Social norm complexity and past reputations in the evolution of cooperation.

Indirect reciprocity is the most elaborate and cognitively demanding of all known cooperation mechanisms, and is the most specifically human because it involves reputation and status. By helping someone, individuals may increase their reputation, which may change the predisposition of others to help them in future. The revision of an individual's reputation depends on the social norms that establish what characterizes a good or bad action and thus provide a basis for morality. Norms based on indirect reciprocity are often sufficiently complex that an individual's ability to follow subjective rules becomes important, even in models that disregard the past reputations of individuals, and reduce reputations to either 'good' or 'bad' and actions to binary decisions. Here we include past reputations in such a model and identify the key pattern in the associated norms that promotes cooperation. Of the norms that comply with this pattern, the one that leads to maximal cooperation (greater than 90 per cent) with minimum complexity does not discriminate on the basis of past reputation; the relative performance of this norm is particularly evident when we consider a 'complexity cost' in the decision process. This combination of high cooperation and low complexity suggests that simple moral principles can elicit cooperation even in complex environments.

Risk sensitivity and theory of mind in human coordination.

What humans do when exposed to uncertainty, incomplete information, and a dynamic environment influenced by other agents remains an open scientific challenge with important implications in both science and engineering applications. In these contexts, humans handle social situations by employing elaborate cognitive mechanisms such as theory of mind and risk sensitivity. Here we resort to a novel theoretical model, showing that both mechanisms leverage coordinated behaviors among self-regarding individuals. Particularly, we resort to cumulative prospect theory and level-k recursions to show how biases towards optimism and the capacity of planning ahead significantly increase coordinated, cooperative action. These results suggest that the reason why humans are good at coordination may stem from the fact that we are cognitively biased to do so.

Cooperation dynamics under pandemic risks and heterogeneous economic interdependence.

The spread of COVID-19 and ensuing containment measures have accentuated the profound interdependence among nations or regions. This has been particularly evident in tourism, one of the sectors most affected by uncoordinated mobility restrictions. The impact of this interdependence on the tendency to adopt less or more restrictive measures is hard to evaluate, more so if diversity in economic exposures to citizens' mobility are considered. Here, we address this problem by developing an analytical and computational game-theoretical model encompassing the conflicts arising from the need to control the economic effects of global risks, such as in the COVID-19 pandemic. The model includes the individual costs derived from severe restrictions imposed by governments, including the resulting economic interdependence among all the parties involved in the game. By using tourism-based data, the model is enriched with actual heterogeneous income losses, such that every player has a different economic cost when applying restrictions. We show that economic interdependence enhances cooperation because of the decline in the expected payoffs by free-riding parties (i.e., those neglecting the application of mobility restrictions). Furthermore, we show (analytically and through numerical simulations) that these cross-exposures can transform the nature of the cooperation dilemma each region or country faces, modifying the position of the fixed points and the size of the basins of attraction that characterize this class of games. Finally, our results suggest that heterogeneity among regions may be used to leverage the impact of intervention policies by ensuring an agreement among the most relevant initial set of cooperators.

Governance of risky public goods under graduated punishment.

Ensuring global cooperation often poses governance problems shadowed by the tragedy of the commons, as wrong-doers enjoy the benefits set up by right-doers at no cost. Institutional punishment of wrong-doers is well-known to curtail their impetus as free-riders. However, institutions often have limited scope in imposing sanctions, more so when these are strict and potentially viewed as disproportionate. Inspired by the design principles proposed by the late Nobel Prize Elinor Ostrom, here we study the evolution and impact of a new form of institutional sanctioning, where punishment is graduated, growing with the incidence of free-riding. We develop an analytical model capable of identifying the conditions under which this design principle is conducive to the self-organization of stable institutions and cooperation. We employ evolutionary game theory in finite populations and non-linear public goods dilemmas in the presence of risk of global losses whose solution requires the self-organization of decision makers into an overall cooperative state. We show that graduated punishment is more effective in promoting widespread cooperation than conventional forms of punishment studied to date, being also less severe and thus, presumably, easier to implement. This effect is enhanced whenever the costs of its implementation are positively correlated with the severity of punishment. We frame our model within the context of the global reduction of carbon emissions, but the results are shown to be general enough to be applicable to other collective action problems, shedding further light into the origins of Human institutions.

Trypanosoma sp. diversity in Amazonian bats (Chiroptera; Mammalia) from Acre State, Brazil.

