Robert J. Aumann (2014) - Collectives as Individuals

Thank you very much. Let’s get started. In applications of game theory a 'player' is a person. A household, a family. A team - in sports. A country. A persuasion - political, religious, social. A community. A corporation - you could have Microsoft, Apple. A work place - like a hospital, a department in a university, a research centre. It could be a species or any other kind of population of living things. You get the idea, ok. It’s a collective. A player in game theory is a collective. But it isn’t really that way. Usually this is understood as an idealisation, a kind of 'small worlds' principle a la Savage. Remember Savage had a decision theory. And in this decision theory he had to give probabilities and utilities to all kinds of eventualities. And in fact a person had to really think of anything that could happen to him in the future. And this obviously is not practical. So Savage said, it’s true that people should make their decisions based on every possible eventuality. But since this is impractical we talk about 'small worlds', about making this or that specific decision and what its consequences might be. But you don’t formalise the consequences. So in games where say countries are modelled as players. The real players are the individual citizens with their individual goals. And individual decisions. And individual free will. It’s only because this 'true' game is too big and unwieldy to analyse that, it is held, game theorists model players as they do. Today I am going to try to sell you the idea that it is really that way. That in large part collectives are like individual people and may be thought of as such. And perhaps not only in game theory. This is something from the National Geographic website. It’s a school of fish with a hole in the middle. And in the hole in the middle there’s a sea lion. The fish in the school or the school itself feels sort of threatened by the sea lion. The sea lion looks like a diver but it’s not a diver, it’s a sea lion. So we have a school of fish over here. And I suggest that this is in a sense symbolic of the idea that a collective is like an individual. Let’s spell that out a little bit. Individual people are composed of cells, including neurons. And collectives are composed of people. Individual people are grouped in organs and limbs. And collectives are grouped in economic, social, political entities. The organs and limbs are interdependent. And the social, political, economic entities are also interdependent. The organs and limbs change over time. And the people change over time; in particular, they age and they die. And the collectives change over time; in particular, they age and they die. The individual people have diseases. And so do the collectives - crime, pollution. The individual people have internal mechanisms to fight the diseases: They have white blood cells. They have antibodies. They have all kinds of mechanisms. And so do the collectives: They have police, courts, public awareness. The individual people have relationships with each other which could be friendly or hostile. And the collectives also have such relationships: They have alliances. They have wars. They have economic cooperation. They have economic barriers. The individual people have internal struggles. Anybody who ever had to make a decision knows that you struggle with yourself about something. And the collectives also have internal struggles. The individual people make decisions, consciously or otherwise, and so do the collectives. They make decisions. They do something, centrally or otherwise. And you have other collective phenomena. You have a collective horizon or discount rate. Which is different from the individual discount rate. You have environmental considerations. When you take into account environment considerations, this is something entirely different from the discount rate which an individual applies. Collectives have a collective memory. I remember World War 2 personally. I was a child but I remember it personally. I remember reading about it in the newspaper. That’s also part of the collective memory. But most of the people in this room don’t remember World War 2. But they know about World War 2. The collective memory, even an individual could have a memory which is derived from other people. They think it’s a memory. Oliver Sachs wrote in the New York Review of books about a year ago: Memory is dialogic. What does 'dialogic' mean? It’s a word I had to look up in the dictionary. It means it’s the result of dialogue. It comes from the word dialogue. And arises not only from direct experience but from the intercourse of many minds. Oliver describes the situation where he remembered very well an incendiary bomb falling in his parents’ house. And he had this picture of the bomb hissing and emitting sparks. And afterwards it turned out that he was in fact away in school at the time. And his brother wrote to him about this. But he thought it’s a real memory. A memory is a result of intercourse of many minds. And we have a collective memory. What about the free will of people? Each individual presumably has his own free will. I can’t deny that each person has an individual free will. But this is heavily influenced by the collective. You can look in the family. Just as a simple example: A choice of careers by children is heavily influenced by what their parents do. The children of lawyers are lawyers - not necessarily. The children of doctors are doctors. Even the children of mathematicians often turn out to be mathematicians. This is heavily influenced because of the context in which their parents live. So this gives ... a lawyer lives in the context of lawyers. A lot of the discussion, a lot of the friends of the family are lawyers, so it’s natural for the child to go into law. I’m not talking even about businessmen where the child often goes into the family business. By and large, people don’t change persuasions, by and large. Religious