#### 期刊菜单

Evolution of Expectation-Based Probabilistic Dormancy Promote Cooperation
DOI: 10.12677/MOS.2024.131066, PDF, HTML, XML, 下载: 150  浏览: 205  国家自然科学基金支持

Abstract: In response to the generation and evolution of cooperation in evolutionary games, this paper pro-poses a probabilistic dormant mechanism evolutionary model based on node expectations. We fo-cus on the effects of expectation and dormancy mechanism on node strategy behavior and group cooperation, and validate the model by simulation on square lattice network. The simulation results show that cooperation occurs in the system only when the expected payoffs of the nodes are in a range, and that there exists an optimal expected payoff that can lead to the highest cooperation rate in the system. The node dormancy time is too short and too long for the evolution of cooperation, and the existence of an optimal dormancy time for different betrayal temptations can make the co-operation rate highest. There exists an optimal participation game parameter that can make the system have the highest cooperation rate, the cooperation phenomenon can not exist at small par-ticipation game parameter, and even if the betrayal temptation is large when the participation game parameter is large, there still exists a low cooperation rate in the system. Through simulation verification, we find that the expectation-based probabilistic dormancy mechanism can effectively promote the generation and evolution of cooperation.

1. 引言

2. 演化模型

$M=\left(\begin{array}{cc}R& S\\ T& P\end{array}\right)$ (1)

$R=1,S=P=0,T=b,b\in \left(1,2\right)$ 表示节点受到的背叛诱惑。在每一轮的博弈中，系统中所有节点依次与自己的四个邻居进行博弈，记节点i收到的收益为Pi，计算如(2)式：

${P}_{i}=\underset{j\in {\Omega }_{i}}{\sum }{S}_{i}^{T}M{S}_{j}$ (2)

${E}_{i}=\alpha \ast K$ (3)

$\alpha \in \left(0,1\right)$ 称为期望收益参数，通过α来调整节点获得的期望收益，其中K表示的是节点i的邻居个数，固定为4。

${Q}_{i}=\frac{1}{1+\mathrm{exp}\left[-\beta \left({P}_{i}-{E}_{i}\right)\right]}$ (4)

${T}_{i}\left(t+1\right)=\left\{\begin{array}{c}{T}_{i}\left(t\right)+1\\ 0\end{array}\begin{array}{c},\\ ,\end{array}\begin{array}{c}{T}_{i}\left(t\right)<{T}_{d}\\ {T}_{i}\left(t\right)={T}_{d}\end{array}$ (5)

$W\left({S}_{i}\to {S}_{j}\right)=\frac{1}{1+\mathrm{exp}\left[\left({P}_{i}-{P}_{j}\right)/k\right]}$ (6)

3. 仿真与分析

Figure 1. Evolutionary results of the cooperation rate under the combined effect of expected payoff α and betrayal temptation b, where β = 4, Td = 10, and k = 0.1

Figure 2. (a) Denotes the evolution result of the cooperation rate Fc; (b) denotes the evolution result of the participation game rate Gc; and (c) denotes the evolution result of the node’s average payoff Poff; where α = 0.3, Td = 10, k = 0.1

Figure 3. Evolution results of the cooperation rate under the joint action of the betrayal temptation b and the participation game parameter β, where α = 0.3, Td = 10, k = 0.1

Figure 4. Evolution of cooperation rate with dormancy duration Td, where β = 4, α = 0.3, and k = 0.1

Figure 5. Evolutionary results of node strategy snapshots over time (Yellow for collaborators, blue for betrayers), (a~e): b = 1.2; (f~j): b = 1.4; (k~o): b = 1.6. where β = 4, α = 0.3, Td = 10, k = 0.1

Figure 6. Evolutionary results of node strategy snapshots over time (Yellow for collaborators, blue for betrayers), (a~e): β = 2; (f~j): β = 4; (k~o): β = 6. where b = 1.4, α = 0.3, Td = 10, k = 0.1

4. 结论

NOTES

*通讯作者。

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