Okay. so let's just wrap-up our discussion of,

learning. And, in terms of a summary, in terms of

what we saw in the Degroup Model, we found convergence and consensus if and

only if we had aperiodicity. the limiting influence was related to

iten vector, concepts and gives a nice foundation for that and in fact.

Has this nice intuition that how important how influential a given

individual is depends on how much weight they get in which depends on how much

weight they're the indirect weight that they're getting from their neighbors and

so forth. getting wisdom out in terms of a overall

society converging nobody's retains too much influence that's going to be

important. now in terms of the learning models that

we've gone through. We saw that the Bayesian model was

computationally demanding in a number of setting, of ways, in terms of the kinds

of calculations that people might have to do and the gaming that might go on in

that kind of setting. So those models can be quite set

difficult. The restricted Bayesian version we saw

gives a consensus, but the, the network didn't play much of a roll.

Understanding this sort of limits in the Bayesian setting is something that is

still being studied there's a number of paper's looking at this the DeGroot model

is a very attractable alternative model it, it is much more naive in terms of the

way that people update non the less it can be accurate so that's an interesting

aspect of it as long as it's somewhat balanced in terms of the way that people

are getting weights in. And nobody's retaining too much

influence, it still be a very accurate way of updating.

the nice thing is that it, it, it, the mathematics behind it are simple, it has

some intuitive feels to it and it can be useful in terms of working with data.

Now, in terms of the to-do list there's a lot that, that is missing from these

models and you know, there, there are models being developed of, they're sort

of between myopic and rational combine some of these things.

There's also richer settings that we might want to think about and so,

obviously there's a lot of the world where consensus is not reached.

And this model, the models we were looking at were very simple ones in the

sense that first of all we're running time to infinite.

we're assuming some stationarity in terms of what is going on.

It's not as if the world was changing and, and, as we were going along.

And the there wasn't any strategy involved.

So wasn't just if people had different preferences for what other people want to

believe. So if you think about voting in election

and you want certain, you have a bias in terms of what kinds of programs you'd

like to be enacted then you might want to convince somebody there's somebody is a

better politician than somebody else and so strategic communication could be very

different than the kind of. Of settings that we were looking at where

everybody's just trying to estimate more or less the same thing and there wasn't

any strong preference involved. So you know, we could enrich things and,

and begin to look at that and there's some work being done on that.

there's also a lot that we can do that it, that I didn't talk about here but

that has been done in terms of beginning you know so for instance beginning to the

group models very attractable in understanding how the speed of learning

depends on say the segregation structure of the network.

So if we bring the homophily into play. And try to understand how things work.

You can do that. you can begin to, to understand more

about how speed depends on the, the structure of the network and how it

relates to different properties of the network.

So there's a lot of tractable things that can be done here.

And so this is sort of an important area of research in, in understanding how

society Forms opinions and another thing that's sort of missing here is, you know,

the, the in terms of the network, we've a little bit agnostic about what nodes are.

And you could imagine that some nodes are news outlets, some are individuals, so,

so we get our news and, and information in different ways.

You could begin to enrich the models by taking into account different types of

nodes and things. So there's a lot to be done and a lot

that we need to still understand about how learning works.

The nice thing is that there are things that we, one can do to make things

reasonably tractable and to work with models where we can begin to say

something systematic about how the network structure and influence the

eventual beliefs And there's sort of an active area for things to be looked at.

Okay, so that wraps up our discussino of learning.

And the next thing we're going to be taking a look at is looking at games and

networks. So now we're going to be looking at

situations where people's decisions of whether or not they're going to take an

action really depends on what they think their friends are doing, and That will

give us a game structure. And then we can try and analyze what

happens in that setting.