Game theory Study notes (eight) position selection, segregation and the randomization of positions

Another location model

Assuming that there are two small towns, Ben is called Dong Town and West town, each town can accommodate up to 100,000 people, and then we assume that there are 200,000 people in the world, there are two kinds of people, the big and the small. The strategy is whether you choose Dong Town or West town. The profit is related to the number of participants in the town in which they belong. And we assume that if there are more than 100,000 people in a small town, we will take a random strategy to pick out a part of the extra person and move them to another town.
The relationship between the profit earned by each person and the number of his peers in his town is as follows:

There are three Nash equilibria here:

1. The big men all concentrated in the Dong Town, the small men all concentrated in the West town, or the big man all concentrated in the West town, the small man all concentrated in the Dong Town.
• Because when things were not equal, the people who were in the minority in the towns had to make the most profit or choose to go to another town, which led to the apartheid
2. The proportion of big and small in every town is just 50%/50%.
• In this case, everyone has reached the maximum profit. This is actually a weak Nash equilibrium, because the change in smiles is likely to cause the trend to move like a person.
3. All the people moved to Dong Town or all the people moved to the west town.
• In this case 50% people will randomly be selected to move to the other town. Because according to the theorem of large numbers, the proportion of big and small people in randomly generated populations is close to 50%/50%

Conclusion:

1. Sometimes the Nash equilibrium can be obtained from the restrictive conditions, such as the above strategy randomization

Rock, scissors, rock, Scissor and Paper

	R	S	P
R	0,0	1,-1	1,-1
S	-1,1	0,0	1,-1
P	1,-1	0,0	-1,1

Randomization of Strategies

Game theory Study notes (eight) position selection, segregation and the randomization of positions