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.

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.

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.

Children cooperate more with in-group members than with out-group members in an iterated face-to-face Prisoner's Dilemma Game.

Adults are more likely to cooperate with in-group members than with out-group members in the context of social dilemmas, situations in which self-interest is in conflict with collective interest. This bias has the potential to profoundly shape human cooperation, and therefore it is important to understand when it emerges in development. Here we asked whether 6- to 9-year-old children (N = 146) preferentially cooperate with in-group members in the context of a well-studied social dilemma, the iterated Prisoner's Dilemma Game. We assigned children to minimal groups and paired them with unfamiliar same-age and same-gender peers. Consistent with our predictions, children were more likely to cooperate with in-group members than with out-group members in this minimal group context. This finding adds to the current literature on group bias in children's prosocial behavior by showing that it affects decision making in a context that calls on strategic cooperation. In addition, our analyses revealed an effect of gender, with girls more likely to cooperate than boys regardless of the group membership of their partner. Exploring this gender effect further, we found an interaction between gender and age across condition, with older girls showing less sensitivity to the group membership of their partner than younger girls and with older boys showing more sensitivity to the group membership of the partner than younger boys. Our findings suggest that risky cooperation in the face of social dilemmas is shaped by group bias during childhood, highlighting the potentially deeply rooted ties between cooperation and parochialism in humans.

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.

A game of raids: Expanding on a game theoretical approach utilising the prisoner's dilemma and ethnography in situ.

In this commentary, we set out the specifics of how Glowacki's game theoretical framework for the evolution of peace could be incorporated within broader cultural evolutionary approaches. We outline a formal proposal for prisoner's dilemma games investigating raid-based conflict. We also centre an ethnographic lens to understand the norms surrounding war and peace in intergroup interactions in small-scale communities.

People punish defection, not failures to conform to the majority.

Do people punish others for defecting or for failing to conform to the majority? In two experiments, we manipulated whether the participants' partners cooperated or defected in the majority of the trials of a Prisoner's Dilemma game. The effects of this base-rate manipulation on cooperation and punishment were assessed using a multinomial processing tree model. High compared to low cooperation rates of the partners increased participants' cooperation. When participants' cooperation was not enforced through partner punishment, the participants' cooperation was closely aligned to the cooperation rates of the partners. Moral punishment of defection increased when cooperation rates were high compared to when defection rates were high. However, antisocial punishment of cooperation when defection rates were high was much less likely than moral punishment of defection when cooperation rates were high. In addition, antisocial punishment was increased when cooperation rates were high compared to when defection rates were high. The latter two results contradict the assumption that people punish conformity-violating behavior regardless of whether the behavior supports or disrupts cooperation. Punishment is thus sensitive to the rates of cooperation and defection but, overall, the results are inconsistent with the idea that punishment primarily, let alone exclusively, serves to enforce conformity with the majority.

Computer anthropomorphisation in a socio-economic dilemma.

In the study of human behaviour, non-social targets are often used as a control for human-to-human interactions. However, the concept of anthropomorphisation suggests that human-like qualities can be attributed to non-human objects. This can prove problematic in psychological experiments, as computers are often used as non-social targets. Here, we assessed the degree of computer anthropomorphisation in a sequential and iterated prisoner's dilemma. Participants (N = 41) faced three opponents in the prisoner's dilemma paradigm-a human, a computer, and a roulette-all represented by images presented at the commencement of each round. Cooperation choice frequencies and transition probabilities were estimated within subjects, in rounds against each opponent. We found that participants anthropomorphised the computer opponent to a high degree, while the same was not found for the roulette (i.e. no cooperation choice difference vs human opponents; p = .99). The difference in participants' behaviour towards the computer vs the roulette was further potentiated by the precedent roulette round, in terms of both cooperation choice (61%, p = .007) and cooperation probability after reciprocated defection (79%, p = .007). This suggests that there could be a considerable anthropomorphisation bias towards computer opponents in social games, even for those without a human-like appearance. Conversely, a roulette may be a preferable non-social control when the opponent's abilities are not explicit or familiar.

Behavioral evidence for global consciousness transcending national parochialism.

While national parochialism is commonplace, individual differences explain more variance in it than cross-national differences. Global consciousness (GC), a multi-dimensional concept that includes identification with all humanity, cosmopolitan orientation, and global orientation, transcends national parochialism. Across six societies (N = 11,163), most notably the USA and China, individuals high in GC were more generous allocating funds to the other in a dictator game, cooperated more in a one-shot prisoner's dilemma, and differentiated less between the ingroup and outgroup on these actions. They gave more to the world and kept less for the self in a multi-level public goods dilemma. GC profiles showed 80% test-retest stability over 8 months. Implications of GC for cultural evolution in the face of trans-border problems are discussed.

The effect of similarity perceptions on human cooperation and confrontation.

By assuring aversive actions are followed by similarly aversive reactions, legislators of antiquity aimed to reduce belligerence and aggression. In the present study we show how similarity perceptions drive cooperation and confrontation across several strategic decision types. Examining the choices made in three one-shot symmetric conflict games: the prisoner's dilemma, the chicken, and the battle of the sexes, we show how a short encounter with a stranger accounts for the formation of subjective similarity perceptions, which together with the expected payoffs of the game determine the choice of the preferred alternative. We describe the role of similarity perceptions for all two-by-two games, specifically for a subset of fifty-seven games that are sensitive to similarity perceptions with the opponent. We then suggest that this mechanism, by which individuals maximize expected payoffs, is key to the understanding of the evolution of cooperation and confrontation.

Emotions and courtship help bonded pairs cooperate, but emotional agents are vulnerable to deceit.

Coordinated pair bonds are common in birds and also occur in many other taxa. How do animals solve the social dilemmas they face in coordinating with a partner? We developed an evolutionary model to explore this question, based on observations that a) neuroendocrine feedback provides emotional bookkeeping which is thought to play a key role in vertebrate social bonds and b) these bonds are developed and maintained via courtship interactions that include low-stakes social dilemmas. Using agent-based simulation, we found that emotional bookkeeping and courtship sustained cooperation in the iterated prisoner's dilemma in noisy environments, especially when combined. However, when deceitful defection was possible at low cost, courtship often increased cooperation, whereas emotional bookkeeping decreased it.