Is that correct? The other thing I should apologize at this stage of the class is my accent. So once again if you both put Alpha then my pair gets a B-. If I put Alpha and my pair puts Beta, then she gets a C. And if I put Beta and she puts Alpha, then she gets an A. So I now have all the information that was on the sheet of paper that you just handed in.
So notice what I did here. The first grade corresponds to the row player, me in this case, and the second grade in each box corresponds to the column player, my pair in this case.
So this is a nice succinct way of recording what was in the previous two tables. This is an outcome matrix; this tells us everything that was in the game. Okay, so now seems a good time to start talking about what people did.
How many of you chose Alpha? Leave your hands up so that Jude can catch that, so people can see at home, okay. All right and how many of you chose Beta? Let me try and find out some reasons why people chose. We can ask you why? Okay, so you chose Alpha right? So why did you choose Alpha? Student: [inaudible] realized that my partner chose Alpha, therefore I chose [inaudible].
Professor Ben Polak: All right, so you wrote out these squares, you realized what your partner was going to do, and responded to that. Any other reasons for choosing Alpha around the room? Can we get the woman here? Student: The reason I chose Alpha, regardless of what my partner chose, I think there would be better outcomes than choosing Beta.
Professor Ben Polak: All right, so let me ask your names for a second-so your name was? Professor Ben Polak: Clara Elise. So slightly different reasons, same choice Alpha. Oh come on! There was a Beta right here. You were a Beta right? You backed off the Beta, okay. So how can I get a mike into a Beta? Is that a Beta right there? Are you a Beta right there?
Can I get the Beta in here? Who was the Beta in here? Can we get the mike in there? Is that possible? In here - you can leave your hand so that - there we go.
I mean those are similar kind of ranges but it certainly is a reason. Other reasons for choosing? Yeah, the guy in blue here, yep, good. Student: Well I guess I thought we could be more collusive and kind of work together, but I guess not. So I chose Beta. Stand up a second, so we can just hear you. Student: Sure. My name is Travis. I thought we could work together, but I guess not. Professor Ben Polak: Good, so Travis is giving us a different reason, right?
I mean you all know each other in class. You all go to the same college. For example, if we played this game up in the business school—are there any MBA students here today? One or two. There might be ethical reasons—perfectly good, sensible, ethical reasons—for choosing Beta in this game.
And perhaps, the lesson I want to draw out of this is that right now this is not a game. What are we missing here? Game Theory, me, professors at Yale, cannot tell you what your payoff should be. However, once we know what your payoffs are, once we know what your goals are, perhaps Game Theory can you help you get there.
Well the first idea is that these numbers represent utiles or utilities. These are people—people with these payoffs are people—who only care about their own grades. So these people only care about their own grades. They only care about their own grades.
What do we call people who only care about their own grades? So now we can ask a different question. Suppose, whether these are actually your payoffs or not, pretend they are for now. Suppose these are all payoffs. Now we can ask, not what did you do, but what should you do? Now we have payoffs that can really switch the question to a normative question: what should you do? So just explain what you did and why again. Professor Ben Polak: Why did you choose Alpha?
Just repeat what you said before. Student: Because I thought the payoffs - the two different payoffs that I could have gotten—were highest if I chose Alpha. If the pair chooses Alpha and she chooses Alpha, then she gets 0. If the pair chooses Alpha and she chose Beta, she gets If the pair chooses Beta, then if she chooses Alpha she gets 3, Beta she gets 1, and 3 is bigger than 1.
So in both cases, no matter what the other person does, she receives a higher payoff from choosing Alpha, so she should choose Alpha. Does everyone follow that line of reasoning?
So the woman, I have immediately forgotten the name of, in the red shirt, whose name was -. It kind of implies your reason. I think I can fit it in here. Definition: We say that my strategy Alpha strictly dominates my strategy Beta, if my payoff from Alpha is strictly greater than that from Beta, [and this is the key part of the definition] , regardless of what others do.
Shall we just read that back? But a few bits of jargon are going to be helpful in allowing the conversation to move forward and this is certainly one. Actually, so you can still read that, let me bring down and clean this board. So Lesson One of the course is: do not play a strictly dominated strategy. Do not play a strictly dominated strategy. Somebody want to tell me why? Do you want to get this guy? Stand up - yeah.
So we look at the definition of a strictly dominated strategy. What else could we have? Could we get this guy in the pink down here? Professor Ben Polak: The payoffs are lower, okay. That sounds like a convincing argument. It sounds like too obvious even to be worth stating in class, so let me now try and shake your faith a little bit in this answer. Okay, so how about the following argument? Look at the payoff matrix again and suppose I reason as follows.
