Audio recorded at Tibetan Buddhist Institute, Adelaide. Transcript auto-generated and AI-corrected; may contain errors.
About this talk. In this 92-minute talk, Ilia S. Durovic introduces game theory as a tool for examining ethical behavior through logic and rational decision-making. Beginning with how to prove statements using description logic and geometry, he moves to the prisoner’s dilemma—a foundational game where two rational agents must choose between cooperation and defection, showing that logic alone points toward defection as the optimal strategy. He then presents the ultimatum game, where one player divides money and the other accepts or rejects, and reveals experimental evidence that Buddhist meditators reject unfair offers at significantly lower rates than controls, suggesting meditation enhances rational choice-making. Moving from single games to repeated games played over time, Durovic demonstrates that when the end is unknown, cooperation becomes the winning strategy—one that closely mirrors the logic of karma. He introduces tit for tat with forgiveness as the dominating strategy, proven by Robert Axelrod’s computer tournaments. The talk concludes by exploring why humans still act unethically despite accepting karma and cause-and-effect: the concept of the discount factor, or present bias, causes people to value immediate gains over future consequences. Aimed at thoughtful observers interested in the intersection of mathematics, ethics, and Buddhist philosophy.
File metadata (for organising)
File: 01-700101_1002.mp3
UUID: db65f6f9-bb88-4701-8809-d255f0af1b35
Teacher: Ilia S. Durovic
Collection: Dependent Origination
Date: 1970-01-01
Recorded at: Tibetan Buddhist Institute, Adelaide
Words: ~12,556
Many people in my office were very happy with that because they come to the end of the day even though I wanted to say something or disagree, nothing came out of my mouth. So the reason I’m saying this is the presentation. It’s not your hearing. It’s actually my So, I work at the University of Adelaide and I guess my area of speciality, I’m told not to use expertise because people believe then that you know something when, in fact, the more you know anything anybody who studies something, the more you know, the less you actually really can say about the particular subject. So my area of speciality is something called that most people would not heard of financial econometrics.
The only time I’ve ever seen someone who’s an econometrician on television was this show that I did not watch. I just saw a little caption so I’m denying it if haven’t seen it. There’s something called Beauty and the Nerds and basically it was a show where you try to team up nerds and geeks with beautiful women and basically the involvement of how that related. The first person to get kicked out, I’m told, was the econometrician. So there you go.
So what am I going to talk about today? Well, was very intrigued because where Pamela left off is in fact sort of partly related to what I’m going to cover. But from a very different perspective, I haven’t even made my mind up whether what I’m presenting is something in disagreement to what Pamela said or not. I don’t think it is. I don’t know if I’m trying to naturalize ethics or not.
But because I come from a mathematical background, I see things quite differently to maybe psychologists or behavioral biologists. So what I’m going to present today is a discussion and a proof because I deal with logic basically at the end of the day of why there are selfish reasons to be ethical. So whether you’re basically a Buddhist or not, what I’m going to try to provide is that the answer to behavior is that it’s natural. In fact, I guess you could say maybe I’m trying to naturalize ethics. Natural to take an ethical route.
Not all the time, but I explain how the dynamics work. Now another sort of subtitle I’ve got that I’ll explain later, I won’t talk too much about it at the moment, is what is your discount factor? Because this whole discussion revolves around rationality and really how rational you as a human being are. The last thing that Pamela mentioned for her presentation in answer to a question from the gentleman at the back was we can’t really determine how empirically valid our experiences are. So really this is sort of relating to what I’m going to talk about, about how rational our behaviour is.
It’s related to something called a discount factor which I’ll explain later. Now we’re going to examine this sort of topic through what’s called game theory and some of you may have heard about game theory, others have not. So I’m going to explain what that is. We’re going to play some games together. So I’m asking you to speak up and sort of partake in this sort of discussion.
We’ll cover the concepts of rationality and bounded rationality. These are used throughout my field of study primarily in economics and finance but in other pseudo disciplines where we try to model what we call agent behaviour. I’ll talk a little bit more what agents are. They’re synonymous, in fact, to what we would here refer to as sentient beings, those that have the ability to make decisions. So we’re going to explore that as well.
And we’re going to explore apply games to determine whether ethical behavior is a winning strategy for both Buddhist and non-Buddhist alike. So if you have any questions, my preference is actually for you to ask me as I go through the presentation rather at the end. Yes, sir. Let’s see if we can do that. This way?
Is that better? Okay. Yep. Absolutely. So in order to answer the question what game theory is, really what we need to do is understand what it means to prove something.
Although this is not directly related to the subject matter, I do need to establish what it means to what a proof is. So formatively, it’s a statement that must true a 100% of the time. There are a number of ways you can actually prove something. So I’m just giving you two simple examples. The first is through what we call description.
We actually refer to as description logic. Anyone who’s actually studied computer sciences will actually have a knowledge of this because that’s what computer language is. I’m going to give you an example. We’re going to start off with a premise and a premise basically is a statement that usually has three things. One is referred to as the subject.
In my case, it’s my grandparents. The second is what we call the premise and that is that my grandparents are mortal. And thirdly, we have something called a copula. Copula is the relationship between them. In this case they are or were mortal because they are dead.
I then from there can allude one further premise that my grandparents are human. Then I come to a conclusion. Therefore, you all humans are mortal. Now is this a sort of a fair statement to make or not? No.
What’s wrong with it? Sorry? That’s right. Well, it’s sort of a small sample. I’m actually what Aristotle referred this to and it happens all the time and a lot of it’s to do with discrimination and racism and etcetera, etcetera, is that it’s referred to as a fallacy of generalization.
Now the way we actually turn, logically speaking, the way we would work out description logic is to take these predicates and copulas and subjects and we actually turn it into notation. So it becomes a sort of it looks like it’s mathematics but it’s not. It’s a notation method and from there you can deduce whether something is correct or not. What we’ve got here is a summation that all humans are mortal because I have a sample or because I’m looking at a smaller subset of humans which have obviously died. Technically speaking, you cannot prove that all humans are mortal.
In order to do that, what must you observe? All humans. Can we do that? No. We observe all humans today and that have previously existed, but not into the future.
I’m not claiming that you will be immortal. All I’m saying is that the proof of which I’m using is not substantiated through the method I’m applying. So what I’ve got here is a little caption where the lady laboretus is saying this is not proof. It’s actually evidence. I’ve got evidence that some have died and therefore I’m assuming that all have.
So it’s a very simple example. In fact, it’s more of a conjecture. I can make a conjecture which seems to be true in all instances but cannot be proved to be a stated fact. So that’s actually what a conjecture is. We can also look at mathematical proofs.
