That leads us to our next question. So for society as a whole, I said this is uniquely efficient. But what about the individual nodes? Because nodes we said, yes. The connections have benefits for nodes, but they also have costs. If you look at the star configuration, well, the node in the middle, the node in the hub, actually has the most connections, a lot of direct benefits but it also carries a lot of the costs. The other one's going with indirect benefits like free read, they have don't have so many go. So let's look a little bit in more detail about that. How is the fairness of the network actually among these network configurations? We are all nodes equally happy inside the network node as a society, as a whole. Okay so let's look at this. We said that's our best social configuration, and we said there are six direct benefit, six direct costs and six indirect benefits. You can go back and look at why that is. Let's calculate the benefits for each one of them. How does the total benefit of 7.44 or whatever the number is, how does it distributed among these four nodes? So our middle node has three direct benefits and three direct costs. So just for the sake of seeing if you're still with me, what would that be? Three direct benefits, three direct costs according to our assumptions. Three times 0.8 minus three times 0.2, so 1.8. So the net benefit, benefit minus cost, the net benefit of the middle node is 1.8. What about the dependent nodes, the connection nodes? So here there is no benefit, one direct benefit and one direct costs. This node only has one connection going into it and then two indirect benefits, and we said the indirect benefits don't have any costs, because this person doesn't have to maintain more than one connection, and the to indirect benefits that look like this. Now, what's the overall net benefit of this node? Just for the sake, making sure you use the with me, please do me a favor, think about that. It's 1.88. So it's higher. So net costs and benefits considered, this node actually has a higher benefit, than the middle node. What about the other two pendant nodes? Well, they are the same. I mean we can do the same calculation now again, also one direct benefit, one direct cost and two indirect gives also 1.88. So actually, the middle one is kind of like worse off here. If you sum that up, all of these, 1.88, plus 1.88, plus, 1.8, plus 1.88 you get the 7.44 of total societal benefit. We see that this total societal benefit is unequally distributed. Some, especially the middle node, actually has a less net benefit and it will start complaining. I have to do the work here with the mediating, you guys are benefiting from these indirect benefits and I'm right here in the middle just passing on messages all the time and you guys over there, you only have to worry about one connection with me and I have to talk with all three of you. So that's not comfortable. That's not a really comfortable situation. I'm just like, I'm out of here, I also want to be one of these pendant nodes and you give me the possibility somehow to do that. The societal pressure will try to keep him in, but it's not a fair network, even though from a societal point of view, it's uniquely efficient. So what can we do here? What do you think could be done? Well, nothing that a little money couldn't solve. Basically, we bribe the one in the middle. So formally in terms of if we have a private sector, and it would be private negotiation, what then will happen, you can bargain a favor among individual, and you basically would reimburse the middle one for this extra effort as the middle one is doing. If you are public sector authority, that means if you make the rules of the game, you want to make sure that the middle hub is there. So what you would do, is that you would subsidize, cross-subsidize, for example you would tax the other ones, and you say, "Hey I put a tax on you, I take some money from you now, we distributed to subsidize this middle node." That's how we maintain this hub, which is crucial to benefit all of us. It benefits all of us with a small average path length, messages or airplanes can travel quicker and we need this. So it's mix of private and public sector negotiations. That's how these things then are maintained in order to maintain the centralized happen and keep it happy and reimbursed the central hub for the effort. So how could we do that now here? Keeping up with our idealized model. Here down we 0.88, what about if we take two cents away. It's a 0.2, we take away and give these 0.2 to the middle hub. So let's say $1.88, we take two cents away and give these two cents to the middle. Now, this pendent node reduced its benefits. It was taxed, so it went down from 1.88 to 1.86, and the value $1.86 it lost. It lost two cents. What about the other two? Well, for fairness reasons we will tax them with the same rate, also two cents. Everybody chips in two cents, I take to cents from this one, give it to the central node. I take two cents from that one and give it to the central node. End of story is that, all of my pendants have now a net benefit of 1.86, and my central node as well, 1.86. So now with this cross-subsidy, everybody's happy. With this tax and redistribution or it might be out of a private sector negotiation in order to find now this will be also fair and now everyone is happy. The middle one says, "Okay, now I'm as good as all of you." Now we really have a long-term stable network due to this strategic network intervention that you've had. By the way again, if you do the math just to see I didn't invent anything or throw anything or throw any money in, if you take the total social value which was 7.44, lots of numbers I know, 7.44 is the same as four times 1.86. So that's how you get the social. While then the social values is now uniformly equally distributed among all four nodes. Now, we are good and we achieved a stable and efficient equilibrium thanks to this intervention. That's how you can think about, that's how you create networks. You try to make them efficient, you try to make them as stable as possible in the long term in order to also maintain them. Then there's some market dynamics. You can think about it. So market dynamics that actually make the network evolve towards some states and sometimes and also well, you can invest strategic intervention in order to make a network stable at the point where it is, because the market sometimes might drive it to inefficient state, a state that is not as efficient, or always go between two states and then you can never do something because you always switching back and forth and you just want a stable configuration in order to be able to build something like societies, or market structures, be it in the economy. That also applies to social dynamics and social configurations, that you want stable social networks.
