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 Cooperation and competition between pair and multi-player social games in spatial populations

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Attila Szolnoki ◽  
Xiaojie Chen
Keyword(s):  
Public Goods ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Pair Interaction ◽  
Public Goods Game ◽  
Point Interactions ◽  
Social Games ◽  
The Public ◽  
Specific Parameter ◽  
Group Members

AbstractThe conflict between individual and collective interests is in the heart of every social dilemmas established by evolutionary game theory. We cannot avoid these conflicts but sometimes we may choose which interaction framework to use as a battlefield. For instance some people like to be part of a larger group while other persons prefer to interact in a more personalized, individual way. Both attitudes can be formulated via appropriately chosen traditional games. In particular, the prisoner’s dilemma game is based on pair interaction while the public goods game represents multi-point interactions of group members. To reveal the possible advantage of a certain attitude we extend these models by allowing players not simply to change their strategies but also let them to vary their attitudes for a higher individual income. We show that both attitudes could be the winner at a specific parameter value. Interestingly, however, the subtle interplay between different states may result in a counterintuitive evolutionary outcome where the increase of the multiplication factor of public goods game drives the population to a fully defector state. We point out that the accompanying pattern formation can only be understood via the multipoint or multi-player interactions of different microscopic states where the vicinity of a particular state may influence the relation of two other competitors.

scholarly journals Aspiration dynamics of multi-player games in finite populations

2014 ◽  
Vol 11 (94) ◽  
pp. 20140077 ◽  
Author(s):  
Jinming Du ◽  
Bin Wu ◽  
Philipp M. Altrock ◽  
Long Wang
Keyword(s):  
Evolutionary Game ◽  
Pairwise Comparison ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Weak Selection ◽  
Additional Information ◽  
Average Abundance ◽  
Imperfect Rationality ◽  
Update Rules ◽  
Limiting Case

On studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics. In the former case, individuals imitate the strategy of a more successful peer. In the latter case, individuals adjust their strategies based on a comparison of their pay-offs from the evolutionary game to a value they aspire, called the level of aspiration. Unlike imitation processes of pairwise comparison, aspiration-driven updates do not require additional information about the strategic environment and can thus be interpreted as being more spontaneous. Recent work has mainly focused on understanding how aspiration dynamics alter the evolutionary outcome in structured populations. However, the baseline case for understanding strategy selection is the well-mixed population case, which is still lacking sufficient understanding. We explore how aspiration-driven strategy-update dynamics under imperfect rationality influence the average abundance of a strategy in multi-player evolutionary games with two strategies. We analytically derive a condition under which a strategy is more abundant than the other in the weak selection limiting case. This approach has a long-standing history in evolutionary games and is mostly applied for its mathematical approachability. Hence, we also explore strong selection numerically, which shows that our weak selection condition is a robust predictor of the average abundance of a strategy. The condition turns out to differ from that of a wide class of imitation dynamics, as long as the game is not dyadic. Therefore, a strategy favoured under imitation dynamics can be disfavoured under aspiration dynamics. This does not require any population structure, and thus highlights the intrinsic difference between imitation and aspiration dynamics.

scholarly journals Two conceptions of evolutionary games: reductive vs effective

2017 ◽  
Author(s):  
Artem Kaznatcheev
Keyword(s):  
Game Theory ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Theoretical Work ◽  
Structured Populations ◽  
Agent Based ◽  
Specific Interpretation ◽  
The Difference ◽  
Games Theory ◽  
Future Work

Evolutionary game theory (EGT) was born from economic game theory through a series of analogies. Given this heuristic genealogy, a number of central objects of the theory (like strategies, players, and games) have not been carefully defined or interpreted. A specific interpretation of these terms becomes important as EGT sees more applications to understanding experiments in microscopic systems typical of oncology and microbiology. In this essay, I provide two interpretations of the central objects of games theory: one that leads to reductive games and the other to effective games. These interpretation are based on the difference between views of fitness as a property of individuals versus fitness as a summary statistic of (sub)populations. Reductive games are typical of theoretical work like agent-based models. But effective games usually correspond more closely to experimental work. However, confusing reductive games for effective games or vice-versa can lead to divergent results, especially in spatially structured populations. As such, I propose that we treat this distinction carefully in future work at the interface of EGT and experiment.

