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? 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. Once we have that last best action we take the information and use it to determine what to do in an penultimate stage. 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. 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. 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 low quality for the Organizing Committee to renegotiate the price. So we know what's going to happen in Month 4, and we know what's going to happen in Month 5. It's not going to be cooperation. So, in Month 3, the threat of retaliation is really not credible again. So, we take that situation as if it were the last time we play the game. 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. 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.