Emergence of cooperation and selection of interactions

From human societies to the simplest biological systems, cooperative interactions thrive at all levels of organization. A cooperative act typically involves a cost (c) to the provider while conferring a benefit (b) to the recipient (with b> c)[Hamilton (1996); Trivers (1985); Wilson (1975); Axelrod and Hamilton (1981)]. Individuals try to maximize their own resources and are therefore expected to avoid paying any costs while gladly accepting all the benefits offered by others.

Every living structure was produced and shaped according to the fundamental mechanisms of natural selection. However, such mechanisms do not suffice to explain the emergence of the complex reciprocal ties we find so essential in the sustainability of human society. These ties provide a clear example of the type of cooperative behavior not expected to emerge naturally through the evolutionary mechanisms of natural selection, which predict a world filled with selfish entities. How cooperation emerges is thus a major scientific challenge. One particular suited framework, called Evolutionary Game Theory, assumes that individuals interact according to well-known social dilemmas of cooperation and evolve through natural selection. Conventionally, Evolutionary Game Theory assumes infinite well-mixed populations, resulting in a set of coupled non-linear ordinary differential equations known as replicator equations. When individuals engage in a Prisoner's Dilemma of cooperation, cooperation does not emerge. Additional mechanisms were proposed to explain the emergence of cooperation. A key mechanism assumes finite and structured populations in which individuals interact through the links of complex networks. The most successful types of networks are heterogeneous, hence characterized by the diversity among the number of links individuals possess. Here we investigate the emergence of cooperation when a new aspect of diversity is introduced, associated with individuals that have limited resources. Furthermore, we introduce a quantity called Gradient of Selection, which extracts the population-wide dynamics on populations structured according to different types of complex networks. We use this quantity to study the impact that different types of structures have on the effective dilemma faced by the population as a whole.

2007

Often the selfish and strong are believed to be favored by natural selection, even though cooperative interactions thrive at all levels of organization in living systems. Recent empirical data shows that networks representing the social interactions between people exhibit typically high average connectivity and associated single-to-broad-scale heterogeneity, a feature which precludes the emergence of cooperation in any static network.

Nature, 2006

A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals 1-4 . Human society is based to a large extent on mechanisms that promote cooperation 5-7 . It is well known that in unstructured populations, natural selection favors defectors over cooperators. There is much current interest, however, for studying evolutionary games in structured populations and on graphs 8-17 . These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks 18-24 . Here we describe a surprisingly simple rule, which is a good approximation for all graphs that we have analyzed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks 25,26 : natural selection favors cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbors, k. Therefore, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity. A cooperator is someone who pays a cost, c, for another individual to receive a benefit, b. A defector pays no cost and does not distribute any benefits. In evolutionary biology, cost and benefit are measured in terms of fitness. Reproduction can be genetic or cultural. In the latter case, the strategy of someone who does well is imitated by others. In an unstructured population, where all individuals interact equally likely with each other, defectors have a higher average payoff than unconditional cooperators. Therefore, natural selection increases the relative abundance of defectors and drives cooperators to extinction. These evolutionary dynamics hold for the deterministic setting of the replicator equation 27,28 and for stochastic game dynamics of finite populations 29 . In our model, the players of an evolutionary game occupy the vertices of a graph. The edges denote links between individuals in terms of game dynamical interaction and biological reproduction. We assume that the graph is fixed for the duration of the evolutionary dynamics. Consider a population of N individuals consisting of cooperators and defectors. A cooperator helps all individuals to whom it is connected. If a cooperator is connected to k other individuals and i of those are cooperators, then its payoff is bi -ck. A defector does not provide any help, and therefore has no costs, but it can receive the benefit from neighboring cooperators. If a defector is connected to j cooperators, then its payoff is bj. The fitness of an individual is given by a constant term, denoting the baseline fitness, plus the payoff that arises from the game. Strong selection means that the payoff is large compared to the baseline fitness; weak selection means the payoff is small compared to the baseline fitness.

