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So welcome back and I hope you're as excited as me about

the Olympics, and about finding out how the tale of the contractor and the

Organizing Committee eventually played out.

Okay. Remember what happened here.

We had a contractor having to deliver street lights either of high or low

quality and we had a the Organizing Committee

deciding whether to pay the full price or to renegotiate the price down.

And we have this game. This game would last

for five months, okay, every time we had a hundred street lamps.

So, let's see how this plays out. But, to do that, we'll have to revisit a

concept that we did in the last session, which is backward

induction. What is backward induction?

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It's basically a technique that can be used to analyze repeated games with

finite repetitions. It's a process of reasoning backward in

time. So we first consider the last stage of a

game, and we determine the best action at that time.

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And we keep on repeating that process until the best strategy for every stage

of the game is likely to be found. So let's just recap the

situation with the Olympics. We know the installation takes five

months, and we know that every month, 100 street lights can be manufactured and

installed. We know that the contractor can threaten

the Organizing Committee and say, well, if you ever renegotiate the price in any

one month, then we'll deliver low quality from then onwards.

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And by the same token, vice versa the organizing committee can threaten the

contractor and say, well, if you ever deliver low

quality in one month, then we'll renegotiate the price for all future

periods, for all future months. So with that information let's take the

situation and start analyzing it from the back as we would in backward induction.

Okay? So what are the payoffs in Month 5?

This is the last month of interaction, meaning that no threat of retaliation

exists in the subsequent period. So, we have this game matrix again with a

contractor, with the organizing committee who can accept or renegotiate the price,

and there, the contractor will deliver high or low quality.

Okay? So this is going to be our game matrix.

And given that you already know how to figure out the equilibria for these

kinds of situations, let me take a moment and have you find out what the Nash

Equilibrium in this game is. And I'll see you after this.

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Okay, so I hope you all knew, or you all were able to show that the equilibrium of

this game is that the contractor will deliver low quality and the Organizing

Committee will renegotiate the price. Let's just repeat how we did that.

If the Organizing Committee accepts the price, the contractor has an incentive to

deliver low quality. If the organizing committee renegotiates

the price, then again the contractor has an incentive to deliver low quality,

because 8000 is a higher payoff than 5000.

If the contractor delivers high quality, then it's better for the organizing

committee to renegotiate the price, because that gives him a payoff of 25,000

rather than 15,000. And if the contractor goes for low

quality, then it's better for the organizing committee to renegotiate the

price. Okay?

So, looking at that, this shows us that the equilibrium in Month 5 is going to be

for the contractor to deliver low quality for the organizing committee to

renegotiate the price. The future does not matter because there

is no future. This is the last month of the game.

This is the last time we'll play the game.

So, let's see how this plays out in Period 4, in Month 4.

We've already figured out that in month five there's not going to be cooperation.

It breaks down, for sure. Threatening to retaliate if there's no

cooperation in month four is completely useless.

So it's not credible, meaning that. If we take the game in Month 4, this is

what we have and we can analyze it as if it were the last period of the game.

So if this is the last period of the game and we play it just a single time, we

know that the outcome again is going to be low quality by the contractor and

renegotiate price by the Organizing Committee.

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And again, I guess you sort of get the message,

again the equilibrium of this game is going to be for the contractor to deliver

low quality for the Organizing Committee to renegotiate the price.

We skip Month 2 because by now you figured out that basically Month 2 is

going to look very much like Months 3, 4 and 5.

So let's go back to the very start of the game.

Month 1, surely if reputation, if a threat ever matters it would be in the

first period you play this game. Okay?

Building up a reputation is going to be most useful if you do it in period one.

But you know already in period one, in month one, that there is no cooperation in

months 2,3,4 and 5. So therefore, the threat of retaliation

in month one is not credible again. So therefore, this is how the game looks

like and this is what the outcome is going to

be in month one. So, to summarize, if we follow backward

induction, the process of looking at the end of the game and solving it and moving

it forward, we find that the contractor will deliver

low quality in all months, the organizing committee will always renegotiate a lower

price, and so, therefore, we will end up in a

suboptimal equilibrium. We will end up in a situation where

cooperation between the two parties never even gets going.

This outcome is triggered by the fact that in the last stage of the game, there's no

further threat of retaliation. Okay?

We called this the endgame effect. Even if we have a game that

goes on for a very, very long time the closer we get to the end of this game,

the more likely it is that cooperation will simply break down.

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And this holds for any prisoners' dilemma with a finite number of repetitions.

So, it doesn't matter if we play it five times as here, if we play it two times, if you

played 15 times. As soon as we can use backward

deduction the game is going to unfold in the way that we have just shown.

So, in this video we've analyzed the prisoners dilemma that's played a finite

number of times. Given the fact that the threat of

retaliation is not an issue in the last round of the game.

The players that are involved will act selfishly in all rounds of the game, and

they won't be able to coordinate in a way, such that they both realize higher

payoffs. So the threat of retaliation is not

credible in any stage of the game. Which is what we call the End Game

Effect. Because there is an end to the game, it

unfolds. So in the following video, we'll look at

another type of repeated games. And in these games, the number of

repetitions is not clear from the beginning, so there's no end point that

we can identify from the start. There might even be no end point at all.

So stay with me. And then we'll analyze if cooperation can

be, and maintained, or enabled more successfully in this kind of repeated

games, repeated indefinitely, or

infinitely. Okay?

See you in a second. Thanks very much.