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

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

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

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

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

Â Has this nice intuition that how important how influential a given

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

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

Â so forth. getting wisdom out in terms of a overall

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

Â important. now in terms of the learning models that

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

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

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

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

Â difficult. The restricted Bayesian version we saw

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

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

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

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

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

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

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

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

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

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

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

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

Â of between myopic and rational combine some of these things.

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

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

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

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

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

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

Â And the there wasn't any strategy involved.

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

Â believe. So if you think about voting in election

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

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

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

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

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

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

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

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

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

Â group models very attractable in understanding how the speed of learning

Â depends on say the segregation structure of the network.

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

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

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

Â relates to different properties of the network.

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

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

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

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

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

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

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

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

Â that we need to still understand about how learning works.

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

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

Â something systematic about how the network structure and influence the

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

Â Okay, so that wraps up our discussino of learning.

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

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

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

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

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

Â happens in that setting.

Â