Expertise increases planning depth in human gameplay.

A hallmark of human intelligence is the ability to plan multiple steps into the future1,2. Despite decades of research3-5, it is still debated whether skilled decision-makers plan more steps ahead than novices6-8. Traditionally, the study of expertise in planning has used board games such as chess, but the complexity of these games poses a barrier to quantitative estimates of planning depth. Conversely, common planning tasks in cognitive science often have a lower complexity9,10 and impose a ceiling for the depth to which any player can plan. Here we investigate expertise in a complex board game that offers ample opportunity for skilled players to plan deeply. We use model fitting methods to show that human behaviour can be captured using a computational cognitive model based on heuristic search. To validate this model, we predict human choices, response times and eye movements. We also perform a Turing test and a reconstruction experiment. Using the model, we find robust evidence for increased planning depth with expertise in both laboratory and large-scale mobile data. Experts memorize and reconstruct board features more accurately. Using complex tasks combined with precise behavioural modelling might expand our understanding of human planning and help to bridge the gap with progress in artificial intelligence.

Confusion cannot explain cooperative behavior in public goods games.

Some scholars find that behavioral variation in the public goods game is explained by variations in participants' understanding of how to maximize payoff and that confusion leads to cooperation. Their findings lead them to question the common assumption in behavioral economics experiments that choices reflect motivations. We conduct two experiments, in which we minimize confusion by providing participants with increased training. We also introduce a question that specifically assesses participants' understanding of payoff maximization choices. Our experimental results show that the distribution of behavior types is significantly different when participants play with computers versus humans. A significant increase in contributions is also observed when participants play with humans compared to when they play with computers. Moreover, social norms may be the main motive for contributions when playing with computers. Our findings suggest that social preferences, rather than confusion, play a crucial role in determining contributions in public goods games when playing with humans. We therefore argue that the assumption in behavioral economics experiments that choices reveal motivations is indeed valid.

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.

Indirect reciprocity undermines indirect reciprocity destabilizing large-scale cooperation.

Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation [K. Panchanathan, R. Boyd, Nature 432, 499-502 (2004)]. The logic behind these models and experiments [J. Gross et al., Sci. Adv. 9, eadd8289 (2023) and O. P. Hauser, A. Hendriks, D. G. Rand, M. A. Nowak, Sci. Rep. 6, 36079 (2016)] is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem. However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, "local" group embedded within a larger, "global" group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation.

Computational evolution of social norms in well-mixed and group-structured populations.

Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative-unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure.

Efficiency and resilience of cooperation in asymmetric social dilemmas.

Direct reciprocity is a powerful mechanism for cooperation in social dilemmas. The very logic of reciprocity, however, seems to require that individuals are symmetric, and that everyone has the same means to influence each others' payoffs. Yet in many applications, individuals are asymmetric. Herein, we study the effect of asymmetry in linear public good games. Individuals may differ in their endowments (their ability to contribute to a public good) and in their productivities (how effective their contributions are). Given the individuals' productivities, we ask which allocation of endowments is optimal for cooperation. To this end, we consider two notions of optimality. The first notion focuses on the resilience of cooperation. The respective endowment distribution ensures that full cooperation is feasible even under the most adverse conditions. The second notion focuses on efficiency. The corresponding endowment distribution maximizes group welfare. Using analytical methods, we fully characterize these two endowment distributions. This analysis reveals that both optimality notions favor some endowment inequality: More productive players ought to get higher endowments. Yet the two notions disagree on how unequal endowments are supposed to be. A focus on resilience results in less inequality. With additional simulations, we show that the optimal endowment allocation needs to account for both the resilience and the efficiency of cooperation.

Social bond dynamics and the evolution of helping.

Empiricists often struggle to apply game theory models to real-life cases of animal cooperation. One reason is that many examples of cooperation occur in stable groups, where individuals form social bonds that influence exchanges of help in ways that are not well described by previous models, including the extent of reciprocity and how relationships are initiated. We present a game theory model exploring the conditions under which social bonds between group members promote cooperation. In the model, bonds build up from exchanges of help in a similar way as the strength of association increases in learning, as in the Rescorla-Wagner rule. The bonds in turn affect partner choice and influence helping amounts. The model has a mechanism of reciprocity for bonded pairs, which can evolve toward either loose or strict reciprocation. Several aspects of the model are inspired by observations of food sharing in vampire bats. We find that small social neighborhoods are required for the evolutionary stability of helping, either as small group sizes, or if bonded members of larger groups can form temporary (daily) smaller groupings. The costs of helping need to be fairly low, while the benefits can be substantial. The form of reciprocity that evolves is neither immediate nor very strict. Individuals in need request help based on bond strength, but there is also an evolved preference for initiating bonds with new group members. In contrast, if different groups come into temporary contact, the evolved tendency is to avoid forming bonds between groups.

Mutation enhances cooperation in direct reciprocity.

