 So, my name is Lev. I would like to talk about games here. It has been said that life is a game. Do you know by chance who says this? Well, it turns out that quite a few people did say that very quickly. But the games I will be talking about today are not life. Instead, they will be a model of life. And being a model has some implication. For one thing, they are incomplete. They are simplified. The life is complex, multifaceted. And the games we are going to be talking about today are very simplified models of life. They include some particular features of life and ignore other features. From the other hand, being a model makes that it is computable. So we only model a few features of life and because of this we can actually find a solution numerically for the situation. And the other consequence of this simplification is that they are universal. So there is a number of different life situations that are complex that can be modeled with one simple model, same model. And finding solution for one model will make this solution applicable to other situations that can be modeled in the same way. Okay, anyway, so what are the games I am talking about? Give me some examples. So one example really simple is a coordination game. Coordination game is a folding. There are two people that are heading towards each other. They have no interest in each other whatsoever. But if they just keep going, they will collide and they will be unhappy about it. So they have to step aside. The problem is that if they step in the same direction, they will still collide and still be unhappy. If they step in different directions, they will pass by each other and they will be happy. So very simple decision to make. The other game I will be talking about is called Martian Penis. In this variation of games there are two players, say me and you. Each player has a coin, a penny, and each player can put his coin heads or tails. And this pen is much. If there are two heads or two tails, I take both points. If they don't match, if there is one head and one tail, then you take both points. Okay, so another really simple game. What game theory can allow us to do with games like this? So we study these games with so-called normal form of the game. And I will present you a normal form of coordination game. So we write down a table like this and there are two players. So one table is modeled in rows and the other is modeled in rows. And in each column we write down strategies for one player. In rows we write down strategies for the player. So in the coordination games there are two strategies possible. Step left and step right. Because people are facing in opposite directions, then step left actually means different directions. So if they roll step left, they pass by each other and they are happy. We denote this by writing down something like this. So at the intersection of some row and some columns we know what one player did, we know what other player did, so we know what exactly happened in this round of game. And we can judge how much each player liked what happened. But we denote it with some numbers. Higher numbers correspond to situations that the player liked more. Because there are two players, there are two numbers that denote how much each player liked this particular outcome. So this one slash one means that player one has liked this outcome. One unit of utility and player two liked it as a one unit of utility. They passed by each other. If they didn't pass by each other, they collide and they are both unhappy and their payoff is minus 1. Okay, so that's a normal form of coordination game. Let's write down a normal form for games of matching pennies. So if we both had heads, we put our coins heads, then I've got one penny. I'm happy my payoff is plus one. You are not happy, you lost your penny, your payoff is minus one. Same for two tails and if pennies didn't match, if you took my pennies, then I am not happy and you are happy. So again, very, very simple game with very, very simple decisions to be made. However, when we compare these two games, we already see that there is something interesting different about these games. Specifically, we see that in this game, the sum of payoffs for two players is different. Sometimes it's plus two, sometimes it's minus two. With game of matching pennies, the sum of payoffs is always zero. Hence, we have so-called zero sum games like matching pennies. These games are characterized by the fact that sum of payoffs for both players is constant. It would be more correct to call them constants of games, but traditionally I call them zero sum games. If sum of payoffs is constant, this means that my wish is death is necessarily your loss. I can only win and get more utility by you having less utility. Because of this, this game encourages competition. However, with positive sum games like the games of coordination, sum of payoffs depends on the outcome. There might be some outcomes that are beneficial to everybody. And my win is necessary, is not necessary your loss. My win can also be your win. So sometimes this game can encourage competition. So we have some games which encourage competition, which we have some games that encourage cooperation. Interesting. Let's study more complex game. And this will be a prisoner's dilemma. So the setup for prisoner's dilemma is as follows. There are two criminals who committed a series of crimes. And during their most recent crime, they were caught by police. And police interrogates each of them separately and asks them to provide evidence for the past crimes