Indirect reciprocity with stochastic and dual reputation updates.

Cooperation is a crucial aspect of social life, yet understanding the nature of cooperation and how it can be promoted is an ongoing challenge. One mechanism for cooperation is indirect reciprocity. According to this mechanism, individuals cooperate to maintain a good reputation. This idea is embodied in a set of social norms called the "leading eight". When all information is publicly available, these norms have two major properties. Populations that employ these norms are fully cooperative, and they are stable against invasion by alternative norms. In this paper, we extend the framework of the leading eight in two directions. First, we include norms with 'dual' reputation updates. These norms do not only assign new reputations to an acting donor; they also allow to update the reputation of the passive recipient. Second, we allow social norms to be stochastic. Such norms allow individuals to evaluate others with certain probabilities. Using this framework, we characterize all evolutionarily stable norms that lead to full cooperation in the public information regime. When only the donor's reputation is updated, and all updates are deterministic, we recover the conventional model. In that case, we find two classes of stable norms: the leading eight and the 'secondary sixteen'. Stochasticity can further help to stabilize cooperation when the benefit of cooperation is comparably small. Moreover, updating the recipients' reputations can help populations to recover more quickly from errors. Overall, our study highlights a remarkable trade-off between the evolutionary stability of a norm and its robustness with respect to errors. Norms that correct errors quickly require higher benefits of cooperation to be stable.

Grouping promotes both partnership and rivalry with long memory in direct reciprocity.

Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in the iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized into one of two classes, 'partners' and 'rivals.' More recently, another class, 'friendly rivals,' has been identified in longer-memory strategy spaces. Friendly rivals qualify as both partners and rivals: They fully cooperate with themselves, like partners, but never allow their co-players to earn higher payoffs, like rivals. Although they have appealing theoretical properties, it is unclear whether they would emerge in an evolving population because most previous works focus on the memory-one strategy space, where no friendly rival strategy exists. To investigate this issue, we have conducted evolutionary simulations in well-mixed and group-structured populations and compared the evolutionary dynamics between memory-one and longer-memory strategy spaces. In a well-mixed population, the memory length does not make a major difference, and the key factors are the population size and the benefit of cooperation. Friendly rivals play a minor role because being a partner or a rival is often good enough in a given environment. It is in a group-structured population that memory length makes a stark difference: When longer-memory strategies are available, friendly rivals become dominant, and the cooperation level nearly reaches a maximum, even when the benefit of cooperation is so low that cooperation would not be achieved in a well-mixed population. This result highlights the important interaction between group structure and memory lengths that drive the evolution of cooperation.

Evolution of direct reciprocity in group-structured populations.

People tend to have their social interactions with members of their own community. Such group-structured interactions can have a profound impact on the behaviors that evolve. Group structure affects the way people cooperate, and how they reciprocate each other's cooperative actions. Past work has shown that population structure and reciprocity can both promote the evolution of cooperation. Yet the impact of these mechanisms has been typically studied in isolation. In this work, we study how the two mechanisms interact. Using a game-theoretic model, we explore how people engage in reciprocal cooperation in group-structured populations, compared to well-mixed populations of equal size. In this model, the population is subdivided into groups. Individuals engage in pairwise interactions within groups while they also have chances to imitate strategies outside the groups. To derive analytical results, we focus on two scenarios. In the first scenario, we assume a complete separation of time scales. Mutations are rare compared to between-group comparisons, which themselves are rare compared to within-group comparisons. In the second scenario, there is a partial separation of time scales, where mutations and between-group comparisons occur at a comparable rate. In both scenarios, we find that the effect of population structure depends on the benefit of cooperation. When this benefit is small, group-structured populations are more cooperative. But when the benefit is large, well-mixed populations result in more cooperation. Overall, our results reveal how group structure can sometimes enhance and sometimes suppress the evolution of cooperation.

Evolution of global development cooperation: An analysis of aid flows with hierarchical stochastic block models.

Despite considerable scholarly attention on the institutional and normative aspects of development cooperation, its longitudinal dynamics unfolding at the global level have rarely been investigated. Focusing on aid, we examine the evolving global structure of development cooperation induced by aid flows in its entirety. Representing annual aid flows between donors and recipients from 1970 to 2013 as a series of networks, we apply hierarchical stochastic block models to extensive aid-flow data that cover not only the aid behavior of the major OECD donors but also that of other emerging donors, including China. Despite a considerable degree of external expansion and internal diversification of aid relations over the years, the analysis has uncovered a temporally persistent structure of aid networks. The latter comprises, on the one hand, a limited number of major donors with far-reaching resources and, on the other hand, a large number of mostly poor but globally well-connected recipients. The results cast doubt on the efficacy of recurrent efforts for "aid reform" in substantially changing the global aid flow pattern.

