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.

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.

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.

Reputations for treatment of outgroup members can prevent the emergence of political segregation in cooperative networks.

Reputation systems promote cooperation and tie formation in social networks. But how reputations affect cooperation and the evolution of networks is less clear when societies are characterized by fundamental, identity-based, social divisions like those centered on politics in the contemporary U.S. Using a large web-based experiment with participants (N = 1073) embedded in networks where each tie represents the opportunity to play a dyadic iterated prisoners' dilemma, we investigate how cooperation and network segregation varies with whether and how reputation systems track behavior toward members of the opposing political party (outgroup members). As predicted, when participants know others' political affiliation, early cooperation patterns show ingroup favoritism. As a result, networks become segregated based on politics. However, such ingroup favoritism and network-level political segregation is reduced in conditions in which participants know how others behave towards participants from both their own party and participants from the other party. These findings have implications for our understanding of reputation systems in polarized contexts.

Game-theoretical description of the go-or-grow dichotomy in tumor development for various settings and parameter constellations.

A medically important feature of several types of tumors is their ability to "decide" between staying at a primary site in the body or leaving it and forming metastases. The present theoretical study aims to provide a better understanding of the ultimate reasons for this so-called "go-or-grow" dichotomy. To that end, we use game theory, which has proven to be useful in analyzing the competition between tumors and healthy tissues or among different tumor cells. We begin by determining the game types in the Basanta-Hatzikirou-Deutsch model, depending on the parameter values. Thereafter, we suggest and analyze five modified variants of the model. For example, in the basic model, the deadlock game, Prisoner's Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types, such as battle of the sexes, route-choice, and stag-hunt games. For some game types, all cells are predicted to stay on their original site ("grow phenotype"), while for other types, only a certain fraction stay and the other cells migrate away ("go phenotype"). If the nutrient supply at a distant site is high, all the cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction and limitations of the supply of vitamins or methionine. Our results may help devise treatments to prevent metastasis.

Action planning and execution cues influence economic partner choice.

Prudently choosing who to interact with and who to avoid is an important ability to ensure that we benefit from a cooperative interaction. While the role of others' preferences, attributes, and values in partner choice have been established (Rossetti, Hilbe & Hauser, 2022), much less is known about whether the manner in which a potential partner plans and implements a decision provides helpful cues for partner choice. We used a partner choice paradigm in which participants chose who to interact with in the Prisoners' Dilemma. Before choosing a cooperation partner, participants were presented with information about the potential partners' decision-related actions in another round of the Prisoners' Dilemma. They received either information about the potential partners' planning during decision making (i.e., decision-time; Experiment 1) or action execution during decision implementation (i.e., movement directness; Experiment 2). Across both games, participants preferred to interact with those who planned actions quickly or executed actions with direct and smooth movements, indicating that they were cooperating confidently and without deliberation. This demonstrates that action cues present in either the planning or implementation of economic decisions influence partner choice. We discuss implications of this finding for human decision-making and perception-action coupling in action understanding.

Communicating emotions, but not expressing them privately, reduces moral punishment in a Prisoner's Dilemma game.

The existence of moral punishment, that is, the fact that cooperative people sacrifice resources to punish defecting partners requires an explanation. Potential explanations are that people punish defecting partners to privately express or to communicate their negative emotions in response to the experienced unfairness. If so, then providing participants with alternative ways to privately express or to communicate their emotions should reduce moral punishment. In two experiments, participants interacted with cooperating and defecting partners in a Prisoner's Dilemma game. After each round, participants communicated their emotions to their partners (Experiments 1 and 2) or only expressed them privately (Experiment 2). Each trial concluded with a costly punishment option. Compared to a no-expression control group, moral punishment was reduced when emotions were communicated to the defecting partner but not when emotions were privately expressed. Moral punishment may thus serve to communicate emotions to defecting partners. However, moral punishment was only reduced but far from being eliminated, suggesting that the communication of emotions does not come close to replacing moral punishment. Furthermore, prompting participants to focus on their emotions had undesirable side-effects: Privately expressing emotions diminished cooperation, enhanced hypocritical punishment (i.e., punishment of defecting partners by defecting participants), and induced an unspecific bias to punish the partners irrespective of their actions.

Asymmetry of individual activity promotes cooperation in the spatial prisoner's dilemma game.

We consider an aspiration-based asymmetric individual activity co-evolutionary prisoner's dilemma game model on the square lattice. In detail, each player has an individual weight that evolves with its strategy. We introduce an asymmetric setting that only µ fractions of players in the network chosen to be active can update their individual weights according to whether their payoffs satisfy their aspirations. Therefore, our individual weights can be regarded as a type of intrinsic motivation satisfaction. Through Monte Carlo simulations on the square lattice, our co-evolution mechanism has been proven to significantly promote cooperation. Furthermore, we find that the moderate µ leads to the highest cooperation level. By dividing the players into four types according to their strategies and weights, we prove that the inversion of the dominant relationship between cooperators and defectors with low weights leads to a conversion cycle of the four types of players, which enhances spatial reciprocity to promote cooperation. Moderate µ results in an appropriate number of low-weight players in this cycle. Interestingly, our results show that higher weight heterogeneity does not lead to higher levels of cooperation, which is contrary to the intuition formed in the previous work.

