A review of evolutionary graph theory with applications to game theory

Shakarian, Paulo; Roos, Patrick; Johnson, Anthony N.

doi:10.1016/j.biosystems.2011.09.006

Cited by 132 publications

(131 citation statements)

References 48 publications

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“…We have developed a birth-death dynamics for this framework so that for the first time we can carry out a dynamic analysis. We note that for evolutionary graphs, there is a wide variety of dynamic models considered including a number of common dynamics used, for example the invasion process (Lieberman et al, 2005), BD-D process (Masuda, 2009), voter model , DB-B process (Ohtsuki et al, 2006), and link dynamics (Lieberman et al, 2005), see also Shakarian et al (2012); Allen and Nowak Line, average fixation probability Line, average temperature Triangle, average fixation probability Triangle, average temperature Fig. 12: Dependence of the fixation probability on the graph.…”

Section: Discussionmentioning

confidence: 99%

A study of the dynamics of multi-player games on small networks using territorial interactions

et al. 2015

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Citation: Broom, M., Lafaye, C., Pattni, K. & Rychtar, J. (2015). A study of the dynamics of multi-player games on small networks using territorial interactions.. Journal of Mathematical Biology, doi: 10.1007/s00285-015-0868-1 This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection. Permanent

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Section: Discussionmentioning

confidence: 99%

A study of the dynamics of multi-player games on small networks using territorial interactions

et al. 2015

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“…However, in many scenarios, players' spatial locations may lead to an incomplete graph structure. Graphical evolutionary game theory is introduced to study the strategies evolution in such a structured population [32]. In graphical EGT, in addition to the entities of players, strategy and payoff matrix, each game model is associated with a graph structure, where the vertexes represent players and the edges determine which player to interact with.…”

Section: A Basic Concepts Of Graphical Evolutionary Game Theorymentioning

confidence: 99%

Graphical Evolutionary Game for Information Diffusion Over Social Networks

Jiang

Chen

Liu

2014

IEEE J. Sel. Top. Signal Process.

124

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Abstract-Current social networks are of extremely largescale generating tremendous information flows at every moment. How information diffuse over social networks has attracted much attention from both industry and academics. Most of the existing works on information diffusion analysis are based on machine learning methods focusing on social network structure analysis and empirical data mining. However, the dynamics of information diffusion, which are heavily influenced by network users' decisions, actions and their socio-economic interactions, is generally ignored by most of existing works. In this paper, we propose an evolutionary game theoretic framework to model the dynamic information diffusion process in social networks. Specifically, we derive the information diffusion dynamics in complete networks, uniform degree and non-uniform degree networks, with the highlight of two special networks, Erdős-Rényi random network and the Barabási-Albert scale-free network. We find that the dynamics of information diffusion over these three kinds of networks are scale-free and the same with each other when the network scale is sufficiently large. To verify our theoretical analysis, we perform simulations for the information diffusion over synthetic networks and real-world Facebook networks. Moreover, we also conduct experiment on Twitter hashtags dataset, which shows that the proposed game theoretic model can well fit and predict the information diffusion over real social networks.

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“…In [11], a generalisation of the Moran process was introduced by arranging the population on a directed graph, see also [13], [18] and [19]. In this model, each vertex represents an individual in the population, and the offspring of each individual only replace direct successors, i.e.…”

Section: Introductionmentioning

confidence: 99%

Fast and asymptotic computation of the fixation probability for Moran processes on graphs

Cuesta¹,

Sequeiros

Rojo

2015

Biosystems

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Evolutionary dynamics has been classically studied for homogeneous populations, but now there is a growing interest in the non-homogenous case. One of the most important models has been proposed in [11], adapting to a weighted directed graph the process described in [12]. The Markov chain associated with the graph can be modified by erasing all non-trivial loops in its state space, obtaining the so-called Embedded Markov chain (EMC). The fixation probability remains unchanged, but the expected time to absorption (fixation or extinction) is reduced. In this paper, we shall use this idea to compute asymptotically the average fixation probability for complete bipartite graphs Kn,m. To this end, we firstly review some recent results on evolutionary dynamics on graphs trying to clarify some points. We also revisit the 'Star Theorem' proved in [11] for the star graphs K1,m. Theoretically, EMC techniques allow fast computation of the fixation probability, but in practice this is not always true. Thus, in the last part of the paper, we compare this algorithm with the standard Monte Carlo method for some kind of complex networks.

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A review of evolutionary graph theory with applications to game theory

Cited by 132 publications

References 48 publications

A study of the dynamics of multi-player games on small networks using territorial interactions

A study of the dynamics of multi-player games on small networks using territorial interactions

Graphical Evolutionary Game for Information Diffusion Over Social Networks

Fast and asymptotic computation of the fixation probability for Moran processes on graphs

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