A second-order stability analysis for the continuous model of indirect reciprocity.

Reputation is one of key mechanisms to maintain human cooperation, but its analysis gets complicated if we consider the possibility that reputation does not reach consensus because of erroneous assessment. The difficulty is alleviated if we assume that reputation and cooperation do not take binary values but have continuous spectra so that disagreement over reputation can be analysed in a perturbative way. In this work, we carry out the analysis by expanding the dynamics of reputation to the second order of perturbation under the assumption that everyone initially cooperates with good reputation. The second-order theory clarifies the difference between Image Scoring and Simple Standing in that punishment for defection against a well-reputed player should be regarded as good for maintaining cooperation. Moreover, comparison among the leading eight shows that the stabilizing effect of justified punishment weakens if cooperation between two ill-reputed players is regarded as bad. Our analysis thus explains how Simple Standing achieves a high level of stability by permitting justified punishment and also by disregarding irrelevant information in assessing cooperation. This observation suggests which factors affect the stability of a social norm when reputation can be perturbed by noise.

Social norms in indirect reciprocity with ternary reputations.

Indirect reciprocity is a key mechanism that promotes cooperation in social dilemmas by means of reputation. Although it has been a common practice to represent reputations by binary values, either 'good' or 'bad', such a dichotomy is a crude approximation considering the complexity of reality. In this work, we studied norms with three different reputations, i.e., 'good', 'neutral', and 'bad'. Through massive supercomputing for handling more than thirty billion possibilities, we fully identified which norms achieve cooperation and possess evolutionary stability against behavioural mutants. By systematically categorizing all these norms according to their behaviours, we found similarities and dissimilarities to their binary-reputation counterpart, the leading eight. We obtained four rules that should be satisfied by the successful norms, and the behaviour of the leading eight can be understood as a special case of these rules. A couple of norms that show counter-intuitive behaviours are also presented. We believe the findings are also useful for designing successful norms with more general reputation systems.

Deep Learning Exploration of Agent-Based Social Network Model Parameters.

Interactions between humans give rise to complex social networks that are characterized by heterogeneous degree distribution, weight-topology relation, overlapping community structure, and dynamics of links. Understanding these characteristics of social networks is the primary goal of their research as they constitute scaffolds for various emergent social phenomena from disease spreading to political movements. An appropriate tool for studying them is agent-based modeling, in which nodes, representing individuals, make decisions about creating and deleting links, thus yielding various macroscopic behavioral patterns. Here we focus on studying a generalization of the weighted social network model, being one of the most fundamental agent-based models for describing the formation of social ties and social networks. This generalized weighted social network (GWSN) model incorporates triadic closure, homophilic interactions, and various link termination mechanisms, which have been studied separately in the previous works. Accordingly, the GWSN model has an increased number of input parameters and the model behavior gets excessively complex, making it challenging to clarify the model behavior. We have executed massive simulations with a supercomputer and used the results as the training data for deep neural networks to conduct regression analysis for predicting the properties of the generated networks from the input parameters. The obtained regression model was also used for global sensitivity analysis to identify which parameters are influential or insignificant. We believe that this methodology is applicable for a large class of complex network models, thus opening the way for more realistic quantitative agent-based modeling.

Do economic effects of the anti-COVID-19 lockdowns in different regions interact through supply chains?

To prevent the spread of COVID-19, many cities, states, and countries have 'locked down', restricting economic activities in non-essential sectors. Such lockdowns have substantially shrunk production in most countries. This study examines how the economic effects of lockdowns in different regions interact through supply chains, which are a network of firms for production, by simulating an agent-based model of production using supply-chain data for 1.6 million firms in Japan. We further investigate how the complex network structure affects the interactions between lockdown regions, emphasising the role of upstreamness and loops by decomposing supply-chain flows into potential and circular flow components. We find that a region's upstreamness, intensity of loops, and supplier substitutability in supply chains with other regions largely determine the economic effect of the lockdown in the region. In particular, when a region lifts its lockdown, its economic recovery substantially varies depending on whether it lifts the lockdown alone or together with another region closely linked through supply chains. These results indicate that the economic effect produced by exogenous shocks in a region can affect other regions and therefore this study proposes the need for inter-region policy coordination to reduce economic loss due to lockdowns.

Local stability of cooperation in a continuous model of indirect reciprocity.