Many, many years ago, the ability to use algebra wasn’t really there. And so what Pythagoras used to prove the relationship between different angles was geometry. And basically he showed literally on the sand by drawing different squares of different sizes that the diagonal of this triangle will be its square will be the summation of the square of the other two sides. So the reason I’m just trying to show this is because there’s many ways of proving things. You can prove things through geometry, through language.
They all basically provide a method of logic. Over the last hundred years, the development of mathematical logic has exponentially grown. What we can do today is in far excess of what happened in the previous centuries basically. And in particular, there has been one form of logic that’s really overtaken the world even though you may not have known about it and that is game theory. Now, Myerson is an economist who is quite famous and I’ve just quoted how he described it because it’s quite common.
Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision makers. Now the reason why this is so different to other forms of logic if we go back. Before we’ve got here a static situations. We’ve got statements so we check whether they’re true or false. We’ve got a mathematical model.
We want to see whether it’s true or false. But with game theory, you’ve got a situation where you have particular decision makers who can interact with one another and the question is what is the logical outcome from that interaction? It’s basically a logical proof in what we call a dynamic context. Now the first person, well the person who is attributed of being the forefather of game theory is a gentleman called John von Neumann who was born in Budapest. He moved over to The States.
I think he worked in Princeton if I’m not mistaken. He created two very important texts in the early part of the twentieth century. The theory of games and economic behavior in particular was the beginning, the foundation of it all. And I’ve got a picture of him and against that, guess what it is? It’s not a milling machine or it’s one of the first computers that existed basically.
And the reason I’ve got him against is because to reiterate that game theory is today computer science. The way we program computers is to take into account different scenarios. If then, what happens if certain items are true or false, etc, come to a logical conclusion. Computers, despite the fact you might think that they are irrational because when you boot them up, they don’t work and so you want to throw them out the window. The fact is they are logical pieces of work and you cannot create irrationality per se from them.
In fact, I don’t know if you know this but you know some people who use computers, if you ask for a random number from it in an Excel spreadsheet or in other forms, do you really think that’s random? That the computer has actually has picked something random? No. A computer cannot generate anything random. It has a list, a very long list of numbers and depending on the day and the time that you actually ask for a random number to be picked, it uses an algorithm to pick from that list.
The point I’m trying to make is that there’s nothing random about it. It looks as if it’s random but it’s not. So game theory is a logic tool suited to examining decision making between rational agents. In in my field, what we refer to as sentient beings are agents. So I’m going to basically stick to that.
An agent is any type of entity that can make a decision, a choice. So it could be a small ant, if you allow them some form of decision making ability, right up to humans. So I have to excuse my coughing. Okay, so it was originally constructed to examine economic gains, but it has a far reaching broad spectrum of interest from different disciplines now. They include computer science, biology.
One of the areas that I work in is I work with a very famous professor actually at the University of Adelaide, Professor Michalewicz, Zbigniew Michalewicz. He has got something like 13,000 citations for one of his books. And our research is in what is called evolutionary algorithms. I’ll talk maybe a little bit more about that later on, but essentially speaking what we do is design what we call fitness functions. We try to work out what is the optimal type of way to describe an agent and let them interact with each other and we put them in a simulated universe and from that we get different types of information from it.
So I’ll leave it like that for the moment. And what you can prove for example, simple proofs are that and it’s obvious to us, well not so obvious but one obvious proof is that you can show that the optimal ratio for males and females is roughly one to one. In fact, it’s slightly tilted towards the males and females. But there are ways of actually easily showing that through this type of game theoretic method. It’s also actually embedded in philosophy.
Philosophy. It’s It’s not not my my area but I am going to talk a little bit about it. So with games, you’ve got players, you’ve got agents, you’ve got rules of how they must behave, you have consequences and then you have payoffs. So on that note, we’re going to play our first game and it’s a very famous game. So I’m hoping some of you have actually seen this before and it’s called the prisoner’s dilemma.
Now I know, I’m sure all of you are bodhisattvas with the exception of myself, so it would be hard to put your mindset into that of a convicted criminal. So I will try to aid you in that process. Here what we’ve got is a situation where there are two prisoners. Now they’ve been interrogated in different rooms because they’ve just created they’ve been involved in a crime and let’s say you’re prisoner one. Now you’ve both colluded, you’ve both took part in this crime and you’ve agreed that you’re not going to say anything because if prisoner one says nothing, in other words you’re cooperating with prisoner two, and prisoner two says nothing, you both only get one year in jail.
If on the other hand, I as prisoner one, you as prisoner one, decide that we are going to confess our sins, then what was going to happen is that the police were going to use our evidence against the other prisoner, our previous friend who is not going to be very friendly with us anymore, because we get let off entirely in a bargain deal and they get three years. Alternatively, I could play the game. I could say I’m going to say nothing. I’m going to cooperate, But unfortunately, the rat bag of my previous friend basically cheats on me so I get three years and he gets let out. If we both cheat, we end up with two years being sentenced.
So my question to you is what is the winning strategy for you in this game? If you’re prisoner one, what do you do? Do you cheat on your friend or do you say nothing? Oh, thank you very much, grandma. Thank you.
That’s very good. But as a rational agent who’s just selfish, doesn’t care about anyone else, what would you do? Say nothing? Okay. That’s right, yes, yes you could do that.
So can you give me the rationale why you would actually want to cheat? You don’t want to go to jail. In fact, sorry go on, sorry Richard. Yes. Probably you know this is sort of the plea bargaining sort of situation that exists in The States.
Basically it’s based around prisoner’s dilemma. If you look at it, there’s only one viable strategy for you and that is for you to cheat, for you to defect, to confess your sins in the hope that the other prisoner doesn’t. Why? Well, let’s look at it this way. If I’m thinking whether I’m going to say nothing or confess and I decide to say nothing, then there’s two possibilities.
Either I end up with my the other prisoner can say nothing and we both get one year, but there’s an incentive for that prisoner to cheat, right? So I end up with three years in in the slammer. So the alternative for me is then to think, well, if I cheat, there’s a chance for me being let off completely and there’s no incentive for me to actually cooperate. So in terms of how we actually look at game theory, we tried and this is actually done mathematically but I’ve taken the math out of it. There’s only one possible scenario that leads to the best outcome for you which is for you to confess.
And that’s why particularly in The States where you have plea bargaining, they will put you in separate rooms and they will try to get a confession out of one of you in the hope that basically you will then basically cheat on the other. Alternatively, if you both confessed, that’s great because they get you both into jail. So it’s a technique that’s used quite often. Now the method of actually resolving this, of working this out is through something called the Nash equilibrium. So let me explain what Nash is.