So I should choose Beta: 1 is bigger than 0, I should choose Beta. Yes, Ale - yeah good. Professor Ben Polak: All right, so it involves some notion of agreeing. So certainly part of the problem here, with the reasoning I just gave you—the reasoning that said I should choose Beta, because if we both reason the same way, we both do better that way—involves some kind of magical reasoning.
The X-Men right? What else is wrong with that reasoning? Yeah, that guy down here. Well how about this? Even if I was that guy in the X-Men or the Matrix or whatever it was, who could reason his way into making people do things.
Even if I could make everyone in the room choose Beta by the force of my brain waves, what should I then do? I should choose Alpha. If these are my payoffs I should go ahead and choose Alpha because that way I end up getting 3. The element of truth is this. We both end up with payoffs of 0, rather than payoffs of 1. It is true that by both choosing, by both following this lesson and not choosing the dominated strategy Beta, we ended up with payoffs, 0,0 , that were bad. So rational choice [in this case, people not choosing a dominated strategy; people choosing a dominant strategy] rational choice can lead to outcomes that - what do Americans call this?
Rational choices by rational players, can lead to bad outcomes. So this is a famous example for this reason. Yes, the guy here in orange. This happens in every single episode, so much so that if any of you actually - I mean this might actually be true at Yale—but if you any of you or the TV guys: if any of you know the guy who writes the plots for this, have him come to the class so I guess to see the video now and we get some better plot lines in there.
The grade game and this is not the only example. So how many of you have roommates in your college? How many of you have roommates? Most of you have roommates right? Why is it disgusting? The best thing for you is to have the other guy tidy up and the worst thing for you is to tidy up for the other guy.
Am I being unfair? Are your dorm rooms all perfect? Other examples? Professor Ben Polak: Okay, in divorce struggles, okay. All right, hiring lawyers, bringing in big guns. What about an Economics example? What about firms who are competing in prices? Both firms have an incentive to undercut the other firm, driving down profits for both.
The last thing you want is to have the other firm undercut you, in an attempt to push prices down. What remedies do we see? What kind of remedies do we see? Let me try and get the guy here right in front. Professor Ben Polak: Collusion; so firms could collude. So what prevents them from colluding? One thing they could do, presumably, is they could write a contract, these firms.
What about you with your roommates? Very few of you. Why do you manage to get some cooperation between you and your roommates even without a written contract?
Professor Ben Polak: Well it probably is legally enforceable actually. This guy says not, but it probably is legally enforceable.
He probably could have a written contract about tidying up. The woman in here. Now one person earlier on had mentioned something about communication. I think it was somebody in the front, right? Is communication the problem here? Professor Ben Polak: …Mary, had been able to talk to the person next to her whose name is…? Professor Ben Polak: Erica. Course Materials Download all course pages [zip - 10MB]. Description This course is an introduction to game theory and strategic thinking.
Texts A. Dixit and B. Thinking Strategically , Norton J. Requirements Who should take this course? Survey Please take a few minutes to share your thoughts about this course through the survey linked below. We also invite you to provide general feedback about Open Yale Courses by visiting the Feedback area of the site. Take the survey. A portion of the proceeds from your purchases will be donated for the ongoing support and development of the Open Yale Courses program.
View the catalog for this course. Introduction: Five First Lessons. Putting Yourselves into Other People's Shoes. Iterative Deletion and the Median-Voter Theorem. Best Responses in Soccer and Business Partnerships.
Nash Equilibrium: Dating and Cournot. Nash Equilibrium: Location, Segregation and Randomization. Can apes learn sign language? This course tries to answer these questions and many others, providing a comprehensive overview of the scientific study of thought and behavior.
It explores topics such as perception, communication, learning, memory, decision-making, religion, persuasion, love, lust, hunger, art, fiction, and dreams. We will look at how these aspects of the mind develop in children, how they differ across people, how they are wired-up in the brain, and how they break down due to illness and injury. Arguments for the Existence of the Soul, Part I. This lecture outlines a number of arguments that can be offered for proof of the existence of the soul.
Course description: There is one thing I can be sure of: I am going to die. But what am I to make of that fact? This course will examine a number of issues that arise once we begin to reflect on our mortality. The possibility that death may not actually be the end is considered. Are we, in some sense, immortal?
Would immortality be desirable? Also a clearer notion of what it is to die is examined. What does it mean to say that a person has died? What kind of fact is that?
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