Bats are ancient hosts of Trypanosoma species and their flying ability, longevity and adaptability to distinct environments indicate that they are efficient dispersers of parasites. Bats from Acre state (Amazon Biome) were collected in four expeditions conducted in an urban forest (Parque Zoobotânico) and one relatively more preserved area (Seringal Cahoeira) in Rio Branco and Xapuri municipalities. Trypanosoma sp. infection was detected by hemoculture and fresh blood examination. Isolated parasite species were identified by the similarity of the obtained DNA sequence from 18S rDNA polymerase chain reaction and reference strains. Overall, 367 bats from 23 genera and 32 species were examined. Chiropterofauna composition was specific to each municipality, although Artibeus sp. and Carollia sp. prevailed throughout. Trypanosoma sp. infection was detected in 85 bats (23·2%). The most widely distributed and prevalent genotypes were (in order) Trypanosoma cruzi TcI, T. cruzi marinkellei, Trypanosoma dionisii, T. cruzi TcIV and Trypanosoma rangeli. At least one still-undescribed Trypanosoma species was also detected in this study. The detection of T. cruzi TcI and TcIV (the ones associated with Chagas disease in Amazon biome) demonstrates the putative importance of these mammal hosts in the epidemiology of the disease in the Acre State.

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Social Norms of Cooperation in Small-Scale Societies.

Indirect reciprocity, besides providing a convenient framework to address the evolution of moral systems, offers a simple and plausible explanation for the prevalence of cooperation among unrelated individuals. By helping someone, an individual may increase her/his reputation, which may change the pre-disposition of others to help her/him in the future. This, however, depends on what is reckoned as a good or a bad action, i.e., on the adopted social norm responsible for raising or damaging a reputation. In particular, it remains an open question which social norms are able to foster cooperation in small-scale societies, while enduring the wide plethora of stochastic affects inherent to finite populations. Here we address this problem by studying the stochastic dynamics of cooperation under distinct social norms, showing that the leading norms capable of promoting cooperation depend on the community size. However, only a single norm systematically leads to the highest cooperative standards in small communities. That simple norm dictates that only whoever cooperates with good individuals, and defects against bad ones, deserves a good reputation, a pattern that proves robust to errors, mutations and variations in the intensity of selection.

Climate policies under wealth inequality.

Taming the planet's climate requires cooperation. Previous failures to reach consensus in climate summits have been attributed, among other factors, to conflicting policies between rich and poor countries, which disagree on the implementation of mitigation measures. Here we implement wealth inequality in a threshold public goods dilemma of cooperation in which players also face the risk of potential future losses. We consider a population exhibiting an asymmetric distribution of rich and poor players that reflects the present-day status of nations and study the behavioral interplay between rich and poor in time, regarding their willingness to cooperate. Individuals are also allowed to exhibit a variable degree of homophily, which acts to limit those that constitute one's sphere of influence. Under the premises of our model, and in the absence of homophily, comparison between scenarios with wealth inequality and without wealth inequality shows that the former leads to more global cooperation than the latter. Furthermore, we find that the rich generally contribute more than the poor and will often compensate for the lower contribution of the latter. Contributions from the poor, which are crucial to overcome the climate change dilemma, are shown to be very sensitive to homophily, which, if prevalent, can lead to a collapse of their overall contribution. In such cases, however, we also find that obstinate cooperative behavior by a few poor may largely compensate for homophilic behavior.

Linking Individual and Collective Behavior in Adaptive Social Networks.

Adaptive social structures are known to promote the evolution of cooperation. However, up to now the characterization of the collective, population-wide dynamics resulting from the self-organization of individual strategies on a coevolving, adaptive network has remained unfeasible. Here we establish a (reversible) link between individual (micro)behavior and collective (macro)behavior for coevolutionary processes. We demonstrate that an adaptive network transforms a two-person social dilemma locally faced by individuals into a collective dynamics that resembles that associated with an N-person coordination game, whose characterization depends sensitively on the relative time scales between the entangled behavioral and network evolutions. In particular, we show that the faster the relative rate of adaptation of the network, the smaller the critical fraction of cooperators required for cooperation to prevail, thus establishing a direct link between network adaptation and the evolution of cooperation. The framework developed here is general and may be readily applied to other dynamical processes occurring on adaptive networks, notably, the spreading of contagious diseases or the diffusion of innovations.

Co-evolutionary dynamics of collective action with signaling for a quorum.