Direct reciprocity is a powerful mechanism for the evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here, we report that intermediate mutation rates lead to high levels of cooperation, even if the benefit-to-cost ratio is only marginally above one, and even if individuals only use a minimum of past information. This surprising observation is caused by two effects. First, mutation generates diversity which undermines the evolutionary stability of defectors. Second, mutation leads to diverse communities of cooperators that are more resilient than homogeneous ones. This finding is relevant because many real-world opportunities for cooperation have small benefit-to-cost ratios, which are between one and two, and we describe how direct reciprocity can attain cooperation in such settings. Our result can be interpreted as showing that diversity, rather than uniformity, promotes evolution of cooperation.

Evolutionary dynamics within and among competing groups.

Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible for profound transitions in evolutionary history, including the origin of cellular life, multicellular life, and even societies. Here, we synthesize a growing literature that extends evolutionary game theory to describe multilevel evolutionary dynamics, using nested birth-death processes and partial differential equations to model natural selection acting on competition within and among groups of individuals. We analyze how mechanisms known to promote cooperation within a single group-including assortment, reciprocity, and population structure-alter evolutionary outcomes in the presence of competition among groups. We find that population structures most conducive to cooperation in multiscale systems can differ from those most conducive within a single group. Likewise, for competitive interactions with a continuous range of strategies we find that among-group selection may fail to produce socially optimal outcomes, but it can nonetheless produce second-best solutions that balance individual incentives to defect with the collective incentives for cooperation. We conclude by describing the broad applicability of multiscale evolutionary models to problems ranging from the production of diffusible metabolites in microbes to the management of common-pool resources in human societies.

Adaptations to infer fitness interdependence promote the evolution of cooperation.

The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence-the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape.

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.

Score-mediated mutual consent and indirect reciprocity.

Helping strangers at a cost to oneself is a hallmark of many human interactions, but difficult to justify from the viewpoint of natural selection, particularly in anonymous one-shot interactions. Reputational scoring can provide the necessary motivation via "indirect reciprocity," but maintaining reliable scores requires close oversight to prevent cheating. We show that in the absence of such supervision, it is possible that scores might be managed by mutual consent between the agents themselves instead of by third parties. The space of possible strategies for such "consented" score changes is very large but, using a simple cooperation game, we search it, asking what kinds of agreement can i) invade a population from rare and ii) resist invasion once common. We prove mathematically and demonstrate computationally that score mediation by mutual consent does enable cooperation without oversight. Moreover, the most invasive and stable strategies belong to one family and ground the concept of value by incrementing one score at the cost of the other, thus closely resembling the token exchange that underlies money in everyday human transactions. The most successful strategy has the flavor of money except that agents without money can generate new score if they meet. This strategy is evolutionarily stable, and has higher fitness, but is not physically realizable in a decentralized way; when conservation of score is enforced more money-like strategies dominate. The equilibrium distribution of scores under any of this family of strategies is geometric, meaning that agents with score 0 are inherent to money-like strategies.

Emergence of specialized third-party enforcement.

The question of how cooperation evolves and is maintained among nonkin is central to the biological, social, and behavioral sciences. Previous research has focused on explaining how cooperation in social dilemmas can be maintained by direct and indirect reciprocity among the participants of the social dilemma. However, in complex human societies, both modern and ancient, cooperation is frequently maintained by means of specialized third-party enforcement. We provide an evolutionary-game-theoretic model that explains how specialized third-party enforcement of cooperation (specialized reciprocity) can emerge. A population consists of producers and enforcers. First, producers engage in a joint undertaking represented by a prisoner's dilemma. They are paired randomly and receive no information about their partner's history, which precludes direct and indirect reciprocity. Then, enforcers tax producers and may punish their clients. Finally, the enforcers are randomly paired and may try to grab resources from each other. In order to sustain producer cooperation, enforcers must punish defecting producers, but punishing is costly to enforcers. We show that the threat of potential intraenforcer conflict can incentivize enforcers to engage in costly punishment of producers, provided they are sufficiently informed to maintain a reputation system. That is, the "guards" are guarded by the guards themselves. We demonstrate the key mechanisms analytically and corroborate our results with numerical simulations.

Evolution of norms for judging social behavior.

Reputations provide a powerful mechanism to sustain cooperation, as individuals cooperate with those of good social standing. But how should someone's reputation be updated as we observe their social behavior, and when will a population converge on a shared norm for judging behavior? Here, we develop a mathematical model of cooperation conditioned on reputations, for a population that is stratified into groups. Each group may subscribe to a different social norm for assessing reputations and so norms compete as individuals choose to move from one group to another. We show that a group initially comprising a minority of the population may nonetheless overtake the entire population-especially if it adopts the Stern Judging norm, which assigns a bad reputation to individuals who cooperate with those of bad standing. When individuals do not change group membership, stratifying reputation information into groups tends to destabilize cooperation, unless individuals are strongly insular and favor in-group social interactions. We discuss the implications of our results for the structure of information flow in a population and for the evolution of social norms of judgment.