scholarly journals Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model

2016 ◽  
Author(s):  
A.E.F. Burgess ◽  
P.G. Schofield ◽  
S.F. Hubbard ◽  
M.A.J. Chaplain ◽  
T. Lorenzi
Keyword(s):  
Diffusion Equation ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Reaction Diffusion ◽  
Social Contexts ◽  
Random Motion ◽  
Structured Populations ◽  
Reaction Diffusion Equation ◽  
Modelling Framework ◽  
Dynamical Patterns

AbstractWe present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individual-based model is used to describe the player dynamics, whereas the evolution of the chemoattractant is governed by a reaction-diffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxis-diffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a two-player game, and are awarded a payoff, in terms of reproductive fitness, according to their strategy. As an example, we let individuals play the Hawk-Dove game. Numerical simulations illustrate how random motion and chemotactic response can bring about self-generated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise. In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatially-structured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.

scholarly journals Structural symmetry in evolutionary games

2015 ◽  
Vol 12 (111) ◽  
pp. 20150420 ◽  
Author(s):  
Alex McAvoy ◽  
Christoph Hauert
Keyword(s):  
Population Structure ◽  
Evolutionary Game ◽  
Evolutionary Process ◽  
Evolutionary Games ◽  
Structured Populations ◽  
Fixation Probability ◽  
Matrix Games ◽  
Single Mutant ◽  
Symmetric Games ◽  
Monomorphic Population

In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time , for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be ‘evolutionarily equivalent’ in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term ‘homogeneous’ should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry.

MORE SPATIAL GAMES

1994 ◽  
Vol 04 (01) ◽  
pp. 33-56 ◽  
Author(s):  
MARTIN A. NOWAK ◽  
SEBASTIAN BONHOEFFER ◽  
ROBERT M. MAY
Keyword(s):  
Prisoner's Dilemma ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Reproductive Rate ◽  
Spatial Effects ◽  
Random Drift ◽  
Low Frequencies ◽  
Spatial Games

We extend our exploration of the dynamics of spatial evolutionary games [Nowak & May 1992, 1993] in three distinct but related ways. We analyse, first, deterministic versus stochastic rules; second, discrete versus continuous time (see Hubermann & Glance [1993]); and, third, different geometries of interaction in regular and random spatial arrays. We show that spatial effects can change some of the intuitive concepts in evolutionary game theory: (i) equilibria among strategies are no longer necessarily characterised by equal average payoffs; (ii) the strategy with the higher average payoff can steadily converge towards extinction; (iii) strategies can become extinct even though their basic reproductive rate (at very low frequencies) is larger than one. The equilibrium properties of spatial games are instead determined by “local relative payoffs.” We characterise the conditions for coexistence between cooperators and defectors in the spatial prisoner’s dilemma game. We find that cooperation can be maintained if the transition rules give more weight to the most successful neighbours, or if there is a certain probability that cells may remain unoccupied in the next generations when they are surrounded by players with low payoffs. In this second case the cooperators can survive despite a very large payoff advantage to defectors. We also compute average extinction times for random drift in neutral spatial models. Finally we briefly describe the spatial dynamics of an interaction among three species which dominate each other in a cyclic fashion. The emphasis of this paper is presenting a variety of ideas and possibilities for further research in the evolutionary dynamics of spatial games. The overall conclusion is that interactions with local neighbours in 2- or 3-dimensional spatial arrays can promote coexistence of different strategies (such as cooperators and defectors in the Prisoner’s Dilemma), in situations where one strategy would exclude all others if the interactions occurred randomly and homogeneously.

scholarly journals Controlling evolutionary dynamics to optimize microbial bioremediation

2019 ◽  
Author(s):  
Shota Shibasaki ◽  
Sara Mitri
Keyword(s):  
Theoretical Model ◽  
Flow Rate ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Environmental Parameters ◽  
Public Goods Game ◽  
Public And Private ◽  
Private Goods ◽  
Practical Applications ◽  
Microbial Bioremediation