International Journal of Bifurcation and Chaos, 2008

In this paper, we propose a new very simple mechanism supporting the emergence of cooperation in a population of memoryless agents playing a prisoner's dilemma game. Each agent belongs to a community and interacts with the agents of its community and with the agents belonging to linked communities. A simple rule governs the dynamics of the system: a community grows (resp. decreases) if the average score of its members is superior (resp. inferior) to the average score calculated for the entire population. Starting from a random initialization, the system can evolve towards a majority of cooperators, towards the elimination of cooperators, or towards a situation with periodic evolutions of the populations of cooperators and defectors. The initial presence of clusters of C-strategies accounts for the convergence towards cooperative final states. We consider various topologies: Erdös and Rényi random graphs, square lattices and scale-free graphs. Clusters are not as likely to appear...

Ecology Letters, 2011

The ubiquity of cooperation in nature is puzzling because cooperators can be exploited by defectors. Recent theoretical work shows that if dynamic networks define interactions between individuals, cooperation is favoured by natural selection. To address this, we compare cooperative behaviour in multiple but independent repeated games between participants in static and dynamic networks. In the latter, participants could break their links after each social interaction. As predicted, we find higher levels of cooperation in dynamic networks. Through biased link breaking (i.e. to defectors) participants affected their social environment. We show that this link-breaking behaviour leads to substantial network clustering and we find primarily cooperators within these clusters. This assortment is remarkable because it occurred on top of behavioural assortment through direct reciprocity and beyond the perception of participants, and represents a self-organized pattern. Our results highlight the importance of the interaction between ecological context and selective pressures on cooperation.

Journal of Evolutionary Biology, 2006

The Prisoner's Dilemma (PD) constitutes a widely used metaphor to investigate problems related to the evolution of cooperation. Whenever evolution takes place in well-mixed populations engaged in single rounds of the PD, cooperators cannot resist invasion by defectors, a feature, which is somewhat alleviated whenever populations are spatially distributed. In both cases the populations are characterized by a homogeneous pattern of connectivity, in which every individual is equivalent, sharing the same number of neighbours. Recently, compelling evidence has been accumulated on the strong heterogeneous nature of the network of contacts between individuals in populations.

Chaos, Solitons & Fractals, 2016

As natural systems continuously evolve, the human cooperation dilemma represents an increasingly more challenging question. Humans cooperate in natural and social systems, but how it happens and what are the mechanisms which rule the emergence of cooperation, represent an open and fascinating issue. In this work, we investigate the evolution of cooperation through the analysis of the evolutionary dynamics of behaviours within the social network, where nodes can choose to cooperate or defect following the classical social dilemmas represented by Prisoner's Dilemma and Snowdrift games. To this aim, we introduce a sociological concept and statistical estimator, "Critical Mass", to detect the minimum initial seed of cooperators able to trigger the diffusion process, and the centrality measure to select within the social network. Selecting different spatial configurations of the Critical Mass nodes, we highlight how the emergence of cooperation can be influenced by this spatial choice of the initial core in the network. Moreover, we target to shed light how the concept of homophily, a social shaping factor for which "birds of a feather flock together", can affect the evolutionary process. Our findings show that homophily allows speeding up the diffusion process and make quicker the convergence towards human cooperation, while centrality measure and thus the Critical Mass selection, play a key role in the evolution showing how the spatial configurations can create some hidden patterns, partially counterbalancing the impact of homophily.

2010

This paper offers a new and robust model of the emergence and persistence of cooperation. In the model, interactions are anonymous, the population is well-mixed, and the evolutionary process selects strategies according to material payoffs. The cooperation problem is modelled as a game similar to Prisoner's Dilemma, but there is an outside option of nonparticipation and the payoff to mutual cooperation is stochastic; with positive probability, this payoff exceeds that from cheating against a cooperator. Under mild conditions, mutually beneficial cooperation occurs in equilibrium. This is possible because the non-participation option holds down the equilibrium frequency of cheating.

Scientific reports, 2018

Conditional cooperation declines over time if heterogeneous ideal conditional agents are involved in repeated interactions. With strict assumptions of rationality and a population consisting of ideal conditional agents who strictly follow a decision rule, cooperation is not expected. However, cooperation is commonly observed in human societies. Hence, we propose a novel evolutionary agent-based model where agents rely on social information. Each agent interacts only once either as a donor or as a receiver. In our model, the population consists of either non-ideal or ideal heterogeneous conditional agents. Their donation decisions are stochastically based on the comparison between the number of donations in the group and their conditional cooperative criterion value. Non-ideal agents occasionally cooperate even if the conditional rule of the agent is not satisfied. The stochastic decision and selection rules are controlled with decision intensity and selection intensity, respectively...