It’s a set of strategies which is referred to as a Nash equilibrium if no agent can do better off by unilaterally changing his or her strategy. So we’re not talking about being nice people. We’re talking about what’s the best for ourselves. So Pamela talked about selfish gene. Maybe it sort of alluded to that but I’m looking at purely from a logical standpoint to maximizing your benefit.
The Nash equilibrium was made famous of course by John Nash. Some of you may have also heard about him because that was a basis I think for a Hollywood movie called A Beautiful Mind and he’s actually one of my personal heroes. I don’t actually really have any heroes in my field. I was more impressed with how he actually was able to cope with his schizophrenia. I’ll explain a little bit about that in a second.
So he basically was the sole person responsible for determining how rational agents create dominating strategies. He suffered for the most of his career. He was in and out of mental illness. He’s had electric shock therapy in the seventies. He’s gone through everything apart from the lobotomy, thankfully, because I don’t think he would have been able to do very much after if that had happened to The reason why I’m so impressed with him is because he suffered from delusional psychosis where he would see he would hear things in his mind, he would see things that were not there in terms of objects in front of him and it got to the state later in his career when he started to rationally deduce that what he was seeing was not real.
Now he didn’t do this through any type of religion. He basically just sat down and said to himself, this doesn’t make any sense. So he won the Nobel Prize in economics and I’m just going to quote from you something that he said during his celebration speech. So but after my return to the dream like delusional hypotheses in the nineteen sixties, so he’s referring to his psychosis, I became a person of delusionally influenced thinking and therefore thus time passed. Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which have been characteristic of my orientation.
This began most recognizably with the rejection of politically orientated thinking as essentially a hopeless waste of intellectual effort. I think everyone would agree that politics is a waste of time But he was actually referring to the fact that he actually thought, as most people well, not like myself included. Many people think the FBI and the CIA are spying on them to the extent that he would he would see common objects on the street thinking there was some type of CIA agent that was basically trying to get something from from him. And he basically worked out at the end of the day, why would they bother with him? Now that site might sound obvious to us, but for him having gone through this really seeing these things in front of him, hearing these voices, it was a tremendous effort for him to deny that they were true simply by rationally deducing that.
So he also believes that it was because of his mental orientation that he was able to come up with this way of thinking because it’s all about working out what you would do based on what others would. So it’s a very tremendous improvement in how game theory is now looked at. So the only rational viable strategy is to defect, is to cheat. The non cooperation rules, this is the Nash equilibrium. So that’s what we’ve established so far.
Is everybody happy with that? Okay. So we’re going to play another game and this is called the ultimatum game and we’ll see how they link soon. I don’t personally think I mean you’re putting some other rules, other factors into the play. But separate to that, I don’t even think it would actually change the outcome because at the end of the day, there’s no incentive for you to cooperate.
Incentive is not there. You work out all the strategies and whatever happens, you’re still better off to defect. But you can add other factors and we’ll talk a little bit later about that. There are things that you can do to mold different types of outcomes. I’m not denying that.
But in this simple game, when we’re not looking at anything else, so we call this, ceteris paribus. Everything else is the same and this is what happens. Absolutely. Absolutely. Okay.
There are $100 in five dollars notes on this table. There’s not actually, but there you go. Player one chooses how much to keep and to offer to Player two. Player two chooses whether to accept or reject Player one’s offer and if rejected then neither agent receives anything. So my question to you is, well, what is a Nash equilibrium offer that you as Player one should make?
Yes sir? Half the money? Very generous. Any other takers? Is that the Nash equilibrium?
It’s a fair outcome, sure. What’s the Nash equilibrium? Very good, excellent, very good. You’re all game theorists. Very good.
So basically the outcome for a Nash equilibrium is $95. That’s very good. Is everybody sort of happy with that? I’m to explore this in more depth. Many of you would accept the Nash equilibrium?
So I’m offering there’s a $100 on the table. I’m grabbing $95 giving you $5. How many of you would accept that? One, two, nobody else? Okay.
Very interesting. We’ll come back to that. No other takers? No, okay. Well, let’s be fair.
The real situation is, under experimental circumstances, is that you’ll be in a separate room. You’ll be told that Player one is going to make you an offer and that offer is out of $100 You can either accept it or reject it as Player two. Player one is offering you $5 and he will keep $95 Do you accept or reject? So how many accept? Okay, we’ve got a few more goes.
One, two, three, four, five. Yes, everybody knows that. Everybody knows that. Okay, good. The ultimatum game is a game to test irrationality and I’ll talk you through that.
In fact, in sorry. No, not at all. Not at all. It’s actually a game it’s a game three. In our language, there’s no such thing as irrationality by but I’ll explore that in a second as well later on.
Most experiments have shown that the rejection rate is eighty percent. Now I don’t know if that’s 80%, but I guess it would be close to it. 80% of people reject the minimum transfer offer, the Nash equilibrium offer, because I think you’re alluding to the fact it’s unfair. Because the end of the day, you are getting $5 and $5 is better than zero, right? Right?
Okay. So there are three primary reasons why this actually might materialize and I’ll go through them. One is referred to as absolutes, the second is inequity aversion and the third is neural logic. The first, I’m sorry, I can’t see. Armin Falk is an economist who works at the University of Bonn and he did a very interesting experiment many, many years ago.
It was probably about twenty, thirty years ago. He took the game I just described in US dollars to Indonesia where I guess $100 would be, I don’t know, like three months wages at that time. Because the argument was that if somebody’s just offered $5 it may as well just be zero. It’s not worth people’s time or effort. You may as well, out of spite, reject.
Well, very interestingly, he saw no difference. The ratios of rejection were the same. So even in Indonesia, even though $5 will still be worth something tangible, the reject rate was about 80%. So the argument that you are looking at absolute figures that are very small for the Nash equilibrium doesn’t count very much. The second one is related to inequity or inequality aversion and it explains partly the willingness or unwillingness for people to put up with income and social iniquities.
So a lot of people, you probably if you read the newspaper, you’ll see a lot of talk about why the bank CEOs are getting millions of dollars payouts and bonuses when the banks aren’t looking too good. And the reason why this gets built up is because there’s an intrinsic feeling that there’s inequity in a system whereby you have people who are earning loads and loads of money if the rest aren’t. And there’s literature that basically explores in far more depth to talk about how basically societies actually devolve because of iniquities. I don’t go into that. What I want to do is focus on a little experiment that actually was reported in science in this year.
In fact, occurred in St Andrew’s University in The UK. It’s quite interesting. I don’t think it goes against to what Pamela was talking about because it focuses on one particular issue which is an inequity aversion. So it was basically examining puzzle solving abilities between chimpanzees and three and four year old children. Supposedly, I don’t know if it’s true or not, they have roughly the same intelligence.
