Why are KFC and McDonald's always running together?

Why are KFC and McDonald's always running together? -- Use the iterative deletion method of strict non-optimal policies in game theory for analysis

We often find this kind of discovery. In the prosperous area of a city, you find a KFC and look around and usually find a McDonald's nearby. So, why do KFC and McDonald's always get together to compete with each other and lose people? Here I will try to explain this situation from the iterative deletion method of strict non-optimal policy in game theory.

First, we assume the following model for convenient analysis.

1. A highway is divided into 1-10 roads. Each road has the same number of people. Each road is a group of 1 units.

2. a KFC and a McDonald's will also open a branch on the road. They will select a branch on the 1-10 road of the road.

3. People on each road will choose the nearest store for consumption. If the two shops are the same, 50% of them will go to the two stores respectively.

4. The only goal of KFC and McDonald's address selection is to attract more users to their stores for consumption.

Figure 1 a 10-section Road

Then, we will analyze what branch will they open on the road as a rational KFC store manager and McDonald's store manager? (Note: here, we will not introduce strict non-optimization policies and iterative deletion methods for strict non-optimization policies. If you do not know much about this knowledge, please check the game theory content on your own ). We will first compare the distribution of McDonald's branches in road section 1 and road section 2. When KFC opens a branch in Section 1, If McDonald's also opens a branch in Section 1, McDonald's and KFC will each get 50% of the people, If McDonald's opens a branch in section 2, according to the previous assumption, only one person in road section 1 will go to KFC for consumption, while 2-10 people in road section will go to McDonald's for consumption, so that KFC will get 10% of the people and McDonald's get 90% of the people; when KFC opens a branch in section 2, If McDonald's opens a branch in Section 1, McDonald's will attract road 1, that is, 10% of people, and KFC will attract road 2-10, that is, 90% of people flow. If McDonald's is opened in section 2, KFC and McDonald's will attract 50% of people respectively. In turn, we will continue to analyze the proportion of people that McDonald's will attract when it opens 3-10 branches in road sections 1 and 2. Sorting 2. The percentage on the left of the income matrix is the people attracted by KFC, and the percentage on the right is the people attracted by McDonald's.

Figure 2 Comparison of earnings of McDonald's branches in road section 1 and road section 2

Analysis Figure 2: When KFC chooses road section 1, McDonald's selects road section 1 to get 50% of the traffic, and select road section 2 to get 90% of the traffic. When KFC chooses road section 2, mcDonald's selected road section 1 will get 10% of the people, and select road section 2 will get 50% of the people. In turn, we continue to analyze the selection of 3-10 road sections of KFC, and find that for all the cases of selecting 1-10 road sections of KFC, McDonald's selection of road section 2 will attract more people than McDonald's selection of road section 1, that is to say, McDonald's road section 2 is superior to McDonald's road section 1, and road section 1 is a strict non-optimal strategy. As a rational McDonald's manager, there will be no choice for road section 1 to open a branch, that is, the strict non-optimal strategy of road section 1 will be removed.

Similarly, McDonald's will remove 10 in the rightmost section based on symmetry. Because the KFC store is the same as the McDonald's store, the KFC store manager, who is also a rational person, will not open a branch in Section 1 and section 10. KFC and McDonald's will open branches in the remaining sections 2-9. After the above analysis, after section 1 is removed, Section 2 becomes the leftmost section. As shown above, section 3 is superior to section 2, section 2 should be removed in strict non-optimal conditions, and section 9 should also be removed. The remaining section 3-8 should be removed. Remove the leftmost section 3 and rightmost section 8, and the remaining section 4-7. Continue to remove section 4 and section 7, and the remaining sections 5 and 6. That is, KFC and McDonald's will also open branches in the middle road section 5 or section 6. That's why we can always see KFC and McDonald's in the busiest part of the city.

To sum up, KFC and McDonald's will be adjacent to a prosperous area in the middle.