Evolutionary Games And Opinion Dynamics In Complex Networks

Cooperation is ubiquitous in our world.Cooperative phenomenon between indi-viduals can be observed in many real complex system,from microbial community to global economic system.Therefore,studying on the internal mechanism of the emer-gence and maintenance of the cooperation in complex systems has theoretical and prac-tical significance.Recent decades,the evolutionary game theory has been introduced to investigate the cooperative behavior in complex systems in detail.The complex sys-tems in real world usually have specific structures which can be described by complex networks.Based on the results of former researchers,we study the spatial evolutionary game dynamics from four perspectives in this thesis.Firstly,we put forward a new ana-lytic method of the evolutionary prisoner's dilemma game in random regular networks.Then we study the effects of the planarity and heterogeneity of networks on the evolution of cooperation in two-player games.After that we make a detailed research on the evo-lutionary destiny of memory-one strategies in spatial evolutionary prisoner's dilemma game.Lastly,we study the effects of small world characteristic and the relative time scale of the entangled dynamics on the Kuramoto evolutionary game systematically.Opinion dynamics as a kind of sociophysics mainly concerned with the formation,diffusion and transmission of opinions.In real life,people's opinion may change during the process of communicating with others,which lead to the formation of group opin-ion.Opinion dynamics plays an important role in people's ordinary life,such as public opinion guidance in social media,people's viewpoints about global financial crisis,cli-mate change and environmental sustainability and protection.It is well known that,the structure characteristic of networks has a significant influence on the behavior of the evolutionary dynamics taking place on them.In this thesis,we make a deep investiga-tion on the effect of spatial dimensionality and/or the heterogeneous coupling patterns of the underlying networks on the critical behavior of opinion dynamics.The main contents and innovation of the thesis are as follows.Analysis of the evolutionary prisoner's dilemma game in random regular networks:By assuming that the distribution of the strategies around an individual is homogeneous in the evolutionary game theory in random regular networks,we find three equilib-rium relationship of the steady system under weak selection approximation.By solving them,we obtain an analytic solution of the cooperation frequency of the system which is well coincident with our simulation results.In addition,by using extensive Monte Carlo simulations under different payoff parameters,we find that the fluctuation of the system depends on the selection strength of system only,which indicate that the selec-tion strength here can be used to define the temperature of the system.Meanwhile,we also find that the cooperation frequency has a linear correlation with the corresponding average payoff of the steady system.Effects of planarity and heterogeneity of networks on evolutionary two-player games:We study the effects of the planarity and heterogeneity of networks on the evolutionary two-player symmetric games by considering four different kinds of networks,which include two types of heterogeneous networks:the weighted planar stochastic lattice?a planar scale-free network?and the random uncorrelated scale-free network with the same degree distribution as the weighted planar stochastic lattice,and two types of ho-mogeneous networks:the Hexagonal lattice and the random regular network with the same degree k₀=6 as Hexagonal lattice.By extensive computer simulations,we found that both the planarity and heterogeneity of the network have a significant influence on the evolution of cooperation,either promote or inhibit,which depends on not only the specific kind of game:the harmony,snowdrift,stag hunt or prisoner's dilemma game,but also on the update rule:the Fermi,replicator or unconditional imitation rule.Evolutionary destiny of memory-one strategies in spatial evolutionary prisoner's dilemma game:During the process of strategy updating,each individual keeps in mind all the outcome of the action pairs adopted by himself and each of his neighbors in the last interaction,and according to which the individuals decide what actions they will take in the next round.Computer simulation results imply that win-stay-lose-shift like strategy win out of the memory-one strategy set in the stationary state.This result is robust in a large range of the payoff parameter,and does not depend on the initial state of the system.Furthermore,theoretical analysis with mean field and quasi-static approximation predict the same result.Thus,our studies suggest that win-stay-lose-shift like strategy is a stable dominant strategy in repeated prisoner's dilemma game in homogeneous structured populations.Evolutionary Kuramoto dilemma in small-world networks:We study the influence of small-world topology and relative time scale of the entangled dynamics in the evolu-tionary Kuramoto dilemma.We find that when the relative cost for cooperation is low,more random topology favors better the emergence of collective synchronization and cooperation.Whenever the cooperative behavior becomes costly,high level of global synchronization can only be achieved in the typical small-world region,i.e.,the under-lying interaction should be not too regular,and not too random as well.Furthermore,simulation results with distinct time-scale of the involved synchronization and cooper-ation dynamics show that both the cooperation and synchronization level of the system can be improved by increasing the relative time-scale of strategy updating.Kinetic-exchange-like opinion dynamics in complex networks:The probability of the presence of negative outcome in the pairwise interaction is represented by the con-trol parameter p?[0,1],which indicates that the difference between the opinions of the two focal individuals becomes even more large because of disagreement.Accordingly,with probability 1-p the two opinions become more similar?positive interaction?.We find that in random homogeneous networks the ordering process displays an anomalous jump at some special value of the control parameter p^*,which gives rise to two dis-tinct critical points p_cfor p<p^*and p>p^*,respectively.Whenever the underlying interaction network has heterogeneous interaction patterns and/or planar property,the anomalous ordering phenomenon disappears.Finite-size scaling analysis of the simu-lation results shows that the critical exponents for the opinion dynamics in random net-works are in accordance with those of the mean-field Ising model,no matter whether the degree distribution is homogeneous or heterogeneous and the anomalous jump of the order parameter is presence or absence.The critical exponents for the opinion dynam-ics in spatially embedded networks?in two dimensions?belong to different universality classes,which depend closely on the configuration of local interactions.Particularly,whenever the local interactions are homogeneously distributed,two-dimensional Ising model universality class is recovered.Mean-field theoretical analysis corroborates well our findings.Our results highlight the importance of both the dimensionality and the local topology of the underlying interaction network in the phase transition behavior of the opinion dynamics.