前置课程

第一课什么是norm？（An Evolutionary Approach to Norms）
第二课什么是norm game？（An Evolutionary Approach to Norms）
第三课什么是元规范metanom？《An Evolutionary Approach to Norms》

论文内容

In peer-to-peer systems, agents share resources (hardware, software or information) with others, but if there is no cost to access files nor any limit on the number of files accessible, then there is no incentive to respond to requests and, more generally, to establish cooperation in the system.
在系统中，agents如果没有规范norm，可能就不存在cooperation这样的合作行为。这句话其实暗示了norm的定义

The use of norms to provide a means of ensuring cooperative behaviour has been proposed by many but, as shown by Axelrod [1], norms alone may not lead to the desired outcomes.
这里明确说明norm就是一个工具，来保证合作行为的，但是光有norm是不够的。这里Axelrod写的论文在附件中，是一个非常经典的norm emergency的论文，之后会精析Axelrod的论文

In consequence, metanorms have been proposed as a means of ensuring not that norms are complied with, but that they are enforced. While experiments have shown that metanorms are effective in fully-connected environments as used by Axelrod, there has been limited consideration of metanorms with different but more realistic topological configurations, which fundamentally change the mechanisms required to establish cooperation.
因为光norm不够，所以引出metanorm元规范的概念。这个概念是Axelrod提出来的，但是Axelrod只证明了metanorms在全连接环境中是有效的，本文在更真实拓扑的配置环境中进行

In particular, real-world domains, such as peer-to-peer and wireless sensor networks, are not fully connected, with agents tending to interact with a small subset of others on a regular basis, yet it is only through such interactions that defection can be observed and punishment administered.
在真实世界中，像Axelrod的全连接的环境是不存在的，每个人都只认识他们的邻居，因此他们只能观测到他们的邻居，并且惩罚他们的邻居

First, Axelrod assumes that an agent’s defection penalises all other agents in the population. The introduction of a topology enables us to restrict the penalty to only those agents with which the defector interacts.
第一，Axelrod假定一个人作弊的话，会对所有人产生损害；在拓扑结构中，一个人作弊只会对他的邻居产生损害

Second, Axelrod assumes agents to be able to observe the entire population. By introducing a topology, we employ a more realistic model in which an agent can only observe (with a certain probability) those agents with which it interacts
第二，拓扑中，一个人也只能观测到他的邻居是否作弊，而不是全部的人

Third, Axelrod does not require observation of misbehaviour for punishment. However, by introducing constraints on observation and rendering the model more realistic, an agent should only punish a defector if the agent can observe the defector. In addition, an agent should only metapunish an agent that fails to punish a defector if it can observe both the defector and the agent that fails to punish the defector。
==一个人只能惩罚他能够观测到的人，一个人也只能惩罚那些能观测到的不惩罚的人，如果这个人既可以看到作弊的人，也可以看到看到作弊但不惩罚的人 ==

Finally, in order to enhance an agent’s individual performance, it compares itself to others in the population before deciding whether to modify strategy.
最后，每一个agent也只能向邻居学习他们的策略

论文实验内容

Neighborhood size

作者开始研究Neighborhood size（NS），如果NS是2，就说明一个agent只是跟两个其他的agent认识。作者开始做实验，也就是之前说过的metanorm game，先给定一个NS的值，然后做10次，每次产生1000代，然后逐步增加NS的值，从1到50，然后做了一个图，特别注意一个点，图中的NS的值并不是真正的NS值，应该把横坐标乘2才是真正的NS值，下面我的解释都以图的横坐标为标准：
在这里插入图片描述

可以看出来，在NS在1的时候，是很随机的，没有产生norm，然后再NS为3的时候，boldness已经非常低了接近0
此后NS再增加，就好只是增加了vengefulness而已。

Population size

If we increase population size (PS) while keeping NS static, we decrease the relative number of connections among the overall population. This suggests that convergence to norm establishment should decrease, in line with the above results.
作者认为，保持Neighborhood Size不变，然后增大Population size，就是变相的减小NS
但是作者做的实验发现，NS=3的时候，PS不断增大，但是对boldness和vengefulness并没有显著影响。

在这里插入图片描述

因此作者认为norm establishment 是被一个作弊行为的惩罚总量，作者叫这个为potential peer pressure of a lattics.

small world networks

small world networks作为lattics格子结构的变体
with some of connections replaced by connections to other randomly selected nodes in the network, in line with a specifific rewiring probability (RP)
一些连接，会按照RP概率，重新连接到一些随机的其他的点
这样会比之前的那个lattics好，是因为lattics格子的话，就会有一部分的lattics会被很多的agent观测到，因此这些lattics的压力“potential peer pressure” 就会很大。避免这种情况，提出了RP的概念。
作者在PS为51，NS为3的情况下，做了图：
结论：indicating that increasing the RP decreases the final average vengefulness in the population.
不断增加的RP会降低最终的vengefulness。
作者还发现RP的增加会大幅度降低vengefulness，但是并不会显著升高boldness。