Collective signaling for a quorum is found in a wide range of organisms that face collective action problems whose successful solution requires the participation of some quorum of the individuals present. These range from humans, to social insects, to bacteria. The mechanisms involved, the quorum required, and the size of the group may vary. Here we address the general question of the evolution of collective signaling at a high level of abstraction. We investigate the evolutionary dynamics of a population engaging in a signaling N-person game theoretic model. Parameter settings allow for loners and cheaters, and for costly or costless signals. We find a rich dynamics, showing how natural selection, operating on a population of individuals endowed with the simplest strategies, is able to evolve a costly signaling system that allows individuals to respond appropriately to different states of Nature. Signaling robustly promotes cooperative collective action, in particular when coordinated action is most needed and difficult to achieve. Two different signaling systems may emerge depending on Nature's most prevalent states.

Evolutionary dynamics of collective index insurance.

Index-based insurances offer promising opportunities for climate-risk investments in developing countries. Indeed, contracts conditional on, e.g., weather or livestock indexes can be cheaper to set up than conventional indemnity-based insurances, while offering a safety net to vulnerable households, allowing them to eventually escape poverty traps. Moreover, transaction costs by insurance companies may be additionally reduced if contracts, instead of arranged with single households, are endorsed by collectives of households that bear the responsibility of managing the division of the insurance coverage by its members whenever the index is surpassed, allowing for additional flexibility in what concerns risk-sharing and also allowing insurance companies to avoid the costs associated with moral hazard. Here we resort to a population dynamics framework to investigate under which conditions household collectives may find collective index insurances attractive, when compared with individual index insurances. We assume risk sharing among the participants of each collective, and model collective action in terms of an N-person threshold game. Compared to less affordable individual index insurances, we show how collective index insurances lead to a coordination problem in which the adoption of index insurances may become the optimal decision, spreading index insurance coverage to the entire population. We further investigate the role of risk-averse and risk-prone behaviors, as well as the role of partial correlation between insurance coverage and actual loss of crops, and in which way these affect the original coordination thresholds.

Evolutionary dynamics of group fairness.

The emergence and impact of fairness is commonly studied in the context of 2-person games, notably the Ultimatum Game. Often, however, humans face problems of collective action involving more than two individuals where fairness is known to play a very important role, and whose dynamics cannot be inferred from what is known from 2-person games. Here, we propose a generalization of the Ultimatum Game for an arbitrary number of players--the Multiplayer Ultimatum Game. Proposals are made to a group of responders who must individually reject or accept the proposal. If the total number of individual acceptances stands below a given threshold, the offer will be rejected; otherwise, the offer will be accepted, and equally shared by all responders. We investigate the evolution of fairness in populations of individuals by means of evolutionary game theory, providing both analytical insights and results from numerical simulations. We show how imposing stringent consensuses significantly increases the value of the proposals, leading to fairer outcomes and more tolerant players. Furthermore, we show how stochastic effects--such as imitation errors and/or errors when assessing the fitness of others--may further enhance the overall success in reaching fair collective action.

Evolution of all-or-none strategies in repeated public goods dilemmas.

Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games (PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None (AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

Origin of peer influence in social networks.

Social networks pervade our everyday lives: we interact, influence, and are influenced by our friends and acquaintances. With the advent of the World Wide Web, large amounts of data on social networks have become available, allowing the quantitative analysis of the distribution of information on them, including behavioral traits and fads. Recent studies of correlations among members of a social network, who exhibit the same trait, have shown that individuals influence not only their direct contacts but also friends' friends, up to a network distance extending beyond their closest peers. Here, we show how such patterns of correlations between peers emerge in networked populations. We use standard models (yet reflecting intrinsically different mechanisms) of information spreading to argue that empirically observed patterns of correlation among peers emerge naturally from a wide range of dynamics, being essentially independent of the type of information, on how it spreads, and even on the class of underlying network that interconnects individuals. Finally, we show that the sparser and clustered the network, the more far reaching the influence of each individual will be.

Reward from punishment does not emerge at all costs.

