Hello again, folks. so this is Matt and we're talking about Imperfect Information in the Extensive Form now. So we're going to be talking now about games where we have some sequential moves and there can be some uncertainty in player's minds about both the possible pay-offs of other and the strategies that others might be following. So we'll start let's just by, you know, to, to give you some ideas about this, let's talk a little bit about poker. which, as a game, has been becoming incredibly popular recently both for people playing it on television and other kinds of things. And it's one of the oldest games which has very extensive experience, and for, for a lot of people. And the, the, the, you know, one of the critical aspects of poker is that there's actually sequential play in betting, calling, folding. So, one player gets, you know, to to make a, a decision in terms of how much they're going to make a bet at a certain point in time. Other players have to react to that. So, the sequential play you see some cards in, in many of these games, but not all. So you might see some of the cards that the other players are holding. But you don't know how strong their hand is. And you have to be inferring things about their, their possible cards both from odds in the game and based on what they're doing in terms of their strategy. so you see the bets and you react to them and you have to make inferences based on that. so that involves having beliefs about the motivations, the rationality of other players what their pay-offs are, what their potential pay-offs are, which in poker might come from, from the cards. so when we think about these kinds of games, you know, there's many possible hands that's going to make poker a fairly complicated game to, to keep track of. There's many batting strategies which means that the overall tree that we, we're going to have to work with is, is going to be quite complicated. so it's actually going to be almost impossible to draw the tree in the sense of, of just drawing it out on the screen. but there's nonetheless a lot that we can learn about analyzing such games. And analyzing the types of strategies that they have. How, how do we represent extensive form games with incomplete information? How might we reason about these things? and moreover there'll be simpler settings. you know, poker's actually a fairly complicated game. and there, there's other fairly complicated games but very high stakes games. So, for instance, you know, we could have one country thinking about invading another one and, and, a potential war or a conflict. they're trying to decide what the other country's going to do in response. So, if you invaded, what would they do? That's a game of incomplete information because you might not know exactly how strong they are or how what's the, the willingness of the population to fight. What might happen politically. how, how strong are they, if there was a war. so there's, these are situations where one party might have to move first, anticipating reaction of the other. the second one has to anticipate what the, the, the fact that they're being invaded means about the strength of the other do you surrender? Do you fight? so those are games that are going to have similar kinds of features to these. And it's going to be very important to develop a set of, a way of representing this things, and some thoughts about analyzing those. So that's where we're headed next and we'll see a lot more of this very shortly.