persuasions. Of course people in a religious family can become non-religious and people in a non-religious family can become religious. But it doesn’t happen usually. By and large, people identify with the collectives to which they belong and vice versa. I do imagine that the people in Germany were very happy when Germany won the world cup in soccer. Why? Well, why should a person, why should an individual in Germany be happy because Germany won the world cup? What does it mean to him? He wasn’t playing in the game. But it does, people do identify with the collectives to which they belong. And the collectives identify with the people belonging to them. Work ethic can be very different. Some hospitals are known for the very nice nurses that they have, and the very nice doctors. And some hospitals are known, the whole hospital, for the coldness of the people working over there. People very much are influenced by each other. And, of course, why does this happen? Because it's shaped by communication and incentives. If you go along with the other people, it’s good for you. Yes it’s good. The people feel part of the collective. So the collective becomes a real entity in itself. Let me give you some examples of personification of science. First of all the caption on that picture we had before - remember the picture? Well, we’re going to have to forgo this. (Laughter) But you remember the picture of the school of fish with the sea lion in the middle. So the caption on this said, 'A school of salema attempts to outmanoeuvre a hungry sea lion by circling to confuse the predator.' That’s what the caption said. Hey, wait a minute: A school of salema is outmanoeuvring! It’s attempting something, the school?! It’s not the individual fish - the school is attempting! Here is a very clear example of personification. Suddenly this school has become an individual. This collective has become an individual. We have social insects. We have population equilibrium and that is really the same as Nash equilibrium. This is the insight of Maynard, Smith and Price which set off the big ... One of the most important chapters in game theory is evolutionary game theory where populations are looked at as players. I’ll say a little more about that in a moment. We have von Neumann-Morgenstern’s stable sets. And the theorem of Sergiu Hart which was published in JET about 50 years ago. Let me say something about social insects. With social insects - bees, ants, termites, wasps – there is a school of thought in entomology that thinks of the nest or hive as the 'individual'. They actually think of it without, you know, without this philosophy of collectives and individuals. The nest is, by these biologists, is considered the individual. Not the particular worker or the queen. I mean these are very highly individualised workers, have a different genetic makeup from queens. And they have a different make up from soldiers. But the hive, the social unit is considered the individual. We have the insight of Maynard Smith and Price. A Nash equilibrium, as we know, is a profile of possibly mixed strategies, one for each player, each of which is best possible for that player, given the others' strategies. That’s a definition of a Nash equilibrium. An equilibrium of populations like different species – or let’s say a population of bees and a population of flowers – is a profile of genotypes. So we have different genotypes of the bees. We have a genotype of the bees and we have a genotype of the flowers. Or it could be a distribution of genotypes of bees and a distribution of genotypes of flowers under which the population proportions do not change from generation to generation. So we get - let’s say we have a genotype which makes you have a long proboscis. And let’s say ¾ of the population have a long proboscis and ¼ has a short proboscis. And in the flowers also you have some kind of proportion between flowers with a long nectar tube and flowers with a short nectar tube. And then if we have a population equilibrium if these proportions do not change from generation to generation. So now think of a game whose players are the populations. So you have one player is the bee population and one player is the flower population. And the strategies are the distributions of genotypes. And the pay-offs are changes in fitness of each individual when individuals with those genotypes meet. So if you have a bee with a long proboscis meeting with a flower with a short nectar tube, then this doesn’t work out too well. So the fitness goes down. Fitness means probability of survival. Without going into too much detail, we have this translation of the ideas from game theory into the ideas from population genetics. And the theorem says that the population equilibria in the ecological story coincides with the Nash equilibria in the corresponding game. So we have a sort of identification of collectives with individuals. The populations in the ecological story are like the individuals in the game story. Let me talk just a little bit about Hart’s theorem. As some of you may know von Neumann-Morgenstern’s stable set of a coalitional game, like a market, is a collection of outcomes with certain stability properties which we won’t specify here. In large markets with differentiated players, like let’s say employers and employees, von Neumann-Morgenstern’s stable set of the large market mimics the von Neumann-Morgenstern’s stable set of the small market. That with only one representative of each type. For example, when there are only one employer and one employee, the von Neumann-Morgenstern’s stable set provides that the employer and the employee can divide the surplus which they get by interacting - of course, there is a surplus, otherwise this relationship would not exist - in any way they want. When there are many employers and many employees, the surplus can again be divided arbitrarily - that’s what the stable set theory provides - but all employers must pay, and all employees