I don’t know if that’s true. Guess it’s something that they basically believe it is. Chimps took thirty hours to solve the puzzle, whereas children took two and a half hours. The question was why? So what actually they had to do was press a couple of blue and red knobs and then some reward would come out, whether it’s chocolate or a banana, peanuts, whatever the case may be.
And what they found out was that forty seven percent of children spontaneously shared their rewards, which means even if one child solved the problem, the other children would be able to share it with that reward. 0% of the chimps shared. So it’s quite interesting. The above goes some way to explain player one’s behavior and the reason I mention that is because I didn’t really make a big deal about it, but how often the Nash equilibrium is offered is quite uncommon. Generally speaking, through multiple experiments, there have been thousands of experiments that have been done this, in fact across cultures as well, generally speaking people split the money fiftyfifty.
And you might think, well hang on a second. Maybe it’s because they’re not familiar with the game. They don’t realize that they can actually take it all if they really want to. So they also looked at what’s called reiterated games, where you play the game over and over again. Still nothing changes.
People generally offer the 50% sort of ratio of $50 for myself, $50 for the other player and it’s very hard to explain this logically, I guess you could say. So the reason I put it out is because it’s something that’s sort of intriguing. So this basically gives some sort of evidence why player one’s very rarely make the Nash equilibrium, but it doesn’t solve my question which is why would you not accept the $5 Rationally, there is no reason for a player two to turn down a non zero offer. She is better off to accept than reject. Now there is strong evidence and I don’t talk a lot about this to suggest that behavioral changes are factors that have an impact on your decision making process.
One of them is the level of serotonin levels that are in your bloodstream. They have done tests which show dependent on how much serotonin, the likelihood of you accepting or rejecting changes. But what I find more intriguing is a research paper I came across that was published in 2011 and it looked at, two different groups of people. You had a control group of everyday Janes and Joes and you also had a group of Buddhist meditators ranging from six months to twenty four years of experience in meditation. Now when I went through the paper, I had some issues myself with how they actually worked out the experiment, but results are quite interesting.
The reject rate for the control group was 70%. So that’s basically close to the 80% that we see on average. Most people reject. Why do you reject? The only reason is out of spite.
I was hoping that the ratio might be a little bit different here, but there you go. Fair enough. Basically speaking, if you’re a rational logic agent, it makes no sense to reject. $5 is better than nothing. Worse still, you’re denying that other person the ability to take that money, even if you don’t get anything.
Technically speaking, you should still allow that person to walk out with everything. So I’m not claiming I’m one of those people that would necessarily accept, so don’t feel too bad, but basically, at the end of the day, the ratios were significantly and substantially different. The reject rate was 50%. Now I put a couple of quotes from the paper there. CAT scans revealed differences in brain activity within the posterior insula and the anterior insula of the brain.
I actually have no idea what that means. I just stuck that in because it sort of looked important really. What I did understand is the last bit I’ve written down here which is quite interesting. In summary, when assessing unfairness in the ultimatum game, meditators activate a different network of brain areas compared with controls enabling them to uncouple negative emotional reactions from their behavior. Because the issue really is here are you allowing yourself to be carried away by emotional influences or are you going to make a logical decision?
Well it would seem the majority of people today make the illogical decision and actually reject when really you should accept. So I found that quite interesting. There is a way of, I would argue, of improving your ability to rationalize and actually make rational decisions and that I guess would be through meditation. So that’s sort of the pseudo conclusion I reach to. Okay.
But moving on from here, we talked about a little bit about irrationality and it is a big problem for people who model irrationality because, how do you actually show that? Because the only types of models that we can design are things that follow logic structures, logic frameworks. So what I want to do is introduce you to a concept that has been around for quite a long time in economics. But it doesn’t seem to have spanned very far outside of particular fields. So it would be interesting to talk a little bit about it and that is the concept of bounded rationality.
So what does bounded rationality mean? It’s heavily used economics as a departure from rational agent behavior. So the example I’m going to use is if we pretend that we’re all Viking warriors on one of their Viking ships and we’re sort of sailing across to North America. We don’t know North America exists. There is evidence they’ve been there.
As you go to sleep on your hammock, I don’t even know if they had hammocks, maybe they slept on the wooden floorboards of the boats, You have one fear and that fear is not that you’re going to meet some type of monster and die in battle because then you get to I don’t know what the story is, but I think you get to feast table of Odin or something along those lines. So that’s good news if you die that way, right? Or you meet some other terrible and painful end. It doesn’t matter. You’re a hardened Viking ready for war.
What really you’re scared of is falling over the edge of the earth. So my question to you is, is this fear, there’s real fear there for you, is that fear rational or not? Yes or no? Absolutely. It’s rational.
To us it looks irrational. So how do we model this? Well, we actually refer to the fact that this viking suffers from, as we would contend pretty much everyone does, bounded rationality. Our ability to make conclusions and therefore come to logical outcomes of what should occur is bounded by three main items and I’ve listed them here. The information available to the individual, so this is access to relevant information.
The information is not there that the world is spherical around. Time they have to make that decision. The quicker that you employ to make a decision, the more likely that you’ll make a decision based on either habitual behavior or flee or fight resolutions. So the shorter time span, you will naturally rely on immediate thoughts that come to your mind which is through habituation. Finally, the cognitive ability to utilize information.
In other words, the state of mind. So it’s pointless talking to an ant about whether the earth is circular or flat because unfortunately they don’t have the intellectual capacity to understand that. From a modelling perspective, even though it sounds strange, we would actually say the ant is bounded in their rationality. Of course, you can’t have that conversation. It’s just a theoretical thought discussion.
But basically speaking, that’s how we would look at all agents whether they have the intellectual capacity, the cognitive ability, the time pressure they’re under and the relevant information to make an informed choice. So for the Viking, definitely he or she, it may well be a he, are making an informed rational choice about being scared and there might be outcomes from that where they might get into a fight and say let’s turn the ship back because we’re going to go over the earth. When in fact there’s nothing really there to be scared of. So we might laugh at that person and say this is ridiculous. But in fact for their purposes, they’re making a completely rational choice.
It can be modeled for our purposes mathematically. There’s no problem. Their rationality is bounded, is restricted. Is everybody happy with that idea? So I’ll come back to that.
So what I want to do is return to the prisoner’s dilemma because we can actually start making it a little bit more interesting. Now if some of you are still not happy with the outcome that we came or the conclusion that we came that we need to defect, then just let me know and we can go through that again. But I’m hoping you all sort of get the idea. It’s better to not cooperate, to defect, to cheat on your co criminal colleague to get a better outcome for yourself. Now the different types of games we can play with this simple scenario.
