scholarly journals Evolution of Cooperation in the Presence of Higher-Order Interactions: From Networks to Hypergraphs

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 744
Author(s):  
Giulio Burgio ◽  
Joan T. Matamalas ◽  
Sergio Gómez ◽  
Alex Arenas
Keyword(s):  
Evolutionary Dynamics ◽  
Higher Order ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Mathematical Representation ◽  
Interaction Patterns ◽  
Group Interactions ◽  
Cooperative Phenomena ◽  
Structured Population ◽  
Pairwise Models

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise to network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.

scholarly journals Negotiation and appeasement can be more effective drivers of sociality than kin selection

2016 ◽  
Vol 371 (1687) ◽  
pp. 20150089 ◽  
Author(s):  
Andrés E. Quiñones ◽  
G. Sander van Doorn ◽  
Ido Pen ◽  
Franz J. Weissing ◽  
Michael Taborsky
Keyword(s):  
Genetic Relatedness ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Conditional Cooperation ◽  
Negotiation Strategies ◽  
Structured Population ◽  
The Face ◽  
Kin Structure ◽  
Invasion Analysis ◽  
Individual Based Simulation

Two alternative frameworks explain the evolution of cooperation in the face of conflicting interests. Conflicts can be alleviated by kinship, the alignment of interests by virtue of shared genes, or by negotiation strategies, allowing mutually beneficial trading of services or commodities. Although negotiation often occurs in kin-structured populations, the interplay of kin- and negotiation-based mechanisms in the evolution of cooperation remains an unresolved issue. Inspired by the biology of a cooperatively breeding fish, we developed an individual-based simulation model to study the evolution of negotiation-based cooperation in relation to different levels of genetic relatedness. We show that the evolution of negotiation strategies leads to an equilibrium where subordinates appease dominants by conditional cooperation, resulting in high levels of help and low levels of aggression. This negotiation-based equilibrium can be reached both in the absence of relatedness and in a kin-structured population. However, when relatedness is high, evolution often ends up in an alternative equilibrium where subordinates help their kin unconditionally. The level of help at this kin-selected equilibrium is considerably lower than at the negotiation-based equilibrium, and it corresponds to a level reached when responsiveness is prevented from evolving in the simulations. A mathematical invasion analysis reveals that, quite generally, the alignment of payoffs due to the relatedness of interaction partners tends to impede selection for harsh but effective punishment of defectors. Hence kin structure will often hamper rather than facilitate the evolution of productive cooperation.

scholarly journals Evolutionary dynamics with game transitions

2019 ◽  
Vol 116 (51) ◽  
pp. 25398-25404 ◽  
Author(s):  
Qi Su ◽  
Alex McAvoy ◽  
Long Wang ◽  
Martin A. Nowak
Keyword(s):  
Strong Influence ◽  
Evolutionary Dynamics ◽  
Simple Game ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Altruistic Behavior ◽  
Weak Selection ◽  
Time Step ◽  
Mutual Cooperation ◽  
Connected Populations

The environment has a strong influence on a population’s evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals’ behaviors together with the games that they play in one time step influence the games to be played in the next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: Weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, b, to the corresponding cost, c, exceedsk−k′, where k is the average number of neighbors of an individual andk′captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly connected populations.

scholarly journals Evolutionary dynamics of group interactions on structured populations: a review

2013 ◽  
Vol 10 (80) ◽  
pp. 20120997 ◽  
Author(s):  
Matjaž Perc ◽  
Jesús Gómez-Gardeñes ◽  
Attila Szolnoki ◽  
Luis M. Floría ◽  
Yamir Moreno
Keyword(s):  
Statistical Physics ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Public Goods Game ◽  
Group Interactions ◽  
The Public ◽  
Living Organisms ◽  
Class Representative

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.

scholarly journals Invasion of Cooperation in Scale-Free Networks: Accumulated versus Average Payoffs

2017 ◽  
Vol 23 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Genki Ichinose ◽  
Hiroki Sayama
Keyword(s):  
Evolutionary Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Average Degree ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Scale Free ◽  
Invasion Mechanism ◽  
Cooperative Strategies ◽  
Average Payoff ◽  
Scale Free Networks

It is well known that cooperation cannot be an evolutionarily stable strategy for a non-iterative game in a well-mixed population. In contrast, structured populations favor cooperation, since cooperators can benefit each other by forming local clusters. Previous studies have shown that scale-free networks strongly promote cooperation. However, little is known about the invasion mechanism of cooperation in scale-free networks. To study microscopic and macroscopic behaviors of cooperators' invasion, we conducted computational experiments on the evolution of cooperation in scale-free networks where, starting from all defectors, cooperators can spontaneously emerge by mutation. Since the evolutionary dynamics are influenced by the definition of fitness, we tested two commonly adopted fitness functions: accumulated payoff and average payoff. Simulation results show that cooperation is strongly enhanced with the accumulated payoff fitness compared to the average payoff fitness. However, the difference between the two functions decreases as the average degree increases. As the average degree increases, cooperation decreases for the accumulated payoff fitness, while it increases for the average payoff fitness. Moreover, for the average payoff fitness, low-degree nodes play a more important role in spreading cooperative strategies than for the accumulated payoff fitness.

scholarly journals Evolutionary dynamics in structured populations

2010 ◽  
Vol 365 (1537) ◽  
pp. 19-30 ◽  
Author(s):  
Martin A. Nowak ◽  
Corina E. Tarnita ◽  
Tibor Antal
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Process ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Evolutionary Graph Theory ◽  
Phenotype Space ◽  
Multicellular Organisms

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.

scholarly journals Network clique cover approximation to analyze complex contagions through group interactions

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Giulio Burgio ◽  
Alex Arenas ◽  
Sergio Gómez ◽  
Joan T. Matamalas
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Higher Order ◽  
Structured Populations ◽  
Networked Systems ◽  
Stable Region ◽  
Mean Field Model ◽  
Group Interactions ◽  
Edge Clique Cover ◽  
Network Clique

AbstractContagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work, focusing on interaction structures represented as simplicial complexes, we present a discrete-time microscopic model of complex contagion for a susceptible-infected-susceptible dynamics. Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the higher-order dynamical correlations among the members of the substructures (cliques/simplices). The analytical computation of the critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any mean-field model, the possibility of a bi-stable region is extended to structured populations.

scholarly journals Higher-order temporal network effects through triplet evolution

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen
Keyword(s):  
Real World ◽  
Link Prediction ◽  
Higher Order ◽  
Prediction Algorithm ◽  
Interaction Patterns ◽  
Temporal Networks ◽  
World Systems ◽  
Order Interaction ◽  
Space And Time ◽  
Pairwise Interactions

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

scholarly journals Evolutionary dynamics of higher-order interactions in social networks

2021 ◽  
Author(s):  
Unai Alvarez-Rodriguez ◽  
Federico Battiston ◽  
Guilherme Ferraz de Arruda ◽  
Yamir Moreno ◽  
Matjaž Perc ◽  
...  
Keyword(s):  
Social Networks ◽  
Evolutionary Dynamics ◽  
Higher Order
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