Reproductive variance can drive behavioral dynamics.

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to demographic stochasticity-that is, randomness associated with birth and death processes. In nature, individuals who are more fecund tend to have greater variance in their offspring number. Here, we develop a model for the evolution of two types competing in a population of nonconstant size. The fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, and the variance in offspring number depends upon its mean. Although defectors are preferred by natural selection in classical population models, since they always have greater fitness than cooperators, we show that sufficiently large offspring variance can reverse the direction of evolution and favor cooperation. Large offspring variance produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or with a Poisson offspring distribution.

Individual costs and societal benefits of interventions during the COVID-19 pandemic.

Individual and societal reactions to an ongoing pandemic can lead to social dilemmas: In some cases, each individual is tempted to not follow an intervention, but for the whole society, it would be best if they did. Now that in most countries, the extent of regulations to reduce SARS-CoV-2 transmission is very small, interventions are driven by individual decision-making. Assuming that individuals act in their best own interest, we propose a framework in which this situation can be quantified, depending on the protection the intervention provides to a user and to others, the risk of getting infected, and the costs of the intervention. We discuss when a tension between individual and societal benefits arises and which parameter comparisons are important to distinguish between different regimes of intervention use.

Indirect reciprocity with Bayesian reasoning and biases.

Reputations can foster cooperation by indirect reciprocity: if I am good to you then others will be good to me. But this mechanism for cooperation in one-shot interactions only works when people agree on who is good and who is bad. Errors in actions or assessments can produce disagreements about reputations, which can unravel the positive feedback loop between social standing and pro-social behaviour. Cooperators can end up punished and defectors rewarded. Public reputation systems and empathy are two possible mechanisms to promote agreement about reputations. Here we suggest an alternative: Bayesian reasoning by observers. By taking into account the probabilities of errors in action and observation and their prior beliefs about the prevalence of good people in the population, observers can use Bayesian reasoning to determine whether or not someone is good. To study this scenario, we develop an evolutionary game theoretical model in which players use Bayesian reasoning to assess reputations, either publicly or privately. We explore this model analytically and numerically for five social norms (Scoring, Shunning, Simple Standing, Staying, and Stern Judging). We systematically compare results to the case when agents do not use reasoning in determining reputations. We find that Bayesian reasoning reduces cooperation relative to non-reasoning, except in the case of the Scoring norm. Under Scoring, Bayesian reasoning can promote coexistence of three strategic types. Additionally, we study the effects of optimistic or pessimistic biases in individual beliefs about the degree of cooperation in the population. We find that optimism generally undermines cooperation whereas pessimism can, in some cases, promote cooperation.

Social dilemmas among unequals.

Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1-4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine cooperation and welfare7-10. Most previous models of reciprocity do not include inequality11-15. These models assume that individuals are the same in all relevant aspects. Here we introduce a general framework to study direct reciprocity among unequal individuals. Our model allows for multiple sources of inequality. Subjects can differ in their endowments, their productivities and in how much they benefit from public goods. We find that extreme inequality prevents cooperation. But if subjects differ in productivity, some endowment inequality can be necessary for cooperation to prevail. Our mathematical predictions are supported by a behavioural experiment in which we vary the endowments and productivities of the subjects. We observe that overall welfare is maximized when the two sources of heterogeneity are aligned, such that more productive individuals receive higher endowments. By contrast, when endowments and productivities are misaligned, cooperation quickly breaks down. Our findings have implications for policy-makers concerned with equity, efficiency and the provisioning of public goods.

Information gerrymandering and undemocratic decisions.

People must integrate disparate sources of information when making decisions, especially in social contexts. But information does not always flow freely. It can be constrained by social networks1-3 and distorted by zealots and automated bots4. Here we develop a voter game as a model system to study information flow in collective decisions. Players are assigned to competing groups (parties) and placed on an 'influence network' that determines whose voting intentions each player can observe. Players are incentivized to vote according to partisan interest, but also to coordinate their vote with the entire group. Our mathematical analysis uncovers a phenomenon that we call information gerrymandering: the structure of the influence network can sway the vote outcome towards one party, even when both parties have equal sizes and each player has the same influence. A small number of zealots, when strategically placed on the influence network, can also induce information gerrymandering and thereby bias vote outcomes. We confirm the predicted effects of information gerrymandering in social network experiments with n = 2,520 human subjects. Furthermore, we identify extensive information gerrymandering in real-world influence networks, including online political discussions leading up to the US federal elections, and in historical patterns of bill co-sponsorship in the US Congress and European legislatures. Our analysis provides an account of the vulnerabilities of collective decision-making to systematic distortion by restricted information flow. Our analysis also highlights a group-level social dilemma: information gerrymandering can enable one party to sway decisions in its favour, but when multiple parties engage in gerrymandering the group loses its ability to reach consensus and remains trapped in deadlock.