get, the same wage. So this is something which corresponds a little bit to comparative equilibrium theory. But this is just one example of this theorem, that the stable set of the large market mimics the stable set of the small market, when the employers become like one person and the employees become like one person. There’s remarkable personification in the bible. We have a verse in the bible that says that the children of Israel raise their eyes. Now they raise their eyes, that’s in the plural. And lo! Egypt was pursuing them and the word 'pursuing' and 'Egypt' is in the singular. And the medieval commentator Rashi says that Egypt was of one mind like one person. And then later on in the same, in Exodus, the children of Israel come to the Sinai desert. They came to the Sinai desert. And there Israel camped, singular, using the singular declination of the verb 'camp'. Although they came was plural. They came opposite the mountain, opposite Mount Sinai. And again, Rashi says, like one person, of one mind. It’s interesting that he turns it around. He doesn’t say the same in the same sequence. And I don’t understand exactly what he had in mind. It’s clear he had something in mind when he turned it around. But it’s the same phrase basically. So we have a personification of Egypt pursuing Israel. We have a personification of Israel camping opposite the mountain. Some implications of this. First of all we have what we started with: A 'full world' analysis of game situations. We said before that in game theory collectives are often treated like individuals. And we said, well, this is not an approximation. It’s not a 'small world' principle. It is the way it really is. And we have possible moral implications. I’m full of trepidation in raising this, because it’s a very sensitive subject, very sensitive. So I want to emphasise the word 'possible'. I’m not sure of this at all. It a little bit like Al Roth's presentation yesterday in which he said, So what are the possible moral implications? For one thing we have moral judgement of collectives. We say the Ku Klux Klan is bad. I don’t know, you know, one doesn’t hear about it too much anymore. But this was a group of white supremacists in the southern United States. And we think of them as bad, this is bad. Not an individual person in the Ku Klux Klan. It’s the Ku Klux Klan as a collective is bad. We think of ISIS or IS as it’s sometimes called, the Islamic State which we have been hearing about recently. We think of this as bad. We think of North Korea as a rogue state. We think of the Sierra Club as something good. These are all collectives, they’re good collectives. We like them. We think of the NSF as good, right? This is a wonderful organisation. It gives out money to support research. And research is good, right? So these are good collectives. These are bad collectives. Now we’re getting even - I ask this as a question. Perhaps there’s a greater moral responsibility of collectives. Which implies lesser moral responsibility of individuals. Now I don’t know you people are too young but there was the My Lai massacre in the Vietnam War, in which American troops under the command of Lieutenant William Calley massacred several hundred villagers, non-combatants, in Vietnam. So William Calley was, as many of these soldiers, about 40 of them, were put on trial. Most of them were let go. Calley was sentenced to life imprisonment but he didn’t actually serve it in the end. What were these people doing when they shot these civilians? I think they were acting as part of a collective. Sometimes it’s called herd instinct. But it’s not just herd instinct. They are - the collective is acting, not them personally. Similarly, on the other side, Hang Pin, an individual, lower-level official in the Khmer Rouge massacre. He is part of a larger picture. And the other side of the same coin - so we have lesser moral responsibility of individuals. And we have lesser moral responsibility towards individuals - this is the tough part. An individual who is part of a collective, you can think of him as an individual, but you can also think of him as part of the collective. So like we have lesser moral responsibility, I think, maybe, toward individuals. We have strikes. We have boycotts. We have Gaddafi’s grandchildren. The United States army bombed and strafed Gaddafi’s home and killed 3 of their grandchildren. What do the grandchildren have to do with it? But no, the grandchildren are part of the Gaddafi collective. So maybe, maybe, just maybe there we have also lesser moral responsibility of individuals and toward individuals. On the other hand, perhaps an individual who is in a position to influence the collective, and does so. Like Hugh Thompson, Helicopter pilot, who happened on the My Lai scene, landed and threatened to shoot Calley. And he stopped this massacre. And he was awarded the highest award that a soldier can get in the army. So an individual who can influence the collective and does so like Hugh Thompson, or does not do so like most of us, bears moral responsibility, moral opprobrium or moral - the opposite of opprobrium - honour, yes. Either way. Thank you.

Robert J. Aumann (2014)

Collectives as Individuals

Robert J. Aumann (2014)

Collectives as Individuals

Abstract

In many applications of Game Theory, a player is a collective such as a household, team, political party, country or the like. Usually, this is understood as an idealization. In games where, say, countries are modeled as players, the "real" players are the individual citizens, with their individual goals and individual decisions and individual free will. It's only because this "true" game is too big and unwieldy to analyze that, it is held, game theorists model players as they do.

Here, we advance the thesis that it *IS* really that way: that in large part, collectives are like individual people, and may be thought of as such. And, perhaps, not only in Game Theory.

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