Prisoner's dilemma and the free operant: John Nash, I'd like you to meet Fred Skinner.

In separate chambers, responding by two pairs of pigeons was reinforced under concurrent random-ratio schedules of reinforcement. For each pair, the birds' schedules were coupled in such a manner that left- and right-key reinforcement probabilities were determined by the key being pecked by the other pigeon of the pair. In this way, a reinforcement matrix, like that of the popular Prisoner's Dilemma game of game theory, was created. The responding of all subjects soon gravitated to the choice combination identified by the mathematician John Nash as the equilibrium of the Prisoner's Dilemma game. This was found both before and after reversal of contingencies on the keys. In a second experiment, with a single pair of pigeons, stimuli signaling the choice of the paired pigeon had little lasting effect: responding again gravitated to the game's equilibrium. The results affirm earlier findings, demonstrating that Skinner's principle of positive reinforcement, together with Nashian mathematics, entirely accounts for iterative game-theoretic behavior. They extend these findings to the so-called free operant: to schedules of reinforcement in which responding is not constrained by stimulus-response sequencing (i.e., a trials procedure). The coupled schedule of reinforcement introduced here offers significant promise for the experimental analysis of economic and social behaviors.

Small bots, big impact: solving the conundrum of cooperation in optional Prisoner's Dilemma game through simple strategies.

Cooperation plays a crucial role in both nature and human society, and the conundrum of cooperation attracts the attention from interdisciplinary research. In this study, we investigated the evolution of cooperation in optional Prisoner's Dilemma games by introducing simple bots. We focused on one-shot and anonymous games, where the bots could be programmed to always cooperate, always defect, never participate or choose each action with equal probability. Our results show that cooperative bots facilitate the emergence of cooperation among ordinary players in both well-mixed populations and a regular lattice under weak imitation scenarios. Introducing loner bots has no impact on the emergence of cooperation in well-mixed populations, but it facilitates the dominance of cooperation in regular lattices under strong imitation scenarios. However, too many loner bots on a regular lattice inhibit the spread of cooperation and can eventually result in a breakdown of cooperation. Our findings emphasize the significance of bot design in promoting cooperation and offer useful insights for encouraging cooperation in real-world scenarios.

Cooperation driven by alike interactions in presence of social viscosity.

Cooperation observed in nearly all living systems, ranging from human and animal societies down to the scale of bacteria populations, is an astounding process through which individuals act together for mutual benefits. Despite being omnipresent, the mechanism behind the emergence and existence of cooperation in populations of selfish individuals has been a puzzle and exceedingly crucial to investigate. A number of mechanisms have been put forward to explain the stability of cooperation in the last years. In this work, we explore the evolution of cooperation for alike (assortative) interactions in populations subject to social viscosity in terms of zealous individuals. We present a comprehensive study on how a finite fraction of these committed minorities present in both cooperators and defectors govern the evolutionary game dynamics where interactions among the individuals with same strategy are more probable than random interactions. We perform a detailed analysis concerning this synergy between alike interaction and the social viscosity in the opposing individuals. We scrutinize all three principal social dilemmas, namely, the prisoner's dilemma, the stag-hunt, and the snowdrift game, under such evolutionary setting. We have been successful to delineate this evolutionary scenario theoretically based upon the generalized replicator dynamics in the well-mixed regime.

Inhibition and activation of interactions in networked weak prisoner's dilemma.

In the framework of the coevolution dynamics of the weak prisoner's dilemma, inspired by prior empirical research, we present a coevolutionary model with local network dynamics in a static network framework. Viewing the edges of the network as social interactions between individuals, when individuals play the weak prisoner's dilemma game, they accumulate both payoffs and social interaction willingness based on a payoff matrix of the social interaction willingness we constructed. The edges are then inhibiting or activating based on the social interaction willingness of the two individuals, and individuals only interact with others through activated edges, resulting in local network dynamics in a static network framework. Individuals who receive more cooperation will be more likely to activate the edges around them, meaning they will participate in more social interactions. Conversely, individuals who receive more defects will do the opposite. Specifically, we investigate the evolutionary dynamics of cooperation under different levels of sensitivity to social interaction willingness and the temptation to defect. Through the simulation, we find that sparse cooperator clusters can expand greatly when social interaction sensitivity and temptation to defect are low. In contrast, dense cooperator clusters form rapidly in a high social interaction sensitivity, which protects the cooperation from high temptation.