I should point out that the Prisoner’s Dilemma is one of the most widely, researched and published, games in the world. There are over 1,000 scientific journal articles just on the prisoner’s dilemma by itself and you might think, well how can you talk about that so much and I’ll show you why. So we can start off with a single game and that’s exactly what we play. It’s actually referred to technically as a stage game. You basically go on stage and you play that game once.
So that’s the stage game. There are two different other types of scenarios that exist from this. You have what I refer to as predetermined, finitely repeated games and what that basically means is a long word for saying you’re going to play this game with your same partner a number of times, five times, 10 times, maybe 100 times. Whatever the case is, you know how many times it’s going to be played and when the game is going to end. So the end stage game, the last game is fully predictable.
Everybody sort of happy with that sort of The alternative is to have what we refer to as an indeterminate finitely repeated games or infinitely repeated games. What this basically means is that you go into the game with your partner and the game master tells you you will play this game a finite number of times, but we’re not going to tell you how many times that is. Alternatively, the game master might say to you, you’re going play this game for the rest of your lives and then some. It’s going to go infinite. That’s not really feasible.
They actually have the same outcomes, believe it not. That’s why they’re put in the same context. So let’s go and explore the outcomes that we get. We know from a single game our best strategy is to do what? To cheat, right?
That’s the Nash equilibrium. What about for finitely repeated games? So for the single game we know the Nash equilibrium is to defect. Let’s say we’re going to play this game though twice. So in period one we have to make a choice.
Do we defect or do we cooperate? In game two, period two, we make the same choice. Do we then defect or cooperate? Anybody like to shout out what they think would be the answer answer for period one? Defect or cooperate?
Very good, Madame. And how do you come to that conclusion? You’re sort of on the right track but you’re missing some key ingredient. Anyone help her? Okay.
So the lady basically suggested that we should defect each time. What’s the reason for that? The game is slightly different to the single stage game. Absolutely. Okay.
Maybe from your legal mind it’s not the best case. Let’s change it around. Let’s say you have a yes? Well you’re getting on the right track. So just to change the scenario a bit to make it maybe a little bit easier for people and I give this example later on.
Let’s say you’re going to go for a picnic with another person and you have a choice of either being naughty or nice. If you’re naughty, you’re going to bully that other person. You can hog all the food and a drink and have a great time. Unfortunately your partner who’s going to go for the picnic gets nothing. So you have a choice between being naughty or nice.
Now if we play that game once, what’s the answer? What strategy should we do? We should be naughty or nice. Naughty, right? We should be naughty.
But let’s say we repeat it twice. Are we naughty or nice? Our strategy, as we go in and we’re playing with the same person again, we’re going go for picnic the next day, are we going to be naughty or nice the first time? Consciousness doesn’t. This is purely logic.
Your conscience has no role in this. This is a pure Nash equilibrium. Look, you people are very kind. You’re leaning towards being nice. So I’m going to provide you with a different scenario.
Let’s move on to period two. Are you going to be naughty or nice in the final game? Naughty, you all agree, right? There’s no point continuing on being nice, right? So if you know that the strategy strategy for for your your partner partner for for period period two two is is going going to to be be naughty because they’re as intelligent as you are, in the second period, in the final period, what should you do in the first period?
Be naughty. You also need to be naughty. With a predetermined outcome there is no incentive for you to be nice. I’ll give you one example and that’s from my field. I run a school that has about 100 academics and academics hurdling them and getting to do things is like herding like a bunch of cats.
It’s basically impossible. Impossible. They all hate each other and everyone is better than each other as well. It’s a fact. So the problem is when you have to deal with retirement planning and you’ve got tenure, you start thinking, wow, in five years time I’m going to retire.
The university can’t boot me out if I stop publishing. So I’m not going to do anything anymore. And then you think to yourself, well hang on a second, why am making this conclusion for for you know in five years time? Why don’t I make it now? So suddenly you have people who basically don’t do bugger all once they’ve got tenure, because they’re actually playing the prisoner’s dilemma of a finitely repeated game.
They know when the end game is. What we call this type of logic, the way we actually work it out, is called backward induction. It’s a very powerful logic tool that we use. We don’t work out what we’re going to do in period one and then period two. We start at the end and then we work backwards.
What would we do right at the end and make a decision on that and from that we work back? There’s only one logical conclusion which is that basically you should defect and be naughty. So far what I’ve shown all of you is that there’s no incentives to be nice. So you might leave and say, oh this is very depressing. So I want to put a little positive spin on things and go one step further.
But before I do, just want make sure everybody is already happy with what I’ve presented so far. These are logical conclusions. Sure. Sure. So I’m going to move on from here because your question is very pertinent and actually something I’m going to show you very soon will actually explain ethical behavior.
All I’m doing is building up to it. No. No. No. It’s a very good point, but I think what I’m going to do is show you actually how powerful logic can be.
So what I want to do is that’s fine. We’re going to move on and what I’m going to talk about is the final possibility in terms of time and by the way we don’t modify prisoner’s dilemma. The game stays the same but how we look at it, the conditions we put it under does change. So the final situation, yes, the conditions change. Final situation that I’m going to talk about and I’m going to spend some time on it and you can ignore the blurb at the top.
Basically I’m going to look at a game whereby you’re told you’re going to play it repeatedly but you’re not going to be told when the game ends. And then suddenly something changes. Do you defect or cooperate? And here I’ve got a scenario that takes us away from the legal realm, so hopefully Richard you will feel a bit more happier with it. So every day you are going to go for a picnic with the same party and you have a choice to make and that choice is whether you are going to be naughty or nice.
If you are nice and the second agent is nice, you both have a good time. Is it put you down more? If you are nasty and your partner is nice, you get everything. If your partner is nasty and you are nasty, you both end up constantly fighting with each other and nobody wins. So we’ve got the same sort of scenario.
There’s no difference. This is a prisoner’s dilemma as well. There’s no difference. Prisoner’s dilemma is a concept game. I put it into words but actually it’s a mathematical framework.
This mathematical framework is no different from the other one I’ve given. There is no difference in the payoffs or the language. Now NICE here, I’ve said it’s synonymous with signing up to the social contract. It traces back on down to Hobbes in fact when there’s argumentation why you should sign up. So I want to explore this a little bit.
So if you’re playing this game, you don’t know when the end game is going to be. Are you going to be naughty or are you going to be nice? Good. Anybody else would say that they want to be naughty? Yes, Van.
Well, it it’s Sure. You are on the right track. The fact is if we know that it’s going to finish one day, there is an incentive for us to be naughty. Because we all agree the last time we play the game we may as well be naughty, right? But we don’t know when that game is going to finish and if we don’t know when the game is going to finish, then you may as well be nice because you can’t determine the end game, you can’t determine the final outcome.
