Asymmetric cost in snowdrift game on scale-free networks

Du, Wei; Cao, Xianbin; Hu, Mao-Bin; Wang, W.-X.

doi:10.1209/0295-5075/87/60004

Cited by 186 publications

(73 citation statements)

References 52 publications

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“…Then we choose one of agent x's nearest neighbors at random, and the chosen agent y also acquires its payoff P y by the same rule. We suppose that the probability that agent x adopts agent y's opinion is given by the Fermi function [27][28][29][30]:…”

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confidence: 99%

A consensus opinion model based on the evolutionary game

Yang

2016

EPL

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Abstract. -We propose a consensus opinion model based on the evolutionary game. In our model, both of the two connected agents receive a benefit if they have the same opinion, otherwise they both pay a cost. Agents update their opinions by comparing payo?s with neighbors. The opinion of an agent with higher payoff is more likely to be imitated. We apply this model in scalefree networks with tunable degree distribution. Interestingly, we find that there exists an optimal ratio of cost to benefit, leading to the shortest consensus time. Qualitative analysis is obtained by examining the evolution of the opinion clusters. Moreover, we find that the consensus time decreases as the average degree of the network increases, but increases with the noise introduced to permit irrational choices. The dependence of the consensus time on the network size is found to be a power-law form. For small or larger ratio of cost to benefit, the consensus time decreases as the degree exponent increases. However, for moderate ratio of cost to benefit, the consensus time increases with the degree exponent. Our results may provide new insights into opinion dynamics driven by the evolutionary game theory.Introduction. -The dynamics of opinion sharing and competing and the emergence of consensus have become an active topic of recent research in statistical and nonlinear physics [1]. One of the most successful methodologies used in opinion dynamics is agent-based modeling. The idea is to construct the computational devices (known as agents with some properties) and then simulate them in parallel to model the real phenomena. In physics this technique can be traced back to Monte Carlo simulations. A number of agent-based models have been proposed, which include the voter model [2], the majority rule-model [3,4], the bounded-confidence model [5] and the social impact model [6]. Some models display a disorderorder transition [7][8][9][10][11][12], from a regime in which opinions are arbitrarily diverse to one in which most individuals hold the same opinion. Other models focus the emergence of a global consensus [13][14][15][16][17][18], in which all agents finally share the same opinion.In this Letter, we propose an opinion model based on the evolutionary game. Evolutionary game theory as a powerful mathematical framework, has been widely used to understand cooperative behavior [19,20], traffic flow [21,22], epidemic spreading [23,24] and so on. However, to the best of our knowledge, the impact of evolutionary games on the

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confidence: 99%

A consensus opinion model based on the evolutionary game

Yang

2016

EPL

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“…Consequently, (11) can be proven by induction, which completes the proof. The time when the number of cooperators in the population equals that in A, plays a key role in the rest of the proof.…”

Section: Now Letmentioning

confidence: 64%

“…While these assumptions help to simplify the mathematical setup and gain insight into the theoretical aspects of cooperation mechanisms, an interesting research line that has not been explored to its full potential is to study a finite heterogeneous population of game-playing agents under stochastic discrete-time updating dynamics. [7] Interesting simulation results have been conducted for heterogeneous populations in [11], [12] and [13] where the agents are associated with different payoff matrices. Some mathematical statements have been provided in [14] and [15] The work was supported in part by the European Research Council (ERCStG-307207).…”

Section: Introductionmentioning

confidence: 99%

Analysis and control of strategic interactions in finite heterogeneous populations under best-response update rule

Ramazi

Cao

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Abstract-For a finite, well-mixed population of heterogeneous agents playing evolutionary games choosing to cooperate or defect in each round of the game, we investigate, when agents update their strategies in each round using the myopic best-response rule, how the number of cooperating agents changes over time and demonstrate how to control that number by changing the agents' payoff matrices. The agents are heterogeneous in that their payoff matrices may differ from one another; we focus on the specific case when the payoff matrices, fixed throughout the evolution, correspond to prisoner's dilemma or snowdrift games. To carry out stability analysis, we identify the system's absorbing states when taking the number of cooperating agents as a random variable of interest. It is proven that when all the agents update frequently enough, the reachable final states are completely determined by the available types of payoff matrices. As a further step, we show how to control the final state by changing at the beginning of the evolution, the types of the payoff matrices of a group of agents.

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“…Other prominent mechanisms that support the evolution of cooperation include kin selection [12], mobility and dilution [13,14], direct and indirect reciprocity [15,16], network reciprocity [11,[17][18][19], * marcoantonio.amaral@gmail.com group selection [20], and population heterogeneity [21][22][23][24]. In particular, research in the realm of statistical physics has shown that properties of the interaction network can have far reaching consequences for the outcome of evolutionary social dilemmas [25][26][27][28][29][30][31][32][33][34][35][36][37] (for reviews see Refs. [38][39][40][41][42][43][44]), and moreover, that heterogeneity in general, be it introduced in the form of heterogeneous interaction networks, noisy disturbances to payoffs, or other player-specific properties like the teaching activity or the propensity to acquire new links over time, is a strong facilitator of cooperation [22,37,[45][46][47][48][49][50][51]…”

Section: Introductionmentioning

confidence: 99%

Role-separating ordering in social dilemmas controlled by topological frustration

et al. 2017

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"Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

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Asymmetric cost in snowdrift game on scale-free networks

Cited by 186 publications

References 52 publications

A consensus opinion model based on the evolutionary game

A consensus opinion model based on the evolutionary game

Analysis and control of strategic interactions in finite heterogeneous populations under best-response update rule

Role-separating ordering in social dilemmas controlled by topological frustration

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