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A Review of Evolutionary Graph Theory With Applications to Game Theory
"... Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the “fixation probability ” the probability o ..."
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Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the “fixation probability ” the probability of a mutant taking over a population and focuses on gametheoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.
Invasion and expansion of cooperators in lattice populations: Prisoner’s dilemma vs. snowdrift games
 JOURNAL OF THEORETICAL BIOLOGY
, 2010
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1 Distributed Adaptive Networks: A Graphical Evolutionary GameTheoretic View
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Games on graphs
 EMS Surveys in Mathematical Sciences. 2014; 1(1):113–151. doi: 10.4171/EMSS/3
"... Abstract. Evolution occurs in populations of reproducing individuals. The trajectories and outcomes of evolutionary processes depend on the structure of the population. Evolutionary graph theory is a powerful approach to studying the consequences of spatial or social population structure. The verti ..."
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Abstract. Evolution occurs in populations of reproducing individuals. The trajectories and outcomes of evolutionary processes depend on the structure of the population. Evolutionary graph theory is a powerful approach to studying the consequences of spatial or social population structure. The vertices of the graph represent individuals. The edges determine who interacts with whom for game payoff and who competes with whom for reproduction. Interaction and competition can be governed by the same graph or by two different graphs. In this paper, we review the basic approach for evolutionary games on graphs and provide new proofs for key results. We formalize the method of identity by descent to derive conditions for strategy selection on finite, weighted graphs. We generalize our results to nonzero mutation rates, and to the case where the interaction and competition graphs do not coincide. We conclude with a perspective of open problems and future directions. Mathematics Subject Classification (2010). 91A22; 92B05, 60J20.
Onethird rules with equality: Secondorder evolutionary stability conditions in finite populations
 JOURNAL OF THEORETICAL BIOLOGY
, 2008
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Consolidating BirthDeath and DeathBirth Processes in Structured Populations
, 2012
"... Network models extend evolutionary game theory to settings with spatial or social structure and have provided key insights on the mechanisms underlying the evolution of cooperation. However, network models have also proven sensitive to seemingly small details of the model architecture. Here we inves ..."
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Network models extend evolutionary game theory to settings with spatial or social structure and have provided key insights on the mechanisms underlying the evolution of cooperation. However, network models have also proven sensitive to seemingly small details of the model architecture. Here we investigate two popular biologically motivated models of evolution in finite populations: DeathBirth (DB) and BirthDeath (BD) processes. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Although superficially similar, under DB cooperation may be favoured in structured populations, while under BD it never is. This is especially troubling as natural populations do not follow a strict one birth then one death regimen (or vice versa); such constraints are introduced to make models more tractable. Whether structure can promote the evolution of cooperation should not hinge on a simplifying assumption. Here, we propose a mixed rule where in each time step DB is used with probability d and BD is used with probability 1{d. We derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. We find that the only qualitatively different outcome occurs when using just BD (d~0). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally we show that, for any mixed BDDB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma, including the Snowdrift Game.
Evolutionary game theorybased evaluation of p2p filesharing systems in heterogeneous environments
 International Journal of Digital Multimedia Broadcasting
"... PeertoPeer (P2P) file sharing is one of key technologies for achieving attractive P2P multimedia social networking. In P2P filesharing systems, file availability is improved by cooperative users who cache and share files. Note that file caching carries costs such as storage consumption and proces ..."
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PeertoPeer (P2P) file sharing is one of key technologies for achieving attractive P2P multimedia social networking. In P2P filesharing systems, file availability is improved by cooperative users who cache and share files. Note that file caching carries costs such as storage consumption and processing load. In addition, users have different degrees of cooperativity in file caching and they are in different surrounding environments arising from the topological structure of P2P networks. With evolutionary game theory, this paper evaluates the performance of P2P file sharing systems in such heterogeneous environments. Using micromacro dynamics, we analyze the impact of the heterogeneity of user selfishness on the file availability and system stability. Further, through simulation experiments with agentbased dynamics, we reveal how other aspects, for example, synchronization among nodes and topological structure, affect the system performance. Both analytical and simulation results show that the environmental heterogeneity contributes to the file availability and system stability.
Journal of Theoretical Biology] (]]]])]]]–]]] Contents lists available at ScienceDirect Journal of Theoretical Biology
"... journal homepage: www.elsevier.com/locate/yjtbi How mutation affects evolutionary games on graphs ..."
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journal homepage: www.elsevier.com/locate/yjtbi How mutation affects evolutionary games on graphs
Evolutionary Games on Structured Populations under Weak Selection
"... All biological systems are, at some level, guided by the laws of natural selection and evolutionary dynamics. Adaptations with increased fitness tend to proliferate and fixate within populations. Those situations in which an individual’s fitness depends not only upon a static environment, but upon t ..."
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All biological systems are, at some level, guided by the laws of natural selection and evolutionary dynamics. Adaptations with increased fitness tend to proliferate and fixate within populations. Those situations in which an individual’s fitness depends not only upon a static environment, but upon the fluctuating phenotypes of the surrounding population, fall within the domain of evolutionary game theory. In a beautiful paper, Tarnita et al. (2009c) proved that for a large class of evolutionary games on structured populations with n = 2 strategies, the conditions for a strategy to be selected for in the limit of weak selection could be described entirely by one, realvalued structure coefficient σ. This paper explores a generalization of this result to an arbitrary number of strategies n, and finds that to describe selection conditions for any n we need only three such realvalued structure coefficients σ1, σ2, σ3. In an attempt to describe exactly which games this theorem applies to, we define a new, general class of evolutionary games which may be of independent interest. We also demonstrate a specific application of our results to the evolution of cooperation, a popular research topic. 1