So, welcome back. As we're all familiar with simultaneous games by now, in the next couple of videos, we'll discuss sequential games or dynamic games as we often call them. Sequential games are simply put games with some sort of a time aspect in them. So, one firm acts before the other. It's going to have quite important implications for playing the game. So, the second firm will be able to play the game knowing what the first firm has done. And it's going to be able to adjust its actions accordingly. And the first firm, on the other hand, has to make a decision without the requisition knowledge of the follower, right? I don't know what the second player is going to do. However, the first firm will keep in mind, that there will be a follower and this follower is going to react in some sort, rationally. Okay, so they are going to build up expectations about the reactions of the follower in my own decisions. Now, I want to illustrate this with an example related to the movie ET, the Extra Terrestrial. So, I don't know how much you are a kid of the 70s, but if you are, then you will remember this scene very, very vividly. Okay? So, ET has just landed. He's hiding somewhere. He's terrified. He's hiding in the woods somewhere. And there are a couple of kids, two kids that see that something is out there in the woods. It's fairly close to their house, so they feel, well, you know, we want to make sure that we can find out what this person, what this animal might be. So, to lure out ET, they lay a trail of sweets, small round sweets, colored round sweets. Okay? And they lay the first one right at the edge of the woods. They lay the next one, maybe a step or two ahead, and so on. ET finds the first one, he picks it up, has a look at it, and tries it. And he likes it. Okay? In the second step, so he looks around if there are any more. And he finds another one, takes the next one, likes it, and eats it. And so on and so forth. So, he gets more and more excited, and eventually, follows this trail of sweets into the bedroom of the kids. When he picks up the last piece of sweets he picks it up, eats it, looks up, because there are no more, the kids look up as well and they start screaming, ET starts screaming and chaos ensues. And so that's the story that you have to keep in mind. What you may not know, is that the small pieces that ET picked up, were a small candy called Reese's Pieces produced by a company called Hershey's. Okay, and so, what I want to discuss now is the back drop to this story, the commercial back drop to this particular story. Okay, so we call it the chocolate wars. And keep in mind, these are fictitious numbers that we're using. Universal Studios, which were shooting ET at the time, they were charging, or they were approaching Mars, saying, well, do you want to place a product in this scene in ET? If you do, we're going to charge you $1 million for that. If that had happened, if Mars had agreed to that offer, then Mars' gross profits would have increased by 0.8 million, so 800,000 and Hershey's would have decreased by 100,000. So, to find the net profits, we have to include the payment for that, which is 1 million. So, Mars' gross profits would have been minus 0.2 million. Hershey's, they didn't pay anything, and they suffered, 100,000 in loss of sales. If product placement had taken place by Hershey's, which is actually what took place, what happened, Hershey's gross products would increase by 1.2 million and Mars' profits decrease by 0.5 million. So again, if we calculate the net profits, this is going to be 1.2 minus 1, and that's positive 200,000. If there's no product placement, it's just business as usual, nothing changes, no profits change. So, that situation, obviously, is something that was highly strategic because what happened depended on what the other firm did, and so on and so forth. So, how do we draw this? We can't really draw a matrix, as we'll see in a second. So, how do we take into account the fact that we have sequential decisions here? We draw what's called a game tree. A game tree has the property that the first decision point always starts the game. This decision point, and every decision point that follows represents a node. And from that node, we have decisions of subsequent players, subsequent decisions will branch out accordingly. Okay, sounds very complicated, it's actually very easy and I want to take that example of of Mars and Hershey's to illustrate this. So, the first decision was Mars', okay? Mars got the offer from Universal Studios, and they had the offer of either placing their product or not placing their product, okay. After that, the decision came to Hershey's. If product placement actually takes place, if Mars signs the contract, then Hershey's can't really do anything, all right. So, for them, it's just a question of maintaining the status quo. If Mars does not agree to the deal, then Hershey's again, has the choice between choosing product placement, so signing the contract or not. Okay, so that's the structure of the game. The next thing we need to know is what the payoffs are. So, the payoffs if Mars signs and Hershey's doesn't get to sign are plus 800,000 minus 1 million. That's Mars' profits are going to be minus 0.2 million. Hershey's, as we saw, are going to be minus 0.1. If Mars doesn't sign, but Hershey signs instead then Mars is going to lose half a million and Hershey's is going to win 200,000. Their net profits are going to increase by 200,000. And if neither of them signs, they both get profits of zero. Okay, so that would be a structure that we can then go ahead and analyze, and we'll do that in the next video. But for now, what this is useful for is, it can tell us something about a strategy. What do we need to know if we want to define a strategy of a game? So, we sort of have an idea already. Alright, we have a working definition for this course which was, it's a player's plan of actions in a particular game. But we need to extend this because we need to take into account that these are actions for every possible circumstance of this game. Okay, so in the case of ET and Hershey's and Mars we'll get to that later in the next exercise. Let's now have a look at price setting, okay? Price setting, we have a sequential game, where Firm A first chooses a high or low strategy. And then, Firm B chooses a high or low strategy depending on whether Firm A has chosen high or low. So, what are the possible strategies, the potential strategies for player B, okay? We actually have four strategies for player B. So, what are they? They are high, if high, and high, if low. What does that mean? It means that if Firm A chooses a high price, Firm B is going to choose a high price as well. And if Firm A chooses a low price, Firm B is going to choose a high price again. So that's one strategy. What's the second strategy? Second strategy would be high, if high, and low, if low. In that case, if Firm A chooses high, Firm B is going to choose high, as well. If Firm A chooses low, then Firm B is going to choose low, as well. Okay. And you can figure out what the other two strategies for player B are. Interestingly, if you compare this to Firm A, Firm A only has two strategies, they can either choose high or low. They can't make this dependent on what Player B does because Player B chooses later than Player A. Okay? So, in this short video, we've analyzed the product placement story of Mars and Hershey's as an example of a sequential game. We've drawn up a game tree and we've used it to systematically illustrate the competitive situation of Mars when they are offered the product placement deal. So, in the following video, we'll try to use the game tree to help find the optimal strategy in a competitive situation. But please first, do the in-video quiz. So, we've learned, in most cases, firms can choose between different strategies. And so, please now, have a look at the following game tree and take which strategies seem reasonable for Firm B, okay? And I'll see you in the next video.
