Cooperation, norms, and revolutions: a unified game-theoretical approach

Effect of homophily on coupled behavior-disease dynamics near a tipping point

Understanding the interplay between social activities and disease dynamics is crucial for effective public health interventions. Recent studies using coupled behavior-disease models assumed homogeneous populations. However, heterogeneity in population, such as different social groups, cannot be ignored. In this study, we divided the population into social media users and non-users, and investigated the impact of homophily (the tendency for individuals to associate with others similar to themselves) and online events on disease dynamics. Our results reveal that homophily hinders the adoption of vaccinating strategies, hastening the approach to a tipping point after which the population converges to an endemic equilibrium with no vaccine uptake. Furthermore, we find that online events can significantly influence disease dynamics, with early discussions on social media platforms serving as an early warning signal of potential disease outbreaks. Our model provides insights into the mechanisms underlying these phenomena and underscores the importance of considering homophily in disease modeling and public health strategies.

Signals of belonging: emergence of signalling norms as facilitators of trust and parochial cooperation

Mechanisms of social control reinforce norms that appear harmful or wasteful, such as mutilation practises or extensive body tattoos. We suggest such norms arise to serve as signals that distinguish between ingroup 'friends' and outgroup 'foes', facilitating parochial cooperation. Combining insights from research on signalling and parochial cooperation, we incorporate a trust game with signalling in an agent-based model to study the dynamics of signalling norm emergence in groups with conflicting interests. Our results show that costly signalling norms emerge from random acts of signalling in minority groups that benefit most from parochial cooperation. Majority groups are less likely to develop costly signalling norms. Yet, norms that prescribe sending costless group identity signals can easily emerge in groups of all sizes-albeit, at times, at the expense of minority group members. Further, the dynamics of signalling norm emergence differ across signal costs, relative group sizes, and levels of ingroup assortment. Our findings provide theoretical insights into norm evolution in contexts where groups develop identity markers in response to environmental challenges that put their interests at odds with the interests of other groups. Such contexts arise in zones of ethnic conflict or during contestations of existing power relations. This article is part of the theme issue 'Social norm change: drivers and consequences'.

Ethics of Smart Cities: Towards Value-Sensitive Design and Co-Evolving City Life

The digital revolution has brought about many societal changes such as the creation of “smart cities”. The smart city concept has changed the urban ecosystem by embedding digital technologies in the city fabric to enhance the quality of life of its inhabitants. However, it has also led to some pressing issues and challenges related to data, privacy, ethics inclusion, and fairness. While the initial concept of smart cities was largely technology- and data-driven, focused on the automation of traffic, logistics and processes, this concept is currently being replaced by technology-enabled, human-centred solutions. However, this is not the end of the development, as there is now a big trend towards “design for values”. In this paper, we point out how a value-sensitive design approach could promote a more sustainable pathway of cities that better serves people and nature. Such “value-sensitive design” will have to take ethics, law and culture on board. We discuss how organising the digital world in a participatory way, as well as leveraging the concepts of self-organisation, self-regulation, and self-control, would foster synergy effects and thereby help to leverage a sustainable technological revolution on a global scale. Furthermore, a “democracy by design” approach could also promote resilience.

Consensus towards Partially Cooperative Strategies in Self-Regulated Evolutionary Games on Networks

Cooperation is widely recognized to be fundamental for the well-balanced development of human societies. Several different approaches have been proposed to explain the emergence of cooperation in populations of individuals playing the Prisoner’s Dilemma game, characterized by two concurrent natural mechanisms: the temptation to defect and the fear to be betrayed by others. Few results are available for analyzing situations where only the temptation to defect (Chicken game) or the fear to be betrayed (Stag-Hunt game) is present. In this paper, we analyze the emergence of full and partial cooperation for these classes of games. We find the conditions for which these Nash equilibria are asymptotically stable, and we show that the partial one is also globally stable. Furthermore, in the Chicken and Stag-Hunt games, partial cooperation has been found to be more rewarding than the full one of the Prisoner’s Dilemma game. This result highlights the importance of such games for understanding and sustaining different levels of cooperation in social networks.

