between theoretical predictions and actual human behaviour. In addition, there are two additional essential challenges of experimental research. First, most experimental approaches have focused on games in which two players decide their actions simultaneously, but little is known about alternating games. Another is that there are few experiments on voluntary participation. Here, we conducted experiments on simultaneous games, alternating games, and games with and without voluntary participation for a total of four game patterns and examined the deviation from theoretical predictions for each. The results showed that, contrary to theoretical predictions, humans chose cooperation even after being exploited. We also observed that, with or without voluntary participation, people tended to take the same action they had taken in the previous round. Our results indicate that to understand the mechanisms of human behaviour, we need to integrate findings from behavioural science, psychology, and game theory.

Emergence of cooperation in the one-shot Prisoner's dilemma through Discriminatory and Samaritan AIs.

As artificial intelligence (AI) systems are increasingly embedded in our lives, their presence leads to interactions that shape our behaviour, decision-making and social interactions. Existing theoretical research on the emergence and stability of cooperation, particularly in the context of social dilemmas, has primarily focused on human-to-human interactions, overlooking the unique dynamics triggered by the presence of AI. Resorting to methods from evolutionary game theory, we study how different forms of AI can influence cooperation in a population of human-like agents playing the one-shot Prisoner's dilemma game. We found that Samaritan AI agents who help everyone unconditionally, including defectors, can promote higher levels of cooperation in humans than Discriminatory AI that only helps those considered worthy/cooperative, especially in slow-moving societies where change based on payoff difference is moderate (small intensities of selection). Only in fast-moving societies (high intensities of selection), Discriminatory AIs promote higher levels of cooperation than Samaritan AIs. Furthermore, when it is possible to identify whether a co-player is a human or an AI, we found that cooperation is enhanced when human-like agents disregard AI performance. Our findings provide novel insights into the design and implementation of context-dependent AI systems for addressing social dilemmas.

Evolutionary dynamics of cooperation coupled with ecological feedback compensation.

A simple theoretical model (or a demonstrative example) was developed to illustrate how the evolution of cooperation can be affected by the density-dependent survival competition, in which we assume that the fertility of an individual depends only on the pairwise interaction between him and other individuals based on Prisoner's Dilemma game, while its viability is only related to the density-dependent survival competitiveness. Our results show that not only cooperation could be evolutionarily stable if the advantage of cooperators in viability can compensate for the cost they pay for their fertility, but also the long-term stable coexistence of cooperation and defection is possible if none of cooperation and defection is evolutionarily stable. Moreover, for the stochastic evolutionary dynamics in a finite population, our analysis shows that the increase (or decrease) of the survival competitiveness of cooperators (or defectors) should be conductive to the evolutionary emergence of cooperation.

Memory and target payoff enhance cooperation in evolutionary social dilemmas.

We proposed a neighbor selection mechanism based on memory and target payoff, where the target payoff is the maximum value of the group's average expected payoff. According to this mechanism, individuals prioritize selecting neighbors whose average payoffs in the last M rounds are close to the target payoff for strategy learning, aiming to maximize the group's expected payoff. Simulation results on the grid-based Prisoner's Dilemma and Snowdrift games demonstrate that this mechanism can significantly improve the group's payoff and cooperation level. Furthermore, the longer the memory length, the higher the group's payoff and cooperation level. Overall, the combination of memory and target payoff can lead to the emergence and persistence of cooperation in social dilemmas as individuals are motivated to cooperate based on both their past experiences and future goals. This interplay highlights the significance of taking into account numerous variables in comprehending and promoting cooperation within evolutionary frameworks.

The effect of multi-tasks mechanism on cooperation in evolutionary game.

Human games are inherently diverse, involving more than mere identity interactions. The diversity of game tasks offers a more authentic explanation in the exploration of social dilemmas. Human behavior is also influenced by conformity, and prosociality is a crucial factor in addressing social dilemmas. This study proposes a generalized prisoner's dilemma model of task diversity that incorporates a conformity-driven interaction. Simulation findings indicate that the diversity of multi-tasks and the path dependence contribute to the flourishing of cooperation in games. Conformity-driven interactions also promote cooperation. However, this promotion effect does not increase linearly, and only appropriate task sizes and suitable proportions of conformity-driven interactions yield optimal results. From a broader group perspective, the interplay of network adaptation, task size, and conformity-driven interaction can form a structure of attractors or repellents.

Cooperation dynamics of prisoner's dilemma games on an evolutionary weighted network with heterogeneous preferences.

