The answer is that it doesn't. Sure the business that shut down did have customers who used to shop at that business and will now be looking for a new place to shop, but they have thousands of choices in the market to choose from. You might have a handful of that business' customers come to your shop but it isn't something you are even going to notice. You are still going to produce the same amount of your product. In fact, there isn't much that a competitor does that you are going to care about at all.
Now imagine that you are 1 of three firms that sell a product. Unlike the previous example you are constantly worried about and watching what your two competitors are doing. Why? Because there is a limited pool of people willing to buy this product and the three of you are already dividing that pool up. Thus, if they do something to gain new customers it means that they had to take those customers away from one of the other businesses. If you lose a customer, the customer is going to one of your two competitors. If you gain a customer, you had to have taken that customer from a competitor. You care a LOT about what the other businesses are doing.
That idea is what drives an oligopoly. The economics term is "mutual interdependence". It means that you are linked to and dependent on everything the other businesses in the oligopoly are doing. You do not and cannot act in a vacuum. If they are able to lower their prices, then you are forced to lower yours. If they come up with a new design or feature, then you are forced to match their moves.
One of the ways that works itself out is with game theory. Game theory is the idea that we can only decide what our best action is by looking at what the other firm's best actions are. A business won't act on its own. It will first study its opponents and then decide to act. (If you've ever played chess, it's a lot like chess. You can't just move your pieces. You have to think about how the other player is going to move his pieces.)
The main way that game theory shows up in AP Micro is with a payoff matrix. A payoff matrix can be much bigger, and can be between more than two firms, but for AP Micro it is always a two by two grid that shows how two firms will respond when making a choice between two options.
It's probably best to learn by showing you an example and talking about it. Here is a typical payoff matrix:
A pay off matrix always represents two people, businesses, countries, etc. In this case we have Alex's business and Bob's business. Alex is on the left side and Bob is on the top.
There is always a choice between two options. It could be choosing between: to advertise or to not advertise, to sell product A or sell product B, to have a sale or not have a sale, to upgrade your machinery or to not upgrade it; or, as we have in this matrix, to charge high prices or to charge low prices. It can literally be anything, but for AP Micro there will always be two choices.
So, in our matrix above the top two boxes represent Alex charging high prices. The bottom two boxes represent Alex charging low prices. The left two boxes represent Bob charging high prices. The right two boxes represent Bob charging low prices.
Finally there will a set of two numbers in each box. Typically the first number in EACH box represents the person on the left. The second number in EACH box represents the person on the top. However, DON'T ASSUME. Always read the question fully, as it will tell you for sure which number goes with each person.
The numbers in the box can represent anything. They might be revenue or profit, but they could also represent a cost. Again, DON'T ASSUME. Always read the question fully. It will explicitly tell you what each number represents. This is important because if the numbers represent something good, then you want to pick higher numbers. If the numbers represent costs or something bad, then you want to pick lower numbers. DON'T ASSUME. READ THE QUESTION.
For our matrix, let's have the numbers in the box represent profit in thousands of dollars. And the first number in each box will be Alex's profit and the second number will be Bob's. Given all of that what is the box on the upper left corner telling us?
The box in the upper left says that Alex has decided to have high prices and Bob has also decided to have high prices. When that happens Alex will make $28,000 in profit. Bob will make $24,000.
The box on the lower left says that if Alex decides to have low prices, while Bob has high prices, then Alex will make $18,000 in profit. Bob will make $35,000.
Of these two boxes, clearly Alex would prefer the top box in which Alex makes $28,000. After all $28,000 is better than $18,000. Of those two Bob would prefer the bottom box in which he makes $35,000. After all $35,000 is better than $24,000.
But how did we get from the top box to the bottom? We got there because Alex switched from high prices to low prices. Bob had nothing to do with this switch. That is because Alex is the one that choose whether we are in the top row or the bottom row. Alex chooses which row they are on, by deciding between high and low prices.
Meanwhile Bob decides whether we will be in the left column or the right column. Alex has no control over which column they will be in. Bob choose by deciding whether he will have high or low prices. If he choose high prices, then they will be in the left column. If he choose low prices, then they will be in the right column.
