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ECON-159: GAME THEORY

Lecture 2 - Putting Yourselves into Other People's Shoes [September 10, 2007]

Chapter 1. Recap of Previous Lecture: Prisoners' Dilemma and Payoffs [00:00:00]

Professor Ben Polak: Okay, so last time we looked at and played this game. You had to choose grades, so you had to choose Alpha and Beta, and this table told us what outcome would arise. In particular, what grade you would get and what grade your pair would get. So, for example, if you had chosen Beta and your pair had chosen Alpha, then you would get a C and your pair would get an A.

One of the first things we pointed out, is that this is not quite a game yet. It's missing something. This has outcomes in it, it's an outcome matrix, but it isn't a game, because for a game we need to know payoffs. Then we looked at some possible payoffs, and now it is a game. So this is a game, just to give you some more jargon, this is a normal-form game. And here we've assumed the payoffs are those that arise if players only care about their own grades, which I think was true for a lot of you. It wasn't true for the gentleman who's sitting there now, but it was true for a lot of people.

We pointed out, that in this game, Alpha strictly dominates Beta. What do we mean by that? We mean that if these are your payoffs, no matter what your pair does, you attain a higher payoff from choosing Alpha, than you do from choosing Beta. Let's focus on a couple of lessons of the class before I come back to this. One lesson was, do not play a strictly dominated strategy. Everybody remember that lesson? Then much later on, when we looked at some more complicated payoffs and a more complicated game, we looked at a different lesson which was this: put yourself in others' shoes to try and figure out what they're going to do.

So in fact, what we learned from that is, it doesn't just matter what your payoffs are — that's obviously important — it's also important what other people's payoffs are, because you want to try and figure out what they're going to do and then respond appropriately. So we're going to return to both of these lessons today. Both of these lessons will reoccur today. Now, a lot of today is going to be fairly abstract, so I just want to remind you that Game Theory has some real world relevance.

Again, still in the interest of recapping, this particular game is called the Prisoners' Dilemma. It's written there, the Prisoners' Dilemma. Notice, it's Prisoners, plural. And we mentioned some examples last time. Let me just reiterate and mention some more examples which are actually written here, so they'll find their way into your notes. So, for example, if you have a joint project that you're working on, perhaps it's a homework assignment, or perhaps it's a video project like these guys, that can turn into a Prisoners' Dilemma. Why? Because each individual might have an incentive to shirk. Price competition — two firms competing with one another in prices — can have a Prisoners' Dilemma aspect about it. Why? Because no matter how the other firm, your competitor, prices you might have an incentive to undercut them. If both firms behave that way, prices will get driven down towards marginal cost and industry profits will suffer.

In the first case, if everyone shirks you end up with a bad product. In the second case, if both firms undercut each other, you end up with low prices, that's actually good for consumers but bad for firms. Let me mention a third example.

Lecture 2 - Putting Yourselves into Other People's Shoes [September 10, 2007]

Chapter 1. Recap of Previous Lecture: Prisoners' Dilemma and Payoffs [00:00:00]

Professor Ben Polak: Okay, so last time we looked at and played this game. You had to choose grades, so you had to choose Alpha and Beta, and this table told us what outcome would arise. In particular, what grade you would get and what grade your pair would get. So, for example, if you had chosen Beta and your pair had chosen Alpha, then you would get a C and your pair would get an A.

One of the first things we pointed out, is that this is not quite a game yet. It's missing something. This has outcomes in it, it's an outcome matrix, but it isn't a game, because for a game we need to know payoffs. Then we looked at some possible payoffs, and now it is a game. So this is a game, just to give you some more jargon, this is a normal-form game. And here we've assumed the payoffs are those that arise if players only care about their own grades, which I think was true for a lot of you. It wasn't true for the gentleman who's sitting there now, but it was true for a lot of people.

We pointed out, that in this game, Alpha strictly dominates Beta. What do we mean by that? We mean that if these are your payoffs, no matter what your pair does, you attain a higher payoff from choosing Alpha, than you do from choosing Beta. Let's focus on a couple of lessons of the class before I come back to this. One lesson was, do not play a strictly dominated strategy. Everybody remember that lesson? Then much later on, when we looked at some more complicated payoffs and a more complicated game, we looked at a different lesson which was this: put yourself in others' shoes to try and figure out what they're going to do.

So in fact, what we learned from that is, it doesn't just matter what your payoffs are — that's obviously important — it's also important what other people's payoffs are, because you want to try and figure out what they're going to do and then respond appropriately. So we're going to return to both of these lessons today. Both of these lessons will reoccur today. Now, a lot of today is going to be fairly abstract, so I just want to remind you that Game Theory has some real world relevance.

Again, still in the interest of recapping, this particular game is called the Prisoners' Dilemma. It's written there, the Prisoners' Dilemma. Notice, it's Prisoners, plural. And we mentioned some examples last time. Let me just reiterate and mention some more examples which are actually written here, so they'll find their way into your notes. So, for example, if you have a joint project that you're working on, perhaps it's a homework assignment, or perhaps it's a video project like these guys, that can turn into a Prisoners' Dilemma. Why? Because each individual might have an incentive to shirk. Price competition — two firms competing with one another in prices — can have a Prisoners' Dilemma aspect about it. Why? Because no matter how the other firm, your competitor, prices you might have an incentive to undercut them. If both firms behave that way, prices will get driven down towards marginal cost and industry profits will suffer.

In the first case, if everyone shirks you end up with a bad product. In the second case, if both firms undercut each other, you end up with low prices, that's actually good for consumers but bad for firms. Let me mention a third example.

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