Okay, now we're going to take a look at a signaling game. In a very formal way, look at this thing in front of us. Wow, so this is not meant to be confusing. It's meant to be helpful in thinking about intuition of a signalling game. But we're going to have to walk through it to really get the intuition. This diagram, in the game theory literature is called a signaling game in extensive form. Extensive form is just the form of the diagram sitting right here. Now, what's on this diagram? Well, you have two players. You have an incumbent who's been in the market for quite a while and knows demand conditions. And you have an entrant, a potential entrant, a player that might come into the market if they think the demand conditions are right. So, there are also two possible states of the world. One is good demand conditions, all right, that's given by that right there. So think G equals good, and you also could have bad demand conditions, B equals right bad, we have bad here and good. Now the incumbent firm, they know the state of the world because they've been operating for a while. They know demand conditions, that entrant doesn't. The entrant does know the probability that it'll be good demand conditions or bad conditions, but it doesn't actually know the reality. Now each of these players in this game have kind of two potential options. The incumbent can set a high price or a low price. On the other hand, the potential entrant can decide to either enter the market, or stay out of the market. That's what each of them can decide, and notice, based on our conversations before, this is a sequential game. So, that means that the potential entrant will observe the price that the incumbent sets prior to making a determination whether they're going to enter the market or not. Now the payoffs are given over at the ends of these lines. The first number is the amount of money the incumbent is going to make. So for example, if the state of the market is good and the incumbent sets a high price. And the potential entrant enters, the incumbent makes $3. It's also true that if the demand conditions are good, the incumbent sets a high price, the entrant decides to enter, the entrant will make $1. That's how you read these different payoffs. So in each case you have a price and an entry, no entry combination. And that determines the pay offs of the individual players in this game. Okay, so now let's think about strategy for these players. Suppose it's a good state of the world, let's look at the payoffs for the incumbent. If we go over here, the payoffs for the incumbent are, if they set a high price, their payoff is 3 if the entrant enters, and it is 10 if the entrant stays out. On the other hand, if the state of the world is good, and the incumbent sets a low price. If the entrant enters, the incumbent will make $2. And if the potential entrant stays out, they'll make $9. Now why is this important? It's important to look at these two numbers and these two numbers and realize that in both cases the 3 here is bigger than the 2. And the 10 is greater than the 9. And that means no matter what the entrant decides to do, enter or stay away, if the state of the world is good, then the incumbent is better off setting the high price. That is the best strategy for them, if it's a good state of the world. It doesn't make sense for them to set a low price, because no matter what that entrant firm does, whether they enter or stay out, they make less money then whatever happens on the high price side. So that's a kind of a dominate strategy for them. On the other hand, let's think of a low state of the world, so low demand conditions. In that case, if the incumbent firm plays high, they make 1, if the entrant enters, or 3 if they do not enter. This is the pair, right, that's associated with a high price in a low demand situation. On the other hand, if they play low price in this low demand situation, they make $2 if they enter and $4 if they stay away. So let's look at these pairs again, 2, 4 and 1, 3. And once again, we see that one side sort of dominates the other side. Four is greater than three and two is greater than one and what that means is no matter what that potential entrant decides to do, either enter or stay out. If the demand conditions are bad, the incumbent firm is better off playing low, that's the dominant strategy for them. Okay, what does this mean in terms of the entrants behavior? It means that they know that a high price is a credible signal of good demand conditions. And low price is a credible signal of bad demand conditions. And therefore, they can assume that they're in this space right here. This is the game that they're playing. Sometimes, game theorists call these sub-games, they're like parts of a game. So what are they going to do? Well, if they see high, they're better off entering. Why? Because 1 is greater than 0. So any time they see high from the income firm they're better of entering. On the other hand if they see low from the incumbent firm, four is greater than two. So what are they better off doing? They're better of staying out, right here stay out and enter. So what do we have in this game? We really have two equilibria based on demand conditions. If demand is good, the equilibrium sits right up here. And that equilibrium is what? High, enter, play high price and then enter. If demand conditions are low what's the equilibrium? It's right here, and that is low price and stay out. And notice what's interesting about this game is that incumbent firm was able to infer mark conditions because there was the ability of the incumbent firm. To credibly signal to the entrant firm what was really going on in the market. And because of that, without ever communicating directly with each other, each of the players know what's going on in the market.
