The difference is really going to be in the application.

So this has to be a setting where I can really connect to somebody without them

having to want to, to allow me to connect to somebody.

So it does work in settings like citing somebody's article.

I can do that without their permission, or linking to a webpage.

I can follow somebody on Twitter and so forth without them having to follow me.

So there are setting where you can have this kind of diretic, directed setting.

And so what we'll do is we'll model that as a very simple situation where people

just announce their preferred set of neighbors.

And then a network forms if and he based on which ever links people want to form.

And here we're going to keep track of ordered pairs.

Now, so the fact that ij is in this network, ij is now different from ji, so

this means i is following j. this means j is following i, or, or i

formed a direct link to j, and, and so forth.

And then just look at the Nash set of networks, where each person is forming

some links to some the links that they want.

Given the links that everyone else is forming.

[BLANK_AUDIO] Okay now when we think about these kinds of settings, we have to

think about the flow of payoffs too. So one situation is sort of a one way

flow. If I follow somebody on Twitter and they

don't follow me, then I get to hear what they say but they don't hear what I say.

so that's a setting where the person who pays the cost then hears information from

the, the node that they're accessing. Now two way flow could be that one player

forms a link and bears the cost but both benefit from it.

So it could be that for instance if I add a link to another page on the Internet,

then that's good for me because people can get from my page from the other.

It also helps the other page get new traffic that I direct there.

phone calls, you know, they, they, the, there's you could think of this, as

somebody bears the cost. two people end up but phone calls

actually are across to both people involved if you think about time and so

forth. So there's some situations where we could

think about two way flow. Now the two way flow, there's a paper by

Bala and Goyal in 2000 basically did a directed version of the connections

model. So the model we can think of as being the

same as what we saw from the Jackson Lewinsky version.

But now what's going to be different is instead of having consent to form a

relationship. People can form a relationship

unilateraly. And I can just direct my link to somebody

else. We'll both end up benefiting, so the

benefits will look just like the the connections model we had originally, but

now people can form a link unilaterally. So it's a different formation process but

the same payoff structure. so the person, the benefits structure,

the cost structure is going to be different.

It's only the person forming the link that bears the cost.

So if you just want to go through in terms of efficiency.

The efficiency's going to be exactly the same as before.

Except now that we have half as much costs being born, so instead of having 2c

per link, we're going to have 1c per link.

And then in terms of what that does for the efficient calculations, is it just

factors everything down by a, a factor of 2 in terms of the costs.

So the efficiency in this model is exactly as it was before except for we've

just divided through by 2. and so you get complete networks if costs

are low enough, star networks in the middle range and the empty network when

costs are high enough. One thing here is I put complete and star

in quotes, because complete doesn't mean that every link in both directions is

present. It just means that every two nodes are

connected, and in this case, they're connected by only one link.

It doesn't make sense to have links in both directions because you bear twice

the cost and there's no added information flow in this situation.

So, if you, if you go through this, it's, it's similar architectures.

slightly different cost structure. Somebody has to bear the cost.

But you only want one person bearing the cost between any two individuals, because

things flow in both directions once that's formed.

So efficiency's exactly the same as it was before.

when we begin to look at the Nash stable networks, I'll sort of list through what

you, what you can find. You can check this.

so if, if cost is very low, then the sort of complete network will be Nash stable.

So basically it makes sense to cut an indirect relationship to a direct

relationship. And somebody, if, if the other person's

not doing anything, the other, you know. If one person's not doing it, the second

person will have an incentive to do it. Medium cost range, medium low, all star

networks are Nash stable, plus some other networks.

Whereas a star now could be formed in, in different directions, so it could be that

the centre is forming some of the links. And peripheral agents are forming some of

the others, so you can have a star with multiple directions on the links.

again, you know, it doesn't make sense to form links in both directions because it

doesn't add any benefits, and adds to cost.

so you'll see stars that are going to be Nash stable, and depending on, the

configuration. it, it could be that center's bearing

more cost or the periphery is bearing more cost, there can be combinations of

different types of stars. So any star in that network is going to

be Nash stable. when you get to a higher cost so that c

is bigger than delta, now let's think a little bit about comparing two stars.

So if we look at a situation where we've got a, let's look at two extremes.

One extreme is where the periphery formed a link.

So they all link to the center. Okay.