The conundrum of cooperation has received increasing attention during the last decade. In this quest, the role of altruistic punishment has been identified as a mechanism promoting cooperation. Here we investigate the role of altruistic punishment on the emergence and maintenance of cooperation in structured populations exhibiting connectivity patterns recently identified as key elements of social networks. We do so in the framework of Evolutionary Game Theory, employing the Prisoner's Dilemma and the Stag-Hunt metaphors to model the conflict between individual and collective interests regarding cooperation. We find that the impact of altruistic punishment strongly depends on the ratio q/p between the cost of punishing a defecting partner (q) and the actual punishment incurred by the partner (p). We show that whenever q/p<1, altruistic punishment turns out to be detrimental for cooperation for a wide range of payoff parameters, when compared to the scenario without punishment. The results imply that while locally, the introduction of peer punishment may seem to reduce the chances of free-riding, realistic population structure may drive the population towards the opposite scenario. Hence, structured populations effectively reduce the expected beneficial contribution of punishment to the emergence of cooperation which, if not carefully dosed, may in fact hinder the chances of widespread cooperation.

Social diversity promotes the emergence of cooperation in public goods games.

Humans often cooperate in public goods games and situations ranging from family issues to global warming. However, evolutionary game theory predicts that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments. Here we show how social diversity provides an escape from this apparent paradox. Up to now, individuals have been treated as equivalent in all respects, in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution, cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment. Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications.

Risk of collective failure provides an escape from the tragedy of the commons.

From group hunting to global warming, how to deal with collective action may be formulated in terms of a public goods game of cooperation. In most cases, contributions depend on the risk of future losses. Here, we introduce an evolutionary dynamics approach to a broad class of cooperation problems in which attempting to minimize future losses turns the risk of failure into a central issue in individual decisions. We find that decisions within small groups under high risk and stringent requirements to success significantly raise the chances of coordinating actions and escaping the tragedy of the commons. We also offer insights on the scale at which public goods problems of cooperation are best solved. Instead of large-scale endeavors involving most of the population, which as we argue, may be counterproductive to achieve cooperation, the joint combination of local agreements within groups that are small compared with the population at risk is prone to significantly raise the probability of success. In addition, our model predicts that, if one takes into consideration that groups of different sizes are interwoven in complex networks of contacts, the chances for global coordination in an overall cooperating state are further enhanced.

Success-driven opinion formation determines social tensions.

Polarization is common in politics and public opinion. It is believed to be shaped by media as well as ideologies, and often incited by misinformation. However, little is known about the microscopic dynamics behind polarization and the resulting social tensions. By coupling opinion formation with the strategy selection in different social dilemmas, we reveal how success at an individual level transforms to global consensus or lack thereof. When defection carries with it the fear of punishment in the absence of greed, as in the stag-hunt game, opinion fragmentation is the smallest. Conversely, if defection promises a higher payoff and also evokes greed, like in the prisoner's dilemma and snowdrift game, consensus is more difficult to attain. Our research thus challenges the top-down narrative of social tensions, showing they might originate from fundamental principles at individual level, like the desire to prevail in pairwise evolutionary comparisons.

Evolution of a theory of mind.

Even though the Theory of Mind in upper primates has been under investigation for decades, how it may evolve remains an open problem. We propose here an evolutionary game theoretical model where a finite population of individuals may use reasoning strategies to infer a response to the anticipated behavior of others within the context of a sequential dilemma, i.e., the Centipede Game. We show that strategies with bounded reasoning evolve and flourish under natural selection, provided they are allowed to make reasoning mistakes and a temptation for higher future gains is in place. We further show that non-deterministic reasoning co-evolves with an optimism bias that may lead to the selection of new equilibria, closely associated with average behavior observed in experimental data. This work reveals both a novel perspective on the evolution of bounded rationality and a co-evolutionary link between the evolution of Theory of Mind and the emergence of misbeliefs.

EGTtools: Evolutionary game dynamics in Python.

Evolutionary Game Theory (EGT) provides an important framework to study collective behavior. It combines ideas from evolutionary biology and population dynamics with the game theoretical modeling of strategic interactions. Its importance is highlighted by the numerous high level publications that have enriched different fields, ranging from biology to social sciences, in many decades. Nevertheless, there has been no open source library that provided easy, and efficient, access to these methods and models. Here, we introduce EGTtools, an efficient hybrid C++/Python library which provides fast implementations of both analytical and numerical EGT methods. EGTtools is able to analytically evaluate a system based on the replicator dynamics. It is also able to evaluate any EGT problem resorting to finite populations and large-scale Markov processes. Finally, it resorts to C++ and MonteCarlo simulations to estimate many important indicators, such as stationary or strategy distributions. We illustrate all these methodologies with concrete examples and analysis.