How does that impact the market? In other words how do we "solve" a payoff matrix. In order to figure out what will happen in this market, we have to look at how each person will respond to the other's actions. That will help us to identify boxes that are called "Nash Equilibriums." (Named after John Nash. The movie "A Beautiful Mind" is about him. You should watch it. It's a great movie.)
A Nash Equilibrium is a box in which neither person has an incentive to change their strategy. If we look at a box and can see that one of the people can improve their situation by changing their strategy (in this case changing what level they set their prices) then it is NOT a Nash Equilibrium.
For instance let's look at the lower left box. The box that represents Alex having low prices and Bob having high prices. It says in that situation Alex will make $18,000 in profit. Bob will make $35,000. Do either of them have an incentive to change?
If Bob shifted from high prices to low prices, Bob's profits would drop from $35,000 to $12,000 (Because they would now be in the lower right box). That is a loss of profits. Bob does NOT have an incentive to change.
If Alex shifted from low prices to high prices to high prices profits would shift from $18,000 to $28,000. (Because they would now be in the upper left box.) That is $10,000 more in profits. Alex definitely DOES have an incentive to change strategies. Because of this fact, we know that the lower left box is NOT a Nash Equilibrium.
Here's the matrix again:
Okay, now back to solving the matrix. How you solve the matrix is first you pretend you are one of the two people. Let's start by pretending we are Alex.
If you are Alex and Bob sets his prices high, what do you do in response? If Bob sets his prices high, you will also set your prices high. In that case, Alex would rather set prices high and get $28,000 instead of $18,000.
If you are Alex and Bob sets his prices low, what do you do in response? If Bob sets his prices low, you will still set your prices high. In that case, Alex would rather set prices high and get $43,000 instead of $27,000.
Notice how for Alex it didn't matter what Bob did. Whether he sets his prices high or low, Alex will set prices high. In a situation like this we say that Alex has a "Dominant Strategy". That just means one person doesn't care what the other does. The other person's choices do not impact which option you will choose.
But we aren't done yet. Now we have to switch perspectives and pretend we are Bob.
If you are Bob and Alex sets prices high, what do you do? If Alex sets prices high Bob should set his prices low. After all Bob would rather have $25,000 than $24,000.
If you are Bob and Alex sets prices low, what do you do? If Alex sets prices low Bob should set his prices high. After all Bob would rather have $35,000 than $12,000.
Notice how for Bob it does matter what Alex does. Bob will change his strategy based on what Alex chooses. If Alex chooses high, Bob should choose low. If Alex chooses low, Bob should choose high. Bob does NOT have a dominant strategy. That means one person is going to react to what the other does.
Let's go back through the matrix one more time. This time when we are looking at how a person will respond, let's put a circle around the choice they will pick. As an example, if Bob choose high prices, Alex will pick high prices and make $28,000. So let's put a circle around the number 28. Let's do that for all of the possible outcomes.
When we do that, we get this:
(I color coordinated the two firms so it is clear which circle goes with which outcome.)
What are these circles telling us? The fact that there are two circles in the upper right box tell us that this is Nash Equilibrium. Let's check to be sure.
If we were in the upper right box, does either person have an incentive to change?
If Alex changes from high to low prices, profits drop from $43,000 to $27,000. Alex does not want to change.
If Bob changes from low to high prices, profits drop from $25,000 to $24,000. Bob does not want to change.
That box is a Nash Equilibrium.
The other three boxes are not Nash Equilibriums. In each of them one or both people will have a reason to change. Check on your own to see how that is true.
A matrix can have 0, 1, 2, 3 or even 4 Nash Equilibriums. However, for AP Micro you are likely to see one with 1 or 2 Nash Equilibriums. You might see one with 0. You almost assuredly will not see one with 3 or 4.
In a matrix a dominant strategy can be held by both, one or neither of the people. You could see any of these options.
Here is a power point that has some more practice examples.
Here are two Clifford Videos on this and a Crash Course Econ on it too.
Tomorrow I'll have some more examples for practice.
Also Zoom meeting tomorrow at 10:00. I can do some examples then too.
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