Relationships between people in real life are dynamically changed with the interaction process, and due to the heterogeneous preferences, this change is different from person to person. Based on this observation, we propose a new spatial and weighted prisoner's dilemma game model with heterogeneous individuals. Two types of tags, namely, tag-F (concerned about social fairness) and tag-W (concerned about personal well-being), are introduced to describe individuals' different preferences. The link weights indicating the interaction strength between individuals are updated based on different rules that depend on their tags. Through simulations, we verify that a large link weight control factor and a high proportion of tag-F individuals favor the emergence and persistence of cooperation. In addition, an increase in the link weight sensitivity factor favors the evolution of cooperation when the link weight control factor is small. Moreover, while the level of cooperation increases with the proportion of tag-F type in the population, contrary to our intuition, when the population consists entirely of tag-F individuals, in some cases, cooperation cannot reach a higher level compared with the situation when they are mixed with tag-W type. However, at high dilemma intensities, cooperators emerge only when the entire population consists of tag-F type. These results may provide some new insights into the impact of the evolutionary weighted network with heterogeneous preferences on collective cooperative behavior.

Two-stage strategy update rule based on learning cost in weak prisoner's dilemma.

When players are dissatisfied with their actual payoffs, they will change the actuality by learning strategy of neighbors. The more effort players put in, the more likely they are to succeed in learning. Inspired by this, this paper proposes a two-stage strategy update rule based on learning cost. The players first decide whether to learn strategy according to the updating willingness. If the players imitate the strategy of neighbors, they need to pay the learning cost. Results show that for the well-mixed population, if the updating willingness is homogeneous and remains unchanged, reducing the updating willingness or increasing the learning cost can extend the life cycle of cooperators. If the updating willingness is heterogeneous and dynamically adjusted based on the difference between the actual payoff and the expected payoff, increasing aspiration value and learning cost promotes cooperation. For the structured population, if the updating willingness is homogeneous and remains unchanged, the moderate learning cost is beneficial for cooperators to resist the temptation of defection, and reducing updating willingness makes the system maintain cooperation within a larger parameter range. If the updating willingness is heterogeneous and dynamically adjusted, the larger learning cost and the appropriate aspiration value promote cooperation. This study highlights the complex dynamics of cooperation in paid strategy learning, contributing to the theory of cooperation in the evolutionary game.

Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner's Dilemma.

Establishing and maintaining mutual cooperation in agent-to-agent interactions can be viewed as a question of direct reciprocity and readily applied to the Iterated Prisoner's Dilemma. Agents cooperate, at a small cost to themselves, in the hope of obtaining a future benefit. Zero-determinant strategies, introduced in 2012, have a subclass of strategies that are provably extortionate. In the established literature, most of the studies of the effectiveness or lack thereof, of zero-determinant strategies is done by placing some zero-determinant strategy in a specific scenario (collection of agents) and evaluating its performance either numerically or theoretically. Extortionate strategies are algebraically rigid and memory-one by definition, and requires complete knowledge of a strategy (the memory-one cooperation probabilities). The contribution of this work is a method to detect extortionate behaviour from the history of play of an arbitrary strategy. This inverts the paradigm of most studies: instead of observing the effectiveness of some theoretically extortionate strategies, the largest known collection of strategies will be observed and their intensity of extortion quantified empirically. Moreover, we show that the lack of adaptability of extortionate strategies extends via this broader definition.

Third-party arbitration and forgiving strategies increase cooperation when perception errors are common.

Humans cooperate in groups in which mutual monitoring is common, and this provides the possibility of third-party arbitration. Third-party arbitration stabilizes reciprocity in at least two ways: first, when it is accurate, it reduces the frequency of misunderstandings resulting from perception errors, and second, even when it is inaccurate, it provides a public signal that allows pairs to align their expectations about how to behave after errors occur. Here, we describe experiments that test for these two effects. We find that in an iterated, sequential Prisoner's Dilemma game with errors, players with the highest average payoffs are those who make use of third-party arbitration and who also employ forgiving strategies. The combination of these two behaviours reduces the detrimental effects of errors on reciprocity, resulting in more cooperation.

Time pressure and deliberation affect moral punishment.