Reputation is a powerful mechanism to enforce cooperation among unrelated individuals through indirect reciprocity, but it suffers from disagreement originating from private assessment, noise, and incomplete information. In this work, we investigate stability of cooperation in the donation game by regarding each player's reputation and behaviour as continuous variables. Through perturbative calculation, we derive a condition that a social norm should satisfy to give penalties to its close variants, provided that everyone initially cooperates with a good reputation, and this result is supported by numerical simulation. A crucial factor of the condition is whether a well-reputed player's donation to an ill-reputed co-player is appreciated by other members of the society, and the condition can be reduced to a threshold for the benefit-cost ratio of cooperation which depends on the reputational sensitivity to a donor's behaviour as well as on the behavioural sensitivity to a recipient's reputation. Our continuum formulation suggests how indirect reciprocity can work beyond the dichotomy between good and bad even in the presence of inhomogeneity, noise, and incomplete information.

Crystal structures of aconitase X enzymes from bacteria and archaea provide insights into the molecular evolution of the aconitase superfamily.

Aconitase superfamily members catalyze the homologous isomerization of specific substrates by sequential dehydration and hydration and contain a [4Fe-4S] cluster. However, monomeric and heterodimeric types of function unknown aconitase X (AcnX) have recently been characterized as a cis-3-hydroxy-L-proline dehydratase (AcnXType-I) and mevalonate 5-phosphate dehydratase (AcnXType-II), respectively. We herein elucidated the crystal structures of AcnXType-I from Agrobacterium tumefaciens (AtAcnX) and AcnXType-II from Thermococcus kodakarensis (TkAcnX) without a ligand and in complex with substrates. AtAcnX and TkAcnX contained the [2Fe-2S] and [3Fe-4S] clusters, respectively, conforming to UV and EPR spectroscopy analyses. The binding sites of the [Fe-S] cluster and substrate were clearlydifferent from those that were completely conserved in other aconitase enzymes; however, theoverall structural frameworks and locations of active sites were partially similar to each other.These results provide novel insights into the evolutionary scenario of the aconitase superfamilybased on the recruitment hypothesis.

Friendly-rivalry solution to the iterated n-person public-goods game.

Repeated interaction promotes cooperation among rational individuals under the shadow of future, but it is hard to maintain cooperation when a large number of error-prone individuals are involved. One way to construct a cooperative Nash equilibrium is to find a 'friendly-rivalry' strategy, which aims at full cooperation but never allows the co-players to be better off. Recently it has been shown that for the iterated Prisoner's Dilemma in the presence of error, a friendly rival can be designed with the following five rules: Cooperate if everyone did, accept punishment for your own mistake, punish defection, recover cooperation if you find a chance, and defect in all the other circumstances. In this work, we construct such a friendly-rivalry strategy for the iterated n-person public-goods game by generalizing those five rules. The resulting strategy makes a decision with referring to the previous m = 2n - 1 rounds. A friendly-rivalry strategy for n = 2 inherently has evolutionary robustness in the sense that no mutant strategy has higher fixation probability in this population than that of a neutral mutant. Our evolutionary simulation indeed shows excellent performance of the proposed strategy in a broad range of environmental conditions when n = 2 and 3.

Five rules for friendly rivalry in direct reciprocity.

Direct reciprocity is one of the key mechanisms accounting for cooperation in our social life. According to recent understanding, most of classical strategies for direct reciprocity fall into one of two classes, 'partners' or 'rivals'. A 'partner' is a generous strategy achieving mutual cooperation, and a 'rival' never lets the co-player become better off. They have different working conditions: For example, partners show good performance in a large population, whereas rivals do in head-to-head matches. By means of exhaustive enumeration, we demonstrate the existence of strategies that act as both partners and rivals. Among them, we focus on a human-interpretable strategy, named 'CAPRI' after its five characteristic ingredients, i.e., cooperate, accept, punish, recover, and defect otherwise. Our evolutionary simulation shows excellent performance of CAPRI in a broad range of environmental conditions.

Automata representation of successful strategies for social dilemmas.

In a social dilemma, cooperation is collectively optimal, yet individually each group member prefers to defect. A class of successful strategies of direct reciprocity were recently found for the iterated prisoner's dilemma and for the iterated three-person public-goods game: By a successful strategy, we mean that it constitutes a cooperative Nash equilibrium under implementation error, with assuring that the long-term payoff never becomes less than the co-players' regardless of their strategies, when the error rate is small. Although we have a list of actions prescribed by each successful strategy, the rationale behind them has not been fully understood for the iterated public-goods game because the list has hundreds of entries to deal with every relevant history of previous interactions. In this paper, we propose a method to convert such history-based representation into an automaton with a minimal number of states. Our main finding is that a successful strategy for the iterated three-person public-goods game can be represented as a 10-state automaton by this method. In this automaton, each state can be interpreted as the player's internal judgement of the situation, such as trustworthiness of the co-players and the need to redeem oneself after defection. This result thus suggests a comprehensible way to choose an appropriate action at each step towards cooperation based on a situational judgement, which is mapped from the history of interactions.

