 Hi, folks. So it's time to start into a new topic and a very interesting one at that. What we're going to talk about now is repeated games, and so this will use some of the reasoning we've had in terms of sub-game perfection and extensive forms, but now think of situations where players are playing a game, but they're playing it repeatedly over time. So, you know, when we think of most interactions in the world, there's a lot of them which occur more than once. So, you know, when we think about different kinds of things, you know, firms in a marketplace, they're interacting with their competitors, they're doing it day after day after day. We think about political alliances, countries deciding how they should negotiate with other ones, whether they should have conflicts and so forth. Those are the things where, you know, this happens repeatedly over time, so there's a long history and a long future ahead of them. Friends, you know, do you exchange, do you help your friends out when they need help? Do they help you back when you need it? So, you know, you're going through repeated interactions and how you've performed in the past. If you have friends that have done very well for you, you're more likely to reciprocate. Some of these kinds of things can involve repeated interactions. Workers, team production, you've got to, you know, day after day, you need to help some of your coworkers. Sometimes you have to do tasks that don't go noticed and sometimes they do help you out and so forth. So these are situations where repetition can make a difference and understanding it will be an important aspect of understanding how the repetition affects the play involves a whole series of different kinds of things. Just to fix ideas, let's talk a little bit about OPEC, which was a cartel which was formed in the early 1970s and just in terms of background, if you go back to, you know, the period between 1930 and up to 1973 when OPEC started being put together. The price of oil, so these are all adjusted numbers to reflect, say, $200 and $8, so we adjust for inflation and other kinds of things. But if you adjust everything to the same, to adjust for inflation, at a price of roughly $20 per barrel or less from the period of 1930 to about 1973, OPEC starts to form. What happens, they decide that, you know, they've just been acting, it's a bunch of players, a bunch of different producers, they've been acting on their own for many years and just pumping lots of oil and they pump so much oil that the price is fairly low, it's very easy to buy oil. So they're going to start by restricting production, cut production back down and that will drive the price up. What's the difficulty is if all the other ones are producing very little and driving the price up, I'd like to cheat on the agreement and pump more oil. So you can think of this as looking somewhat like a giant prisoner's dilemma game where we'd all like to pump less oil if we're OPEC or oil producing countries drive the price up but we all have an incentive to cheat a little bit and pump more oil and the repetition can help us police that if we're OPEC. So what happens, by 1976 the price goes up to about $50 a barrel. By the time you get to 1982, these are also in real terms, so these are adjusted for inflation, they've pumped the price up to $90 a barrel and in the early 1980s it does quite well in terms of OPEC, lots of money coming in and then it collapses for a while. So when you look at the period say between about 1986 to 2002, so between 82 and 86 it starts to erode, it kind of falls apart. Between 86 and 2002 the price is basically $40 a barrel or less and then they get back together again. So actually during this period there was the Iran-Iraq war, a whole series of things go on in the Middle East that make it much more difficult to sustain cooperation, things deteriorate and then after a while things are getting back in terms of higher prices. By late 2008 the price is pushed back up to over $100 a barrel. So what we need to begin to understand this, understanding the repeated interaction and understanding the motivations of the players and so forth can help us quite a bit. So when we think about this a cartel is much like a repeated prisoner's dilemma and in order to make sure that other people behave if you want to get people abiding by this you need to be able to observe other people's play and react quickly to that and punish undesired behavior. So if you form a cartel and say, here's our quotas, don't pump more than this, you need to be able to respond to somebody who ends up breaking their agreement and pumping too much. So you need to be able to observe what's going on. You also need to care about the future. So if you stop caring about the future and only care about today, then it's very tempting for one of these countries just to say, okay, forget the agreement, I'm just pumping as much as I can today, the price is very high, I'm going to grab what I can. And war certainly didn't help this, right? So if you have a war, you need cash up front, you're going to want to pump much more oil and that makes it much more difficult to abide by the cartel agreement. You also need a stable set of players and stationarity, so the more complicated the setting becomes and the more sources of oil there are in the world and so forth, so constantly changing sources of production can hurt. Growing demand can help actually, right? So if the world is getting more and more oil dependent and countries come online that have more and more demand for oil, that can help drive the price up. So in understanding repeated games, we'll have to account for a lot of things over time, but we can begin to analyze this using the tools of game theory and looking at situations where people are playing games but they're playing them over and over and over again and trying to understand the consequences of that. How does threats of future play impact play today? So that's the basic idea and let's get into that in a little bit more detail.