The only reason we’re going to be naughty in period one because in game one is because we know we’re definitely going to be naughty in period two, right? If we don’t know period two is the final game, then it changes completely. You may as well be nice. So the upshot of all this is if you don’t know when the last game is going to be played, you may as well be nice. And I’m not going to talk too much about it but people make illusions into the fact that well, here’s one simple example.
In the case where, let’s say, you’re interacting with your fellow colleagues and you need to maintain a reputation not for only yourself but your offspring and for what you’re doing for work, you may as well play nice. If you don’t know when you’re going to die, basically you’re playing an iterated process with an indeterminate outcome. You see people have been told, oh they’ve only got n months, you know five months less to live. Some of them become real asses, right? They run around doing everything they like, you know, the bucket list, they waste their time doing that because they know that end game is in sight.
But if you don’t know when that final game is going occur, then it changes things because the incentive to be nice to exists. And so what I want to do is talk a little bit more about this because I want to explain what the actual optimal strategy is for any agent in a game with an indeterminate period. An indeterminate number of games are going to be played. It turns out to be nice but I have to explain why in a little bit more context and actually the winning strategy. Okay, so for a rational non-Buddhist agent with an indeterminate life span agreeing to the social contract and cooperating is a dominating and winning strategy.
In my field, we actually say that this strategy beats a Nash sub game perfect strategy. What it basically means is it beats a Nash equilibrium. The Nash equilibrium is telling you to defect. In one game, it’s telling you to defect. But in multiple games, when you don’t know when the last game is going to be played, you would need to cooperate.
We know from before that cooperation can be a winning strategy. In fact, Robert Axelrod has made a lot of progress in this field. He published a book called The Evolution of Cooperation and he was responsible over twenty, thirty years ago of creating tournaments for academics to come together and play what I refer to as iterated prisoner’s dilemma. Basically the game that I’ve just discussed. The only difference is you will have hundreds of different academic mathematicians coming together all having their own strategy working out, oh I’m going to first cooperate to pretend that the player I’m playing with that I’m nice and then I’m going to cheat and screw them over.
Others will say I’m going to be nice all the time. And so various mathematical models were created. They were all stuck, of course, into a computer and the tournament began. And as a result, we’ve got some very interesting results. Greedy strategies perform generally very poor, while more altruistic strategies did better as judged by self interest.
So what is the most successful strategy in repeated games? What strategy should you use? Are you always nice? The answer is no. Are you always naughty?
The answer is no. What we end up with is a strategy that Anatol Rapoport developed. He’s a Russian and his strategy sounds so basic and simple you would not believe it but at the end of the day it’s one of the most powerful strategies to use in terms cooperation versus defection and it’s called tit for tat. There was one improvement made on it and the improvement was to add forgiveness. So we ended up tit for tat with forgiveness.
So let me explain how that works. There are four conditions to make a successful strategy and you might want to employ this for yourselves. The first one is that you start off nice and you generally are nice. You never defect if the opponent is being nice. There’s no incentive for you because when you’re both nice you maximize your benefits.
However, you do need to retaliate. The successful strategy must not be a blind optimist. So if the opponent defects and then subsequently you must also defect in the next game to serve as punishment. So there must be a form of punishment there. If you are nice and you’ve been playing these games a number of times, then suddenly your opponent is naughty, well you know you’ve got to show that person that they cannot continue to be naughty all the time.
So you retaliate for one period and for the next time you put out there and you are naughty. You must, however, also be forgiving. A successful strategy must also be forgiving to avoid a revenge play. It means down the track, out of spite, you don’t then suddenly be naughty once as well. There is no value to it because you know your opponent will also be naughty in the next time round.
You lose. So there cannot be any revenge play. And finally, you must be non envious. The last quality is being non envious, that is not striving to score more than the opponent. Just because your opponent was naughty one period and then you had to punish that individual, during the initial when you were nice and they were naughty, they have gained more points.
They have won. They have hogged all the picnic for themselves and you never got that chance to do that yourselves. You cannot then go back and take a revenge on it. You have to ignore how beneficial their situation is to yours. So you cannot be envious basically.
That’s the key. So these are the four points that creates a successful strategy. Now I’m taking a little bit of a long shot here. I’m throwing it out because I find it quite interesting. Basically, what I’m going to say is that the winning dominating strategy shares very similar resemblance to the basic process of karma.
Basically, I’d argue that karma is playing the optimal dominating winning prisoners dilemma strategy. So what is that? Well, if you are nice, you can expect nice things for yourself. If you are naughty, you may be not experienced the negative impact or the seeds of your negative karmic processes in the next life, but sure enough, sometime in the future you will suffer from it. In our prisoner’s dilemma, it’s immediate.
It’s in the next period. It’s in your next life. But if you cooperate again, no grudge will be held and you start winning. In other words, basically as soon as you pay it off your karmic debt, technically speaking, you’re sort of neutral and you should therefore get the benefit of being nice. So really the process of karma and me, at least in a very basic assumptions, work pretty much identically to the dominating strategy for Prisoner’s dilemma.
You are nice until someone’s naughty and then you must pay then they must be paid a punishment and after that it goes to be nice again. A very simple strategy and it wins all the time. So what I want yes, sorry. Sure. We need to change the context of it because I didn’t really, discuss this, but when you play prisoner’s dilemma, it’s not necessarily just one agent against another.
It can be one agent against a whole heap of other agents or alternatively you could say you are playing against Karma. It doesn’t have to be necessarily one prisoner against another. So the context of how we actually refer to them can change. Look, I’m not saying I’m not. As I said, I’m just basically making some very simple assumptions.
The rule is basically, if you’re nice, you can expect nice things to happen to you. If you’re naughty, you’ll pay the price. And essentially speaking, that is the rule base of how tit for tat with forgiveness works. They’re identical in that facet. There is no difference.
Oh yes. Of course, of course. That’s what we do. Think people, when they see because look, what I’m talking about, some of it is quite advanced to a certain context. I’m presenting you, with prisoner’s dilemma and some of you may have never seen it before and so you’re just thinking, okay, you got one prisoner got another.
In fact, it’s not like that. I’m putting words to a formula and really you’ve got sentient beings interacting and you make a choice. Do you cooperate or do you defect? The upshot of all this is that yes, you do cooperate if you do not know when the end game is going to occur. And in fact, the winning strategy is to cooperate as long as you follow these tit for tat with forgiveness strategy.
You cannot just be nice all the time because people will take advantage of you. But if you are nice and you put it out there and someone’s naughty, then there must be a punishment from it. That’s basically the gist of it all. Sorry Pamela. So most of this has been developed during the nineteen seventies and nineteen eighties.