Self-regulation versus social influence for promoting cooperation on networks

Cooperation is a relevant and controversial phenomenon in human societies. Indeed, although it is widely recognized essential for tackling social dilemmas, finding suitable policies for promoting cooperation can be arduous and expensive. More often, it is driven by pre-established schemas based on norms and punishments. To overcome this paradigm, we highlight the interplay between the influence of social interactions on networks and spontaneous self-regulating mechanisms on individuals behavior. We show that the presence of these mechanisms in a prisoner's dilemma game, may oppose the willingness of individuals to defect, thus allowing them to behave cooperatively, while interacting with others and taking conflicting decisions over time. These results are obtained by extending the Evolutionary Game Equations over Networks to account for self-regulating mechanisms. Specifically, we prove that players may partially or fully cooperate whether self-regulating mechanisms are sufficiently stronger than social pressure. The proposed model can explain unconditional cooperation (strong self-regulation) and unconditional defection (weak self-regulation). For intermediate self-regulation values, more complex behaviors are observed, such as mutual defection, recruiting (cooperate if others cooperate), exploitation of cooperators (defect if others cooperate) and altruism (cooperate if others defect). These phenomena result from dynamical transitions among different game structures, according to changes of system parameters and cooperation of neighboring players. Interestingly, we show that the topology of the network of connections among players is crucial when self-regulation, and the associated costs, are reasonably low. In particular, a population organized on a random network with a Scale-Free distribution of connections is more cooperative than on a network with an Erdös-Rényi distribution, and, in turn, with a regular one. These results highlight that social diversity, encoded within heterogeneous networks, is more effective for promoting cooperation.

Evolution of egalitarian social norm by resource management

Social organizations, especially human society, rely on egalitarian social norm, which can be characterized by high levels of fairness, empathy and collective conformity. Nevertheless, the evolution of egalitarian social norm remains a conundrum, as it suffers the persistent challenge from individual self-interest. To address this issue, we construct an evolutionary game theoretical model by employing the Ultimatum Game, in which rational individuals are able to perform resource management. We show that resource management drives a population evolving into an oscillatory state with high equilibrium degrees of fairness, empathy and collective conformity and thus constitutes a key mechanism for the evolution of egalitarian social norm in social dilemma situations. Specifically, it results in (1) the formation of egalitarian social norm from diverse individual norms, (2) the emergence of egalitarian social norm in a selfish and unfair world, and (3) the maintenance of egalitarian social norm despite the presence of norm violators. The constructive role of resource management is explained by a mean-field analysis revealing that resource management can effectively enlarge the attraction basin of egalitarian norms or even change the dynamical property of the mini Ultimatum Game from bistability between egalitarian norms and less egalitarian norms to complete-dominance of egalitarian norms over less egalitarian norms. Furthermore, we find that the capacity of resource management can be evolutionarily selected by a coevolution between egalitarian social norm and resource management. Our study suggests that efficiency and equity are linked to each other.

Homophilic replicator equations

Tags are conspicuous attributes of organisms that affect the behaviour of other organisms toward the holder, and have previously been used to explore group formation and altruism. Homophilic imitation, a form of tag-based selection, occurs when organisms imitate those with similar tags. Here we further explore the use of tag-based selection by developing homophilic replicator equations to model homophilic imitation dynamics. We assume that replicators have both tags (sometimes called traits) and strategies. Fitnesses are determined by the strategy profile of the population, and imitation is based upon the strategy profile, fitness differences, and similarity in tag space. We show the characteristics of resulting fixed manifolds and conditions for stability. We discuss the phenomenon of coat-tailing (where tags associated with successful strategies increase in abundance, even though the tags are not inherently beneficial) and its implications for population diversity. We extend our model to incorporate recurrent mutations and invasions to explore their implications upon tag and strategy diversity. We find that homophilic imitation based upon tags significantly affects the diversity of the population, although not the ESS. We classify two different types of invasion scenarios by the strategy and tag compositions of the invaders and invaded. In one scenario, we find that novel tags introduced by invaders become more readily established with homophilic imitation than without it. In the other, diversity decreases. Lastly, we find a negative correlation between homophily and the rate of convergence.

Lumping evolutionary game dynamics on networks

We study evolutionary game dynamics on networks (EGN), where players reside in the vertices of a graph, and games are played between neighboring vertices. The model is described by a system of ordinary differential equations which depends on players payoff functions, as well as on the adjacency matrix of the underlying graph. Since the number of differential equations increases with the number of vertices in the graph, the analysis of EGN becomes hard for large graphs. Building on the notion of lumpability for Markov chains, we identify conditions on the network structure allowing to reduce the original graph. In particular, we identify a partition of the vertex set of the graph and show that players in the same block of a lumpable partition have equivalent dynamical behaviors, whenever their payoff functions and initial conditions are equivalent. Therefore, vertices belonging to the same partition block can be merged into a single vertex, giving rise to a reduced graph and consequently to a simplified system of equations. We also introduce a tighter condition, called strong lumpability, which can be used to identify dynamical symmetries in EGN which are related to the interchangeability of players in the system.

