Here's an example I want to give you and I want you to actually take three themes and show you what we might see. This man's called Christian Lindgren. He is at Chalmers University in Boston Burg and Sweden. This study caught my eye from 1991. And what Christian did fact he was here about a year ago. This is a classic. So I'm just showing this as a kind of a demo study. What he did was take the standard prisoner's dilemma. I'm not going to describe what a prisoner's dilemma is. You either note, or there's no need to note it. It just think of it as a game. And the games are defined this way. But Lindgren took classical prisoner's dilemma that was played repeatedly. And he said I want to see what happens. So here's the setup. Lindgren has a sort of tournament going the prisoner's dilemma. So the elements in Lindgren's study or strategies. And the strategies tell you how to move and the prisoner's dilemma. So think of each strategy as saying, if these are the circumstances, it's well defined what I'm going to do next. This one's fairly simple. Each strategy is specifies how to move given what your opponent and you have done in the last. We're start with maybe, 100 strategies, and you allow them to play each other two by two randomly. So, strategy 53 might be squaring off against strategy 72 and then they're allowed to play for finite number of moves and you check who's won or what the outcome is. So this is what his game consists of for tournament, all sorts of strategies, being allowed to play each other, the ones that do well, get to replicate and leave copies of themselves. For future tournaments, the ones that do badly there's a trapdoor and they're, they're thrown out. Here's the really interesting thing that Lindgren did and this I think is brilliant. He allowed the strategies, the successful strategies to mutate, that's fine. Now remember this 1991. So these are early days for this sort of agent based kind of tournament. But he also allowed some strategies to deepen, meaning, a strategy might be the same as it was before. But it could look back in the past more deeply. Two plays ago, the guy did such and such. And then two plans go I responded with such and such. So I'm going to deepen my strategy by specifying what I'm going to do best on two or three or four plays go. So the strategy is could get smarter and smarter and smarter. What's the outcome here? So I'll just cut to the chase. How to read this is time. So at this stage Lin grants computer I don't know how we did this 1991 but it's played 60,000 tournaments. So he would have had a laptop in those days, hit return, come back maybe in two weeks. Now it would probably take an hour or two but so this is time along this X-axis. This is the number if you like of strategies of a given type. And the coding here is really a code that linguine cooked up to describe how they plan response. So these are the codes tell us what the strategies are, this is a strategy here probably tit for tat. If prisoner's dilemma that responds one step back this response two steps back. This one's deeper, it responds maybe to the power of three switches eight steps back. This one responds four steps back. So notice that first of all, the strategies are the ones that seem to be dominating here. These are just the numbers of strategies or their proportion in the population. The strategies themselves is getting more and more sophisticated. But here's what I want to point out. Suppose you run this thing, which Lindgren did, and it starts off, there's only four strategies turns out that you can do. If you're only looking one step back and the prisoner's dilemma Can't do much. So it starts off with 25% wage and allows them to play each other. If there's a hundred strategies are to go 25 of them, start off doing each thing pretty soon, fewer sports commentator. Here's how it works. So, we say okay and we start with one of each and then previously when you find ones strategy is starting to dominate so this might be after one or two hours Lindgren computers and wow. You know, like watching the gold tournament. I don't know if you've been watching that. But you say, wow, this strategy is dominating probably tit for tat is probably anti tit for tat or something. But most of the tit for tat 's have replicated they're doing very well. And some of the other strategies have largely disappeared. So if you stopped if he had switched off his computer right here if you say well that's fine we ran the same is pretty trivial and tit for tat. It wins but something gets discovered here. The start to think of this as in palaeontology. Something happens new strategies are discovered here that are deeper. They're looking to steps back and for all the world I would call this, okay, business as usual, nothing unexpected. And suddenly here, you get a Cambrian explosion, new life forms or strategy forms are discovered. And then one of these dominates and rockets up to over 90% of the population pretty soon. So Lindgren stops here and says, well, you know, we got so far we found a winning strategy, but he allows it to go on. And then here I would say something else takes over. And suddenly, right here you're in what column just described as a lot of vultures situation. Oscillating rabbits and wolves or whatever, hares and rabbits or something. Rabbits and wolves and rabbits and foxes, so strategies here are oscillating. And then some deeper strategy comes along then something still deeper and then he quits here. Probably machine died but, and then he says, well, we've arrived at an evolutionary stable strategy at an equilibrium. I don't know and when I quizzed him on it he didn't know why either. So what I'm pointing out here is that, for all the worlds, I don't know if you can read this, but think of this situation. These are like creatures in an economic situation playing a game. And the outcome is a miniature ecology. The ecology is what is created by the presence of other strategies. And I'm trying to exploit the environment created by other existing strategies. Sometimes according to Lindgren, a stable strategy appears I'm dubious because maybe if I had a large enough computer It might have evolved other strategies never settles down. But what struck me when I read this was that it was very paleo zoological. If you read books like Steve Gold, Stephen Jay Gould and things. You begin to see that what Lincoln has is coexistence code. Some strategies help each other. Some there's a spontaneous emergence of mutualism, your sudden collapses or sudden explosions of new things discovered. There's periods where nothing much happens, periods of stasis, periods of very unstable change. So if this is economics it's starting to look like zoology. And when I read this, I thought, wow, this is very interesting.