So it was not too long after people really started looking at Prisoner’s Dilemma. The reason why it didn’t start off straight up that way is because of course you do actually need computers to amalgamate and play the games. These tournaments are not literally where the academics get together and start playing. It’s actually put their code into a computer and let it run. So a lot of the research that’s gone into that and still going on today is based on the power of computer really to come up with logical conclusions.
I Well, I can’t give you a specific date. What I can say is that the text was written September, so you’re looking somewhere between the seventies and eighties. I can’t be more specific. No. Prisoner’s dilemma has been around for bit longer.
Sure. Don’t know if that’s true or not. I can’t really comment too much on it. So what I can say is that this is basically the general view that’s held and the reason why it’s been developed is primarily through computing power. So what I wanted to do is talk a little bit about what happens today because it partly relates to my research.
Nowadays what we do is populate universes with different percentages of nice and naughty agents and we also allow them to have offspring or you can consider them rebirths and we allow them to also change their strategy which means there might be a situation I’m making a provide you a context to it. Let’s say you’re starving, you’ve lost your job, you really don’t have very much to do, the probability of you stealing grows. So we start putting agents under different pressure to see what happens and we see what happens, for example, when we have just naughty people with a few nice in there. What is the outcome? And we get some very interesting results and if you want to have a play at this, there’s a very good website that I’ve put on here and I’ve got some slides I can hand out to people if they’re interest where it’s an interaction website.
I’ve just taken a screenshot on them and you can play different games with your own strategy and see what happens. And by and large, what you will find and here’s one example, you can run different experiments. Can tit for tat succeed in a population of cheaters? The answer is yes. What people find out is that you can create a simulated universe of billions of agents and they might only be two nice agents compared to the billions of naughty.
These universes born and then they die. Nothing changes. You just have naughtiness until there’s a time when those two agents will find a chance to actually play against each other because it’s random whether who you’re going to play with. Right? You might play against a person who’s just going to be naughty.
But eventually there will be a time when two agents are nice and when those two agents are nice, they have the winning strategy because if everybody else playing naughty, that has a very low payoff compared to two agents who are playing nice. Suddenly there’s a massive explosion. I haven’t actually shown it here. You on the screen a massive wave of change if you’re doing it in color. So where, I don’t know, red is naughty and green is nice.
Suddenly you’ve got a whole explosion of populations which are turning where the green is basically taking over the universe. So it’s very interesting the type of games that you can play in these simulations, but by and large the message I want to sort of drum through is that tit for tat with forgiveness, even under modern day’s computer simulations, cannot be beaten. It is a successful strategy. So moving on from here, and I’ve got a little bit of time left, so I have to speed things up a bit. What happens if you’re a Buddhist?
So assuming that you are rational enough to realize that Buddhism really is the answer to all your rules, then the question is, how do you actually put this type of, logic structure into play? Well, there are a couple ways of doing this. I’m not going to spend very much time on it at all. The reason being they’re quite boring for me. One is that you can add in the premise of interdependence.
So rather than say if I defect, I will benefit if the other person cooperate. So if I’m naughty and the other person is nice, I get to hog all the food. If you acknowledge there is a form of interdependence in there, then the payoffs change. You will still lose because you are going to feel really sad that the other person is starving and due to empathy or whatever else you want to throw in there, you end up with a situation that nobody wins. A good example of this is with tax evasion.
It’s optimal for me to cheat on my taxes if I know everybody else is cheating, right? Because I benefit from the infrastructure, from the roads, everything else that has been built up for me. However, if everybody is thinking the same, what happens? Basically, you’re sort of, you know, Greece, yeah, you’re basically screwed. So here’s a typical example whereby the incentive to cheat, even though it looks good for you, you are still taking away something from the whole which could be manifestly better.
So that’s a good example of where you want interdependence through tax evasion. If you end up with interdependence, you end up with something which is called Pareto equilibrium which basically means you end up in a situation where the strategy you adopt is where you cannot make yourself better off without anybody else being made worse off. That’s an economic equilibrium that I don’t talk anymore about but that’s what you end up Another alternative of course is what we’ve covered where you allow rebirth which is through repeated games. But I don’t really want to spend much time on that. The reason being, what I’m more interested in is this question here.
What’s more pertinent is to say, well if you acknowledge that you are a Buddhist, you accept karma, rebirth and the consequences of cause and effect, then why do you not follow and I guess I’m talking about myself here, why do I not follow a winning strategy of being nice all the time if you accept there will be consequences of unethical behaviour? And the answer basically lies, at least the way I present it and because I’m an economist, I think along those terms, is through what’s called a discount factor. So I’m just going to talk a little bit about that. So what do you prefer? A $100 now or $200 in one year’s time?
Don’t think about the logic behind it. Just think instinctively. What would you prefer? A $100 now or me giving it to you in a year’s time with another $100? What’s your preference?
Now. You want a $100 now. I guess it’s certainty, right? I don’t know. Okay, very good.
Very good. Let’s say it’s not a question of trust. I’m very trustworthy. So that’s not a function that should be considered. So it’s just a question of do you want the $100 now or 200 in one year’s time?
Yeah, it does a little bit. I agree. If you really need the cash, you’re going to want to take. You could be thinking along those lines. Yep, there are many things that you could What about if I offer you the following?
$100 in four years time or $200 in five years’ time? Are you indifferent or you prefer one over the other? Extra year. What Wait I’m presenting to you here is something referred to the fact that there’s a general preference for immediate consumption over future consumption. We actually call this the present bias.
In fact, technically speaking, what we actually have is what’s referred to as a hyperbolic discounting factor. What this means is the following: if I know I can get immediate satisfaction today, I will prefer that even though there may be a greater benefit in the future for me. However, if I’m told something is good going to happen to me in the distant future and it will be even better if I wait a little bit longer, I don’t really care because the future is so much into the future, I make no differentiation. So most people are willing to accept $200 in five years but at the same time, illogically, they’re willing to take a $100 now rather than $200 in one year’s time. And the reason being is that for immediate consumption, there’s a preference over that of future consumption and this basically is called the present bias.
It’s what we also term, we can calculate it literally as a discount factor. You discount items that will occur in the future over the present. So how does this relate to ethics? How does it relate to whether you’re to do something nice or naughty? And our point is that this has been true of humans and animals in many, many tests.
It’s sort of overdone in this area. Well, I’m going to give you two examples and I’m hoping the little speakers on the floor will work. It really depends on your mental state and your environment. Essentially speaking, the ability for you to make a rational choice with the bias there of you wanting to consume immediately is dependent on your state of mind, the information you have at hand and the time pressure that you’re at. Basically how bounded your rationality is.
So here’s a first example which is from Campbell’s Soup. Let’s hope this works. Sorry. I think I can put it louder. Whoops.
