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Costly punishment and cooperation in the evolutionary snowdrift game

机译：演化雪堆游戏中代价高昂的惩罚与合作

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摘要

The role of punishments in promoting cooperation is an important issue. We incorporate costly punishments into the snowdrift game (SG) by introducing a third punishing (P) character, and study the effects. The punishers, who carry basically a cooperative (C) character, are willing to pay a cost α so as to punish a non-cooperative (D) opponent by β. Depending on the initial fractions of the characters, α, β, and the cost-to-benefit ratio r in the SG, the three-character system evolves into a steady state consisting either only of C and P characters or only of C and D characters, in a well-mixed population. The former situation represents an enhancement in cooperation relative to the SG, while the latter is similar to the SG. The dynamics in approaching these different steady states are found to be different. Analytically, the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations. The sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points. The analysis also shows the role of P-character agents in preventing a system from invasion by D-character agents. Starting from a population consisting only of C and P agents, a D-character agent intended to invade the system cannot survive when the initial fraction of P agents is greater than rβ. Our model, defined intentionally as a simulation algorithm, can be readily generalized to incorporate many interesting effects, such as those in a networked population.
机译：惩罚在促进合作中的作用是一个重要问题。通过引入第三个惩罚（P）角色，我们将代价高昂的惩罚纳入雪堆游戏（SG）中，并研究其效果。基本上具有合作（C）角色的惩罚者愿意支付费用α，以便用β惩罚不合作（D）的对手。取决于字符的初始分数，α，β和SG中的成本效益比r，三字符系统演变成仅由C和P字符或仅由C和D组成的稳态人物，在高度混合的人群中。前一种情况表示相对于SG的合作有所增强，而后者类似于SG。发现接近这些不同稳态的动力学是不同的。从分析上看，通过一组微分方程可以捕获仿真中动力学和稳态中的关键特征。通过描述相图中的流并分析不动点的性质，研究了对字符初始分布的敏感性。分析还显示了P字符代理在防止系统被D字符代理入侵中的作用。从仅由C和P药剂组成的种群开始，当P药剂的初始分数大于rβ时，旨在入侵系统的D药剂无法生存。我们的模型（有意定义为模拟算法）可以很容易地概括为包含许多有趣的效果，例如网络人口中的效果。

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