they committed. And each of these criminals has two options. Either to keep silence and do not betray his colleague, companion, or to confess and provide evidence for police. So if they both keep silence, they can only be charged with their most recent crime, when they were caught red-handed. And so they receive small prison sentence. And it's a small sentence, so they both receive relatively high pay off, 77. Be mindful that here pay off is something good. So how much did they avoid prison? So more time in prison is lower pay off and so lower number in this paper. So if they both keep silence, they have a small prison sentence. If one of them confess, another keeps silence, then the one who confess and provide evidence gets out of jail free. And the one who did keep silence and was betrayed, he is in prison for a long, long time. So if pay off is zero, and for the betrayers, the pay off is very high. If they both confessed, if they both provided evidence, they receive a small reduction in their sentence based on their cooperation with police. So they both receive a small pay off of three. Now let's imagine it's me, and I am one of these criminals, and I'm trying to figure out what is rational thing to do in this situation. Okay, so I don't know what other person is going to do. If he is going to confess and provide evidence, then I have two options. I need to go in jail for real, real long time, if I remain faithful to him, or I receive small reduction in sentence because I cooperate. So in this case it's more efficient, more reasonable for me to cooperate and to provide evidence. However, if other person kept silence, he was faithful to me, again I have two options. In one case, I receive a small sentence based on our most recent crime, or I go out of jail free if I betray him. Again, the rational decision for me is to betray regardless of what he did, and same for him. So the action done by two rational agents is my mutual betrayal, this one. However, if we look at some of pay offs for two players in this case, we see that this is literally the worst possible scenario. The combined sentence they will get is highest, and the combined pay off is lowest. So what we would like to see, we want to see people cooperate with each other and talk with each other and want to do this, in this case their mutual pay off is the highest. But this is not rational agents likely to do in this case. Okay, so this is sort of the problem, and people are studying different versions of this game, and one of the most known versions of this game is called iterative prisoner's dilemma. In this case, there are two players that play prisoner's dilemma against each other, but they do it several times in a row. So we have a number of iterations, and during making decisions on next iterations we have access to information on what happened during previous iterations. Was I betrayed, or was I not? And because this is a different game, in this game there can be different strategies. I will present you three very simple strategies in this case. Actually, there are a lot of strategies, and people are debating what is the best way to play it, and there are tournaments played, so you can submit your program, and it will compete against other programs, and interesting things happen. But today I will present you three very simple strategies. So Ful is unconditional co-operator. He always co-operates. He never betrays. Villain is the opposite of Ful. He always betrays. And Ful also has this interesting guy called Avenger. This guy had first iteration he co-operates, and every next iteration he repeats the previous action of the opponent. This is also called tit for tat, or eye for an eye, or kazoo. So these are the three possible strategies, and how do they play against each other? So let's start with Avenger and Ful. Neither of them betrays first, so they will just continuously cooperate with each other and receive this payoff 7-7. Then we have villains playing against Fuls, and villains betray Fuls. Fuls allow them to be exploited, and so they pay off this 10 by 0. We have villains playing against villains, and they just constantly betray each other. It's 3 by 3. But Ful also has this interesting measure of Avenger against villain, and what happens is that on first iteration villain betrays Avenger, and Avenger tries to cooperate and he is exploited. But in every next iteration Avenger avenges, and villain betrays each other. On average, the payoff is close to 3 by 3, because there is a lot of defections. But because of this first round, the payoff for the villain is slightly higher, and payoff for the Avenger is slightly lower. So let's say it's 4 for villain and 2 for Avenger. Now let's imagine that there is a whole population of agents. They meet each other, they play this game against each other, and if agent received a lot of payoff, he has a lot of resources, and he does what people with a lot of resources do. He reproduces. And he has a lot of possibilities. And if you did not get a lot of payoff in this game, you have no resources, you cannot reproduce. So what happens? Let's start with a population where there is an equal number of Fuls, villains, and avengers, and Fuls are this blue line, avengers are red, yellow line, and villains are red. So what starts happening? We see that villains are really good at exploiting Fuls, and this is the highest payoff possible in the game. So they have a lot of resources, resources gathered by exploiting Fuls, and their population rises. At the same time Fuls are exploited, they don't have