I’m going to put it louder first of all. I think what I need to do is break from that and put this up and just hope this will work. So I just took a little screenshot there to go over something very simple and it’s to highlight the fact that your consumption changes by simply adding a few words to an advertisement and the reason this occurs of course and marketing academics that work in my school know this all too well is that you’re basically triggering triggering certain certain mental sort of points in people to act in a different way. In fact, I have sort of more humorous discussions about what they’re doing, essentially saying, basically, you’re very unethical in your practices. And in fact, at the end of the day, marketing academics, we they have to teach a course which is called marketing ethics and everybody knows it’s an oxymoron.
They sort of joke about it as they go in to teach it because really the goal of marketing analysts is to work out a model to get you to purchase something to provide immediate consumption now, even the fact when you don’t really need it And the models are quite interesting. What we deal with are what are called antecedent variables. You try to work out if you want someone to act in in this sort of way and the person’s over here, what in between do you need to make that link? And they’re very good at it. Down at University of South Australia, they have a whole marketing department.
Some of them actually look at eye movements of people on screens to work out exactly what they’re focusing on for for certain type of items. So it’s become a very heavy science in fact. But what I’ll do is show you another example. It’s not an example. I’ll show you should I say.
It’s actually a paper I’ve taken from biology letters and the reason I put this out there is because actually it’s quite common and I think most men would recognize it all the time in fact. But this is the first time I could actually see someone actually documenting in an experimental lab. Do pretty females inspire men to discount the future? Well the answer is yes and that’s why you have nice, bikini clad ladies buy sports cars when you’ve got testosterone filled men walking in to purchase something or you need basically even insurance sales person. It’s better to have a lady than a man sell to a gentleman.
I’ve taken some quotes from this paper. Organisms discount in the future when they value imminent goods over the future. The way they actually assessed discounting was on the basis of choices between small money tomorrow or a larger sum at a later date. So they’re playing the game I just went through, discounting game, both before and after the subjects were asked to rate the appeal of 12 photographs. Now they actually had male and female respondents here and they actually showed them both male and female photographs.
So was all a mixture. But everybody there was heterosexual, I believe. So they showed females, male photographs and female photographs. They showed females, males, they showed male and females, all different types of permutations from that. The only one effect that would gain significant output was the fact that in precisely the one they actually predicted, men’s discounting increased after rating attractive women.
We believe that this is the first demonstration of an experimentally induced change in human discounting. The reason I wanted to go through this example is to show that basically very simple visual effects, maybe they’re auditory, can change the way you rationally make a decision and people know this in the marketing schools and they use this to their effect. The reason why I’ve sort of raised it is because at the end of the day, if you’re making a decision of saying just even a little white lie over the issue of having to deal with something of a larger consequence now, you prefer to lie because you suddenly discount the future even if you accept, at least if I do, accept that there might be larger consequences in a future from a negative karmic process at large. So discounting has an impact on us and the reason why we discount incorrectly is because of the environment that we are faced with and how we interact with them. So what is leading us to make unethical decisions despite accepting cause and effect?
Well, what I’m going to put out there is a fact that we are all too willing to discount the future over present consumption and the reason we do this is because our rational decision making processes are restricted or they are bounded by our interaction with the environment, state of mind and time pressure. So these are the three items I highlighted before that creates bounded rationality. So my argument is that if people were truly rational, then a lot of decisions that they would make are very likely would be far more ethical than they are. The fact is that we are bounded and restricted in our logical decision making processes because we can’t see further than what’s in front of us and our interaction with the environment causes us to think in a very different way to how we actually really should. Under the sway of the above, thinking rationally is actually not easy.
Thinking clearly is actually a hard task. So I have one little quiz and I’ll get this out. I don’t know how many people would be interested in this but I told a colleague of mine, I mentioned he was a professor in computer science. I was presenting something on game theory and he said, don’t you give these texts out to people? They give it to me freely.
So if anyone wants to purchase one for me, they’re welcome to. It’s about $20 and the money can go to TBI. The other one I’ll give out for the first person who can answer the question I’m going to mention. Now this is a book on puzzle based learning and this text has been adopted by universities across the world Carnegie Mellon, Illinois, Tel Aviv University, a number of European universities, University of Adelaide. Rather than teach mathematics through the normal process where you learn one method and then you move on to the next because the problem that we have in maths is not that we don’t have the necessary tools to solve problems but we’re not asking the right questions.
So this is actually a text and maybe some of you won’t be of interest but others it will because it does get a little bit mathematical. It’s how do you solve mathematically puzzles. There could be verbal, there can be maybe some of you have seen questions where you have to match up matchsticks and they have to basically count the number of Well there’s ways of solving it and the question is don’t get students to learn routines of how to solve problems but how to think what is the best method to solve a problem. So this is basically taking over the world as a new pedagogy for looking at mathematics. It’s called puzzle based learning.
So there’s a video here. It lasts for six minutes and that’s the end of my presentation and it’s from a game show that’s held in The United Kingdom. It’s called Golden Balls. Now, for my perverted mind, I’m coming up with other type of scenarios but there’s nothing rude about it. Basically, this is a modified prisoner’s dilemma game with two contestants trying to convince each other that they’re going to split the money rather than steal.
But one of the contestants changes the game around entirely. So after the clip, if you can shout out what strategy this contestant had adopted and it’s covered in my lecture, then you’ll get the text. Alright. So let’s go. I just have to find it first of all.
So that’s it basically. So the question is what strategy did the contestant who was very intelligent in fact choosing to say they’re going to steal rather than split was using? It was changing the game. Was it a prisoner’s dilemma game? What was it called?
Did did the other opponent have a choice? There was no choice. It’s the ultimatum. He put it out there saying, I’m not going to give you a choice. I’m going to steal.
So you either split and you have to trust that I’m going to share the money with you later or if you choose steal, we both walk out with nothing. It’s the ultimatum game. So yes, well done, Nick, and you’re welcome to the prize. And really, the reason why I wanted to show you it is because there’s so many permutations of what happens with the prisoner’s dilemma. It can basically explain many different types of scenarios under different circumstances.
This is a modified prisoner because they obviously were talking with each other. But I found it quite sort of insightful. So I hope you enjoyed my presentation and that’s basically it for me. So I’m good friends with the with the author and he’s a very well known field and he’s actually one of the preeminent evolutionary algorithm computer scientists around the world today. So this is a new way we teach mathematics.
So it’s quite interesting. Hopefully, you’ll find some. Fascinating. Oh, yes. Yeah.
Key terms in this teaching
- dependent origination pratityasamutpada (Skt); ten drel (Tib)
- Also called dependent arising. The way that the self and phenomena exist conventionally as relative and interdependent. LYWA
Definitions adapted from the Lama Yeshe Wisdom Archive glossary, as taught in the Gelug tradition.