Sparse cliques trump scale-free networks in coordination and competition

Cooperative behavior, a natural, pervasive and yet puzzling phenomenon, can be significantly enhanced by networks. Many studies have shown how global network characteristics affect cooperation; however, it is difficult to understand how this occurs based on global factors alone, low-level network building blocks, or motifs are necessary. In this work, we systematically alter the structure of scale-free and clique networks and show, through a stochastic evolutionary game theory model, that cooperation on cliques increases linearly with community motif count. We further show that, for reactive stochastic strategies, network modularity improves cooperation in the anti-coordination Snowdrift game and the Prisoner's Dilemma game but not in the Stag Hunt coordination game. We also confirm the negative effect of the scale-free graph on cooperation when effective payoffs are used. On the flip side, clique graphs are highly cooperative across social environments. Adding cycles to the acyclic scale-free graph increases cooperation when multiple games are considered; however, cycles have the opposite effect on how forgiving agents are when playing the Prisoner's Dilemma game.

Plant cooperation

The study of plant behaviour will be aided by conceptual approaches and terminology for cooperation, altruism and helping. The plant literature has a rich discussion of helping between species while the animal literature has an extensive and somewhat contentious discussion of within-species helping. Here, I identify and synthesize concepts, terminology and some practical methodology for speaking about helping in plant populations and measuring the costs and benefits. I use Lehmann and Keller's (2006) classification scheme for animal helping and McIntire and Fajardo's (2014) synthesis of facilitation to provide starting points for classifying the mechanisms of how and why organisms help each other. Contextual theory is discussed as a mechanism for understanding and measuring the fitness consequences of helping. I synthesize helping into four categories. The act of helping can be costly to the helper. If the helper gains indirect fitness by helping relatives but loses direct fitness, this is altruism, and it only occurs within species. Helpers can exchange costly help, which is called mutualism when between species, and reciprocation when within a species. The act of helping can directly benefit the helper as well as the recipient, either as an epiphenomenon resulting from behaviours under natural selection for other reasons, or because the helper is creating a mutual benefit, such as satiating predators or supporting a mutualism. Facilitation between species by stress amelioration, creation of novel ecosystems and habitat complexity often meets the definition of epiphenomenon helping. Within species, this kind of helping is called by-product mutualism. If the helping is under selection to create a mutual benefit shared by others, between species this is facilitation with service sharing or access to resources and within species, direct benefits by mutual benefits. These classifications provide a clear starting point for addressing the subject of helping behaviours.

Impact of small groups with heterogeneous preference on behavioral evolution in population evacuation

Up to now, there have been a great number of mechanisms to explain the individual behavior and population traits, which seem of particular significance in evolutionary biology and social behavior analysis. Among them, small groups and heterogeneity are two useful frameworks to the above issue. However, vast majority of existing works separately consider both scenarios, which is inconsistent with realistic cases in our life. Here we propose the evolutionary games of heterogeneous small groups (namely, different small groups possess different preferences to dilemma) to study the collective behavior in population evacuation. Importantly, players usually face completely different dilemmas inside and outside the small groups. By means of numerous computation simulations, it is unveiled that the ratio of players in one certain small group directly decides the final behavior of the whole population. Moreover, it can also be concluded that heterogeneous degree of preference for different small groups plays a key role in the behavior traits of the system, which may validate some realistic social observations. The proposed framework is thus universally applicable and may shed new light into the solution of social dilemmas.

Conditions for the emergence of shared norms in populations with incompatible preferences

Understanding norms is a key challenge in sociology. Nevertheless, there is a lack of dynamical models explaining how one of several possible behaviors is established as a norm and under what conditions. Analysing an agent-based model, we identify interesting parameter dependencies that imply when two behaviors will coexist or when a shared norm will emerge in a heterogeneous society, where different populations have incompatible preferences. Our model highlights the importance of randomness, spatial interactions, non-linear dynamics, and self-organization. It can also explain the emergence of unpopular norms that do not maximize the collective benefit. Furthermore, we compare behavior-based with preference-based punishment and find interesting results concerning hypocritical punishment. Strikingly, pressuring others to perform the same public behavior as oneself is more effective in promoting norms than pressuring others to meet one's own private preference. Finally, we show that adaptive group pressure exerted by randomly occuring, local majorities may create norms under conditions where different behaviors would normally coexist.

The influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases

Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually been able to maintain elimination or very low incidence of paediatric infectious diseases for long periods of time. Here, we show that including injunctive social norms can reconcile such behaviour-incidence models to observations. Adding social norms to a coupled behaviour-incidence model enables the model to better explain pertussis vaccine uptake and disease dynamics in the UK from 1967 to 2010, in both the vaccine-scare years and the years of high vaccine coverage. The model also illustrates how a vaccine scare can perpetuate suboptimal vaccine coverage long after perceived risk has returned to baseline, pre-vaccine-scare levels. However, at other model parameter values, social norms can perpetuate depressed vaccine coverage during a vaccine scare well beyond the time when the population's baseline vaccine risk perception returns to pre-scare levels. Social norms can strongly suppress vaccine uptake despite frequent outbreaks, as observed in some small communities. Significant portions of the parameter space also exhibit bistability, meaning long-term outcomes depend on the initial conditions. Depending on the context, social norms can either support or hinder immunization goals.

Cooperation promotes the evolution of separate sexes from hermaphrodites with unitary growth

Most animals have specialized into separate sexes but most plants remain hermaphroditic. The underlining cause for this is still unclear. Here we address this question by evolutionary stable strategy analysis and exact calculation of frequency-dependent selection and genetic drift in geographically structured populations. Reproductive investments of hermaphrodites are divided into male and female functions, and each sex requires linear investments that increase linearly with successful gamete number and reusable investments (RIs) that increase less than linearly. Individuals specializing into one sex require RIs of only this sex and thus can produce more gametes. However, these gametes suffer strong kin competition as they are of the same sex and gamete number of the other sex decreases. The success of individuals specializing into one sex requires individuals specializing into the other sex to cooperate with them, providing them with more opposite-sex gametes and relaxing them of the same-sex competition. The evolution of this cooperation does not require two rare mutations to happen simultaneously at the same place, because single-sex mutants can sparsely spread in a hermaphroditic population with RIs despite genetic drift and wait for mutants of the other sex to arise. RI resembles fixed cost in previous theories. However, previous theories considered all costs except for costs for gametes as fixed costs and this does not capture an important plant-animal difference; modular growth of sexual organs in most plants and some animals promotes reproductive investments to increase linearly with offspring number, so their investments in sexual organs are linear investments rather than fixed costs. This study shows the evolution of separate sexes from hermaphrodites as an example of the evolution of cooperation and mutualism as in harmony games, and highlights modular growth as an important factor that prevents most plants and some animals from evolving into separate sexes.

On the fair division of multiple stochastic pies to multiple agents within the Nash bargaining solution

The fair division of a surplus is one of the most widely examined problems. This paper focuses on bargaining problems with fixed disagreement payoffs where risk-neutral agents have reached an agreement that is the Nash-bargaining solution (NBS). We consider a stochastic environment, in which the overall return consists of multiple pies with uncertain sizes and we examine how these pies can be allocated with fairness among agents. Specifically, fairness is based on the Aristotle's maxim: "equals should be treated equally and unequals unequally, in proportion to the relevant inequality". In this context, fairness is achieved when all the individual stochastic surplus shares which are allocated to agents are distributed in proportion to the NBS. We introduce a novel algorithm, which can be used to compute the ratio of each pie that should be allocated to each agent, in order to ensure fairness within a symmetric or asymmetric NBS.

Moving away from nasty encounters enhances cooperation in ecological prisoner's dilemma game

We study the role of migration in the evolution of cooperation. Individuals spatially located on a square lattice play the prisoner's dilemma game. Dissatisfied players, who have been exploited by defectors, tend to terminate interaction with selfish partners by leaving the current habitats, and explore unknown physical niches available surrounding them. The time scale ratio of game interaction to natural selection governs how many game rounds occur before individuals experience strategy updating. Under local migration and strong selection, simulation results demonstrate that cooperation can be stabilized for a wide range of model parameters, and the slower the natural selection, the more favorable for the emergence of cooperation. Besides, how the selection intensity affects cooperators' evolutionary fate is also investigated. We find that increasing it weakens cooperators' viability at different speeds for different time scale ratios. However, cooperation is greatly improved provided that individuals are offered with enough chance to agglomerate, while cooperation can always establish under weak selection but vanishes under very strong selection whenever individuals have less odds to migrate. Whenever the migration range restriction is removed, the parameter area responsible for the emergence of cooperation is, albeit somewhat compressed, still remarkable, validating the effectiveness of collectively migrating in promoting cooperation.

Axelrod's metanorm games on networks

Metanorms is a mechanism proposed to promote cooperation in social dilemmas. Recent experimental results show that network structures that underlie social interactions influence the emergence of norms that promote cooperation. We generalize Axelrod's analysis of metanorms dynamics to interactions unfolding on networks through simulation and mathematical modeling. Network topology strongly influences the effectiveness of the metanorms mechanism in establishing cooperation. In particular, we find that average degree, clustering coefficient and the average number of triplets per node play key roles in sustaining or collapsing cooperation.