The deliberate-morality account implies that moral punishment should be decreased with time pressure and increased with deliberation while the intuitive-morality account predicts the opposite. In three experiments, moral punishment was examined in a simultaneous one-shot Prisoner's Dilemma game with a costly punishment option. The players cooperated or defected and then decided whether or not to punish their partners. In Experiment 1, the punishment decisions were made without or with time pressure. In Experiment 2, the punishment decisions were immediate or delayed by pauses in which participants deliberated their decisions. In Experiment 3, participants were asked to deliberate self-interest or fairness before deciding whether to punish their partners. Different types of punishment were distinguished using the cooperation-and-punishment model. In Experiment 1, time pressure decreased moral punishment. In Experiment 2, deliberation increased moral punishment. So far, the evidence supports the deliberate-morality account. Experiment 3 demonstrates that the effect of deliberation depends on what is deliberated. When participants deliberated self-interest rather than fairness, moral punishment was decreased. The results suggest that unguided deliberation increases moral punishment, but the effects of deliberation are modulated by the type of deliberation that takes place. These results strengthen a process-based account of punishment which offers a more nuanced understanding of the context-specific effect of deliberation on moral punishment than the deliberate-morality account.

The evolution of social behaviors and risk preferences in settings with uncertainty.

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner's Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world.

Game-theoretic agent-based modelling of micro-level conflict: Evidence from the ISIS-Kurdish war.

This article delves into the dynamics of a dyadic political violence case study in Rojava, Northern Syria, focusing on the conflict between Kurdish rebels and ISIS from January 1, 2017, to December 31, 2019. We employ agent-based modelling and a formalisation of the conflict as an Iterated Prisoner's Dilemma game. The study provides a nuanced understanding of conflict dynamics in a highly volatile region, focusing on microdynamics of an intense dyadic strategic interaction between two near-equally- powered actors. The choice of using a model based on the Iterated Prisoner's Dilemma, though a classical approach, offers substantial insights due to its ability to model dyadic, equally-matched strategic interactions in conflict scenarios effectively. The investigation primarily reveals that shifts in territorial control are more critical than geographical or temporal factors in determining the conflict's course. Further, the study observes that the conflict is characterised by periods of predominantly one-sided violence. This pattern underscores that the distribution of attacks, and target choices are a more telling indicator of the conflict nature than specific behavioural patterns of the actors involved. Such a conclusion aligns with the strategic implications of the underlying model, which emphasises the outcome of interactions based on differing aggression levels. This research not only sheds light on the conflict in Rojava but also reaffirms the relevance of this type of game-theoretical approach in contemporary conflict analysis.

Ovarian hormones predict cooperative strategies updating during multiple rounds of the prisoner's dilemma.

Increasing research has focused on how ovarian hormones influence individual prosocial motivation and cooperation. However, most results remain ambiguous and contradictory. Here, we collected progesterone (PROG) and oestradiol from 62 healthy women with regular menstrual cycles to explore whether variations in ovarian hormones could flexibly change their cooperative preference according to their opponents' strategies in multiple rounds of a prisoner's dilemma (PD) game. Participants in different menstrual phases (32 in the follicular phase [FP] and 30 in the luteal phase [LP]) were asked to complete 20 rounds of PD games with each of three computer opponents holding different cooperative strategies. The results revealed that in PD games that did not require cooperation for increased outcomes, women in the LP (high PROG) reduced their cooperation rate more significantly than women in the FP (low PROG). In contrast, when the game design required reciprocity, simultaneously elevated levels of PROG and oestradiol predicted greater instances of participants choosing to cooperate. Furthermore, we found that elevated PROG levels accounted for women's elevated prosocial choices, regardless of the need to increase outcomes through cooperation. These results implied higher levels of PROG and oestradiol influence women's cooperative strategies resulting in increased social interactions.

The Importance of Being Consistent: Attribution of Mental States in Strategic Human-Robot Interactions.

This article investigates the attribution of mental state (AMS) to an anthropomorphic robot by humans in a strategic interaction. We conducted an experiment in which human subjects are paired with either a human or an anthropomorphic robot to play an iterated Prisoner's Dilemma game, and we tested whether AMS is dependent on the robot "consistency," that is, the correspondence between the robot's verbal reaction and its behavior after a nonoptimal social outcome of the game is obtained. We find that human partners are attributed a higher mental state level than robotic partners, regardless of the partner's consistency between words and actions. Conversely, the level of AMS assigned to the robot is significantly higher when the robot is consistent in its words and actions. This finding is robust to the inclusion of psychological factors such as risk attitude and trust, and it holds regardless of subjects' initial beliefs about the adaptability of the robot. Finally, we find that when the robot apologizes for its behavior and defects in the following stage, the epistemic component of the AMS significantly increases.

Belief Updating during Social Interactions: Neural Dynamics and Causal Role of Dorsomedial Prefrontal Cortex.

