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 Evolutionary games on cycles

2006 ◽  
Vol 273 (1598) ◽  
pp. 2249-2256 ◽  
Author(s):  
Hisashi Ohtsuki ◽  
Martin A Nowak
Keyword(s):  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Weak Selection ◽  
Stochastic Effects ◽  
Frequency Dependent Selection ◽  
Game Dynamics ◽  
Case Selection ◽  
Mixed Populations ◽  
Update Rules

Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called ‘birth–death’ (BD), ‘death–birth’ (DB) and ‘imitation’ (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the ‘1/3-law’ of well-mixed populations.

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.

scholarly journals Parent-preferred dispersal promotes cooperation in structured populations

2019 ◽  
Vol 286 (1895) ◽  
pp. 20181949 ◽  
Author(s):  
Xiaojie Chen ◽  
Åke Brännström ◽  
Ulf Dieckmann
Keyword(s):  
Pairwise Comparison ◽  
Small World ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Pair Approximation ◽  
Scale Free ◽  
Scale Free Networks ◽  
Different Types ◽  
Population Structures ◽  
Update Rules

Dispersal is a key process for the emergence of social and biological behaviours. Yet, little attention has been paid to dispersal's effects on the evolution of cooperative behaviour in structured populations. To address this issue, we propose two new dispersal modes, parent-preferred and offspring-preferred dispersal, incorporate them into the birth–death update rule, and consider the resultant strategy evolution in the prisoner's dilemma on random-regular, small-world, and scale-free networks, respectively. We find that parent-preferred dispersal favours the evolution of cooperation in these different types of population structures, while offspring-preferred dispersal inhibits the evolution of cooperation in homogeneous populations. On scale-free networks when the strength of parent-preferred dispersal is weak, cooperation can be enhanced at intermediate strengths of offspring-preferred dispersal, and cooperators can coexist with defectors at high strengths of offspring-preferred dispersal. Moreover, our theoretical analysis based on the pair-approximation method corroborates the evolutionary outcomes on random-regular networks. We also incorporate the two new dispersal modes into three other update rules (death-birth, imitation, and pairwise comparison updating), and find that similar results about the effects of parent-preferred and offspring-preferred dispersal can again be observed in the aforementioned different types of population structures. Our work, thus, unveils robust effects of preferential dispersal modes on the evolution of cooperation in different interactive environments.

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 Evolutionary games on isothermal graphs

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Benjamin Allen ◽  
Gabor Lippner ◽  
Martin A. Nowak
Keyword(s):  
Evolutionary Dynamics ◽  
Cooperative Behavior ◽  
Strong Support ◽  
Evolutionary Games ◽  
Edge Weight ◽  
Cost Ratio ◽  
Weak Selection ◽  
Update Rules ◽  
Effective Degree ◽  
Birth Death

Abstract Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge weight at each node. The conditions for success on isothermal graphs take a simple form, in which the effects of graph structure are captured in the ‘effective degree’—a measure of the effective number of neighbors per individual. For two update rules (death-Birth and birth-Death), cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. For two other update rules (Birth-death and Death-birth), cooperation is never favored. We relate the effective degree of a graph to its spectral gap, thereby linking evolutionary dynamics to the theory of expander graphs. Surprisingly, we find graphs of infinite average degree that nonetheless provide strong support for cooperation.

scholarly journals Evolution of populations with strategy-dependent time delays

2019 ◽  
Author(s):  
Jacek Miȩkisz ◽  
Marek Bodnar
Keyword(s):  
Stationary State ◽  
Time Delays ◽  
Replicator Dynamics ◽  
Evolutionarily Stable Strategy ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Small Time ◽  
Stochastic Perturbations ◽  
New Type ◽  
Novel Behavior

AbstractWe address the issue of stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, an interior stationary state of such dynamics depends continuously on time delays and at some point it might disappear, no cycles are present. In particular, this means that an arbitrarily small time delay changes an interior stationary state. Moreover, at certain time delays, there may appear another interior stationary state.Author summarySocial and biological processes are usually described by ordinary or partial differential equations, or by Markov processes if we take into account stochastic perturbations. However, interactions between individuals, players or molecules, naturally take time. Results of biological interactions between individuals may appear in the future, and in social models, individuals or players may act, that is choose appropriate strategies, on the basis of the information concerning events in the past. It is natural therefore to introduce time delays into evolutionary game models. It was usually observed, and expected, that small time delays do not change the behavior of the system and large time delays may cause oscillations. Here we report a novel behavior. We show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, interior stationary states of such dynamics depend continuously on time delays. This shows that effects of time delays are much more complex than it was previously thought.

scholarly journals Ordering structured populations in multiplayer cooperation games

2015 ◽  
Author(s):  
Jorge Peña ◽  
Bin Wu ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Spatial Structure ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Multiplayer Games ◽  
Spatial Games ◽  
Population Structures ◽  
Single Structure ◽  
Containment Order ◽  
Update Rules

AbstractSpatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure 𝒮1 is greater than population structure 𝒮2 in the containment or the volume order, then 𝒮1 can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.

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