any payoff from it, and their population goes down. Avengers are, at this point, more or less standing because they are benefitted by the fact that Fuls are the share of total payoff held by Fuls is shrinking, so everyone else gets cut off what Fuls lost. So that's the first thing that starts happening, and we see that the population is dominated by villains. However, then we see that some different dynamics starts to happen. When there are almost no Fuls left, villains don't feel that good anymore, because there is nobody to exploit, and villains are terrible in playing against villains, and terrible in playing against avengers. So at the next stage we see that this tendency continues, and actually villains start dying out because there are no Fuls to exploit. And we see that Avengers have their revenge, and they start to dominate the population, and at the end we have a situation when everybody but Avengers die down. So this tit-for-tat strategy is considered the standard response to a prisoner's dilemma game. What's interesting is that at this stage where a population is comprised entirely from Avengers, we add some Fuls back, and Fuls actually will be quite okay in this population because there are no villains to take advantage of them. Okay, so this is the iterated prisoner's dilemma game, and this complicated population dynamics is crazy. What are the applications of this game? Well, one of the applications is arms race. So we have USSR, we have US, and they can create nukes to threaten each other with nuclear war, and actually they have much better things to do with their resources than create nukes. But if you have nukes and your opponent does not, you can force any action upon your opponent, and you're in a very good situation. It's like she cooperated and you betrayed him. So they try to be tough, they try to betray, they try to have a lot of nukes, and they realize that it actually does not play out very well. And we see that by the 30 years after the start of the arm race they actually started reaching agreements about how they both cut the number of nukes. So that's an example of prisoner's dilemma. The other example is known as the tragedy of the commons. This is also a classical story created by some popular guy. But the story is following. This is how we basically got to Hara. There is some tribe, so we are living in pretty historical communities. We are egalitarian, and everybody has cows. And we have some place where we can grease these cows. And this place, this piece of grass doesn't belong to anybody, and we can grease all the cows there as much as we want. But if we grease all the cows a lot, all the cows are getting fed, and we have nice fed cows, but also there is less and less grass in this place, and this shared resources gets exhausted. And this is exactly what happens with commons, with shared resources. Nobody cares, nobody considers them private, nobody cares about them, they are getting exhausted. We already have Sahara, that's how Sahara was created. We have the fertile land once. Now we don't care much about Sahara, but we have the same situation basically with every ecological problem. So all these emissions, greenhouse gases, plastic, that's exactly the, again, the duration of tragedy of the commons. Cartels, like OPC cartels. Again, we have a classical prisoner's dilemma situation. If I am Iran, and you are Saudi Arabia, and we are both producing a lot of oil, we can agree to limit oil production. The oil prices will be high, and we both will receive a high pay off. However, if you limit your production, and I don't limit mine, then I will be able to sell my huge amount of oil at a high price, and I will receive a ton of money, and you will receive a few, because I will be able to drop prices and you will produce a little oil. If we betray each other, we over-saturate the entire market with oil, so not good for anyone. And that's basically what we see in Middle East. So when there is a war in Middle East, if people need money urgently, they break their OPC obligations, they over pump oil, production increases, prices go down. If there is a relative piece there, people try to cooperate, they limit the production and prices go up. Of course, with recent technological developments, this example is getting less and less relevant, but we still have this OPC concept, so I keep showing it in my game theory. Okay, so I was talking about game theory, I was talking about agents, strategies, rational decisions. What about ethics? Maybe ethics is just not there. Well, I don't think so, because if you look at any of the tables I have shown today, like this one, we have these numbers in here, and these numbers denote how much did you like a particular output. So this is an abstraction, and this is an abstraction according to your values. So if your values are egoistic, then these high numbers for you represent high fulfillment of your egoistic values. If you are an altruist, then these numbers represent how efficient you are in fulfilling your altruistic values. So game theory is just a tool which helps you to be rational and receive a high payoff. It doesn't tell you what is your payoff, what are your values, what you carry out. Basically, this dynamic, like trade and freedom of development, is basically the reason why things like free popular science talks are proliferating in the world. So at the end of my talk, I would like to put this guy again, so I have some suggestions for you. Play good, play rational, and remember what your real values are. Thank you for your attention.