AbstractSome microbes have a fascinating ability to degrade compounds that are toxic for humans in a process called bioremediation. Although these traits help microbes survive the toxins, carrying them can be costly if the benefit of detoxification is shared by all surrounding microbes, whether they detoxify or not. Detoxification can thereby be seen as a public goods game, where non-degrading mutants can sweep through the population and collapse bioremediation. Here, we constructed an evolutionary game theoretical model to optimize bioremediation in a chemostat initially containing “cooperating” (detoxifying) microbes. We consider two types of mutants: “cheaters” that do not detoxify, and mutants that become resistant to the toxin through private mechanisms that do not benefit others. By manipulating the concentration and flow rate of a toxin into the chemostat, we identified conditions where cooperators can exclude cheaters that differ in their private resistance. However, eventually, cheaters are bound to invade. To overcome this inevitable outcome and maximize detoxification efficiency, cooperators can be periodically reinoculated into the population. Our study investigates the outcome of an evolutionary game combining both public and private goods and demonstrates how environmental parameters can be used to control evolutionary dynamics in practical applications.

COOPERATION, COLLECTIVES FORMATION AND SPECIALIZATION

2006 ◽  
Vol 09 (04) ◽  
pp. 315-335 ◽  
Author(s):  
CHRISTOPH HAUERT
Keyword(s):  
Evolutionary Dynamics ◽  
Conflicts Of Interest ◽  
Cooperative Behavior ◽  
Evolutionary Game ◽  
Structured Populations ◽  
Drop Out ◽  
Oscillatory Dynamics ◽  
Spatially Extended ◽  
Common Resource ◽  
The Individual

Cooperation in spatial evolutionary game theory has revealed various interesting insights into the problem of the evolution and maintenance of cooperative behavior. In social dilemmas, cooperators create and maintain a common resource at some cost to themselves while defectors attempt to exploit the resource without contributing. This leads to classical conflicts of interest between the individual and the community with the prisoner's dilemma as the most prominent mathematical metaphor to describe such situations. The evolutionary fate of cooperators and defectors sensitively depends on the interaction structure of the population. In spatially extended populations, the ability to form clusters or collectives often supports cooperation by limiting exploitation to the cluster boundaries but often collectives formation may also inhibit or even eliminate cooperation by hindering the dispersal of cooperators. Another attempt at resolving the conflict of interest allows individuals to drop out of unpromising public enterprises and hence changes compulsory interactions into voluntary participation. This leads to a cyclic dominance of cooperators, defectors and loners that do not participate and gives rise to oscillatory dynamics which again subtly depends on the population structure. Here we review recent advances in the dynamics of cooperation in structured populations as well as in situations where cooperative investments vary continuously. In such continuous games, the evolutionary dynamics driven by mutation and selection can lead to spontaneous diversification and specialization into high and low investing individuals which provides a natural explanation for the origin of cooperators and defectors.

scholarly journals Evolution of prosocial punishment in unstructured and structured populations and in the presence of antisocial punishment

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0254860
Author(s):  
Mohammad Salahshour
Keyword(s):  
Large Body ◽  
Theoretical Models ◽  
Free Rider ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Public Goods Game ◽  
The Public ◽  
Free Rider Problem ◽  
Altruistic Punishment ◽  
Public Resource

A large body of empirical evidence suggests that altruistic punishment abounds in human societies. Based on such evidence, it is suggested that punishment serves an important role in promoting cooperation in humans and possibly other species. However, as punishment is costly, its evolution is subject to the same problem that it tries to address. To suppress this so-called second-order free-rider problem, known theoretical models on the evolution of punishment resort to one of the few established mechanisms for the evolution of cooperation. This leaves the question of whether altruistic punishment can evolve and give rise to the evolution of cooperation in the absence of such auxiliary cooperation-favoring mechanisms unaddressed. Here, by considering a population of individuals who play a public goods game, followed by a public punishing game, introduced here, we show that altruistic punishment indeed evolves and promotes cooperation in the absence of a cooperation-favoring mechanism. In our model, the punishment pool is considered a public resource whose resources are used for punishment. We show that the evolution of a punishing institution is facilitated when resources in the punishment pool, instead of being wasted, are used to reward punishers when there is nobody to punish. Besides, we show that higher returns to the public resource or punishment pool facilitate the evolution of prosocial instead of antisocial punishment. We also show that an optimal cost of investment in the punishment pool facilitates the evolution of prosocial punishment. Finally, our analysis shows that being close to a physical phase transition facilitates the evolution of altruistic punishment.

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