Sampling networks by nodal attributes.

In a social network individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links. Since available data sets are usually restricted to a limited number of channels or layers, these autonomous decision making processes by the nodes constitute the sampling of a multiplex network leading to just one (though very important) example of sampling bias caused by the behavior of the nodes. We develop a general setting to get insight and understand the class of network sampling models, where the probability of sampling a link in the original network depends on the attributes h of its adjacent nodes. Assuming that the nodal attributes are independently drawn from an arbitrary distribution ρ(h) and that the sampling probability r(h_{i},h_{j}) for a link ij of nodal attributes h_{i} and h_{j} is also arbitrary, we derive exact analytic expressions of the sampled network for such network characteristics as the degree distribution, degree correlation, and clustering spectrum. The properties of the sampled network turn out to be sums of quantities for the original network topology weighted by the factors stemming from the sampling. Based on our analysis, we find that the sampled network may have sampling-induced network properties that are absent in the original network, which implies the potential risk of a naive generalization of the results of the sample to the entire original network. We also consider the case, when neighboring nodes have correlated attributes to show how to generalize our formalism for such sampling bias and we get good agreement between the analytic results and the numerical simulations.

Structural transition in social networks: The role of homophily.

We introduce a model for the formation of social networks, which takes into account the homophily or the tendency of individuals to associate and bond with similar others, and the mechanisms of global and local attachment as well as tie reinforcement due to social interactions between people. We generalize the weighted social network model such that the nodes or individuals have F features and each feature can have q different values. Here the tendency for the tie formation between two individuals due to the overlap in their features represents homophily. We find a phase transition as a function of F or q, resulting in a phase diagram. For fixed q and as a function of F the system shows two phases separated at Fc. For F < Fc large, homogeneous, and well separated communities can be identified within which the features match almost perfectly (segregated phase). When F becomes larger than Fc, the nodes start to belong to several communities and within a community the features match only partially (overlapping phase). Several quantities reflect this transition, including the average degree, clustering coefficient, feature overlap, and the number of communities per node. We also make an attempt to interpret these results in terms of observations on social behavior of humans.

Seven rules to avoid the tragedy of the commons.

Cooperation among self-interested players in a social dilemma is fragile and easily interrupted by mistakes. In this work, we study the repeated n-person public-goods game and search for a strategy that forms a cooperative Nash equilibrium in the presence of implementation error with a guarantee that the resulting payoff will be no less than any of the co-players'. By enumerating strategic possibilities for n=3, we show that such a strategy indeed exists when its memory length m equals three. It means that a deterministic strategy can be publicly employed to stabilize cooperation against error with avoiding the risk of being exploited. We furthermore show that, for general n-person public-goods game, m ≥ n is necessary to satisfy the above criteria.

What Big Data tells: Sampling the social network by communication channels.

Big Data has become the primary source of understanding the structure and dynamics of the society at large scale. The network of social interactions can be considered as a multiplex, where each layer corresponds to one communication channel and the aggregate of all of them constitutes the entire social network. However, usually one has information only about one of the channels or even a part of it, which should be considered as a subset or sample of the whole. Here we introduce a model based on a natural bilateral communication channel selection mechanism, which for one channel leads to consistent changes in the network properties. For example, while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one, we get a monotonically decreasing distribution as observed in empirical studies of single-channel data. We also find that assortativity may occur or get strengthened due to the sampling method. We analyze the far-reaching consequences of our findings.

Modeling the Role of Relationship Fading and Breakup in Social Network Formation.

In social networks of human individuals, social relationships do not necessarily last forever as they can either fade gradually with time, resulting in "link aging," or terminate abruptly, causing "link deletion," as even old friendships may cease. In this paper, we study a social network formation model where we introduce several ways by which a link termination takes place. If we adopt the link aging, we get a more modular structure with more homogeneously distributed link weights within communities than when link deletion is used. By investigating distributions and relations of various network characteristics, we find that the empirical findings are better reproduced with the link deletion model. This indicates that link deletion plays a more prominent role in organizing social networks than link aging.

Multilayer weighted social network model.

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.

Effects of demographic stochasticity on biological community assembly on evolutionary time scales.

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate 1/f fluctuations are observed with noise, while 1/f2 fluctuations are found for the model without demographic noise.