All right. Let's see what else they have here in the models library Sugarscape number 3 called Wealth Distribution. Okay. Let's see. I think most of it is basically the same. If you go to the description, something here changed down here, and it says, "Each agent also has a maximum age." Also quite a realistic assumption actually which is assigned randomly from the range between 60 to 100 ticks, so might say 60 to 100 years. Then, yes, that's what you do randomly. You use the random variable if you don't really know if some of them, who of them actually lives longer and who not and at the end, yes you just say randomly, that make sense, people live between well 60 and 100, but more about this age range, and then you distribute that you have a certain diversity, it reassembles reality better. When the agent reaches an age beyond its maximum age, it dies. Okay. Whenever an agent dies either from starvation, so we still have that, or old age, a new randomly initialized agent is created somewhere in the world. Hence in this model the global population count stays constant. All right. So we have a global population count because they always get replaced. We also see the population slider here, it's actually not here anymore, there are some other ones, wealth distribution. We start with 400 agents as well, and start with our setup, and then we go. What we also have here, we have two other sliders that measure something and they measure the income distribution, the income inequality, that's called a Lorenz curve. So here is the percentage of population, here is the percentage of wealth. It's not important that you understand it. But think about if income would be uniformly, completely equally distributed, this red curve here, this Lorenz curve would be on this black line. The further the curve goes away and bellies out, it has a belly here, the more inequality we have. If it were to be completely a rectangle here then it will be extremely unequal. So the bigger this area basically, this area between the diagonal and the red curve, the more unequal the income distribution, and this area under the curve is measured with what's called a Gini coefficient which you can see evolving down here and it gets bigger, it gets higher, this blue as the curve bellies out. So basically that's the measure for inequality. The higher it is, the more unequal, and the lower it is, the more equal. All right. So we can now see how it evolves, inequality goes up a little bit. We can also see that because the wealth distribution becomes more unequal. Again, here we have the number of agents, and here we have the amount of sugar, the wealth. We can see eventually that we have, most of our agents have very little sugar. So they're here on the left side of the amount of sugar, and very few Asians here have a lot of sugar, so they have almost 200 sugar whereas those here, almost 200 agents have very little sugar. We see it stabilizes and other inequality, and we get a wealth distribution that is highly unequal. Actually this wealth distribution we know it quite well. It's called a Pareto distribution, and that's how inequality is and historically always has been distributed in society. It's a power law. It's a certain distribution, just as the other distributions, the normal distribution, the exponential distribution. This is a power law, it's a distribution, and what it says is that there are exponentially few agents with exponentially much sugar, and exponentially many agents with exponentially few sugar. That's what's actually said, the power law, you actually encounter it a lot in social systems and in many different complex systems, for example, scale-free networks have an extremely unequal distribution of links. Most of them are aggregating at the hub. So that's also a power-law. If the power-law is presented not as a, now taking some statistics, not as a PDF but as a CDF then it's called a Pareto distribution, but it's the same thing. Maybe you also heard of SIP flaw. SIP flaw it's also the same power law, it's just differently ranked, so Pareto distribution, SIP flaw and power law are all the same thing. Basically what they say is that something is extremely unequally distributed. Again, exponentially few with exponentially much, and exponentially many with exponentially little. So that's what you get here. So basically now we grew the income distribution as it exists in society. We basically replicated, we replicated what happens in society, which is quite amazing because our model is really quite simple. But with that, we can already replicate a phenomenon, emergent phenomenon that we have found over the last hundreds of years in all modern societies. So let's summarize our first three Sugarscape model variations, increasingly more sophisticated variation for Sugarscape. We started with Sugarscape number 1 and things to notice is that we already were able to grow, replicate an evolution of society with regards to their vision and metabolism. So yes, we model evolutionary pressure, evolutionary dynamics which is not a minor thing. Then whatever our modeling assumptions was that there was limited vision and instance rollback of the sugar patches, and together they lead to this terracing so we had our four income groups, and we have a pretty skewed welcome distribution among these four different terraces. So that's what we found in the first model, second model we had, the change was a gradual grow back. So now the sugar didn't grow back instantaneously, and what we found is there was more competition. If the environment changes you have to be fitter in order to adapt, and we also saw a more evolutionary pressure therefore on the vision and the metabolism. We've got more extreme values for both of them. Third, with our third simulation, we found actually that we maybe said, well there was a modeling assumption changes that there's no indefinite valve accumulation, we said that we had a death and a randomly distribution, and that was already enough as actually surprisingly little assumptions if you think about it, like we just walked through it ourselves you can look at the code that's behind there. Feel free to open it up. It's a very simple code and we were able to replicate something that humanity has been struggling with for hundreds of years is this extreme unequal income distribution which is called a Pareto distribution, and that emerged from the bottom up from our assumptions. That's one of the goals often in Asian art or our often one of the goals is to see if we find a macro behavior to use shellings of arts, a macro behavior and we try to find the minimum assumptions, the minimum behavior of the individuals that allow us to grow or to replicate this macro behavior.