In competitive interactions, humans have to flexibly update their beliefs about another person's intentions in order to adjust their own choice strategy, such as when believing that the other may exploit their cooperativeness. Here we investigate both the neural dynamics and the causal neural substrate of belief updating processes in humans. We used an adapted prisoner's dilemma game in which participants explicitly predicted the coplayer's actions, which allowed us to quantify the prediction error between expected and actual behavior. First, in an EEG experiment, we found a stronger medial frontal negativity (MFN) for negative than positive prediction errors, suggesting that this medial frontal ERP component may encode unexpected defection of the coplayer. The MFN also predicted subsequent belief updating after negative prediction errors. In a second experiment, we used transcranial magnetic stimulation (TMS) to investigate whether the dorsomedial prefrontal cortex (dmPFC) causally implements belief updating after unexpected outcomes. Our results show that dmPFC TMS impaired belief updating and strategic behavioral adjustments after negative prediction errors. Taken together, our findings reveal the time course of the use of prediction errors in social decisions and suggest that the dmPFC plays a crucial role in updating mental representations of others' intentions.

What is Quantum in probabilistic explanations of the sure-thing principle violation?

The Prisoner's Dilemma game (PDG) is one of the simple test-beds for the probabilistic nature of the human decision-making process. Behavioral experiments have been conducted on this game for decades and show a violation of the so-called sure-thing principle, a key principle in the rational theory of decision. Quantum probabilistic models can explain this violation as a second-order interference effect, which cannot be accounted for by classical probability theory. Here, we adopt the framework of generalized probabilistic theories and approach this explanation from the viewpoint of quantum information theory to identify the source of the interference. In particular, we reformulate one of the existing quantum probabilistic models using density matrix formalism and consider different amounts of classical and quantum uncertainties for one player's prediction about another player's action in PDG. This enables us to demonstrate that what makes possible the explanation of the violation is the presence of quantum coherence in the player's initial prediction and its conversion to probabilities during the dynamics. Moreover, we discuss the role of other quantum information-theoretical quantities, such as quantum entanglement, in the decision-making process. Finally, we propose a three-choice extension of the PDG to compare the predictive powers of quantum probability theory and a more general probabilistic theory that includes it as a particular case and exhibits third-order interference.

Cooperation transitions in social games induced by aspiration-driven players.

Cooperation and defection are social traits whose evolutionary origin is still unresolved. Recent behavioral experiments with humans suggested that strategy changes are driven mainly by the individuals' expectations and not by imitation. This work theoretically analyzes and numerically explores an aspiration-driven strategy updating in a well-mixed population playing games. The payoffs of the game matrix and the aspiration are condensed into just two parameters that allow a comprehensive description of the dynamics. We find continuous and abrupt transitions in the cooperation density with excellent agreement between theory and the Gillespie simulations. Under strong selection, the system can display several levels of steady cooperation or get trapped into absorbing states. These states are still relevant for experiments even when irrational choices are made due to their prolonged relaxation times. Finally, we show that for the particular case of the prisoner dilemma, where defection is the dominant strategy under imitation mechanisms, the self-evaluation update instead favors cooperation nonlinearly with the level of aspiration. Thus, our work provides insights into the distinct role between imitation and self-evaluation with no learning dynamics.

Complex pathways to cooperation emergent from asymmetry in heterogeneous populations.

Cooperation within asymmetric populations has garnered significant attention in evolutionary games. This paper explores cooperation evolution in populations with weak and strong players, using a game model where players choose between cooperation and defection. Asymmetry stems from different benefits for strong and weak cooperators, with their benefit ratio indicating the degree of asymmetry. Varied rankings of parameters including the asymmetry degree, cooperation costs, and benefits brought by weak players give rise to scenarios including the prisoner's dilemma (PDG) for both player types, the snowdrift game (SDG), and mixed PDG-SDG interactions. Our results indicate that in an infinite well-mixed population, defection remains the dominant strategy when strong players engage in the prisoner's dilemma game. However, if strong players play snowdrift games, global cooperation increases with the proportion of strong players. In this scenario, strong cooperators can prevail over strong defectors when the proportion of strong players is low, but the prevalence of cooperation among strong players decreases as their proportion increases. In contrast, within a square lattice, the optimum global cooperation emerges at intermediate proportions of strong players with moderate degrees of asymmetry. Additionally, weak players protect cooperative clusters from exploitation by strong defectors. This study highlights the complex dynamics of cooperation in asymmetric interactions, contributing to the theory of cooperation in asymmetric games.