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Do biologists or sociologists need mathematicians? It turns out that this is true. Math can describe people's behavior and help solve everyday problems. All you have to do is look at the game theory.

Prisoner's Dilema

Two dangerous criminals have been arrested, let's call them Jack and Buck. Jack and Buck received an offer to testify the against each other. There are three possibilities.

• If none of them agree to go to jail for 1 years.
• If only one of them agrees, he will be pardoned and the other will be sentenced to 4 years in prison.
• If both agree, both will be sentenced to 3 years in prison.

Jack and Buck faced a dilemma known as the prisoner's dilemma, and contrary to what the name implies, he does not refer to criminals only.

Other example

Two companies want to sell the same product. Both can sell the product cheaply then half of the customers will go to one company and the other half to the other company. When one company sells cheaply, all customers will buy the product of this company.

Game Theory

Game theory is the study of equilibrium states named after the creator of the theory Nash Equilibrium. In a state of equilibrium, it is not profitable for any player to change the strategy. The player may be anyone who participates in the game. Villager, company, or people waiting in line. Naturally, you can see why equilibrium states are so important, ll parties have the greatest possible benefits.

Example (almost) taken from life

sorry for the quality

In this city everyone is going from point 4 to point 2. 4 thousand (4000 = N)cars pass that route every minute. There are two types of streets in the city. For one type the travel time is constant and it is equal to 45. For the second type of travel time is dependent on the number of cars. The equilibrium in this case will be that the change of route by any of the cars will not be profitable in term of travel time. We see that if 2000 cars will take the route 4> 1> 2 and 2000 cars will take the route 4> 3> 2 we will reach equilibrium - 65 minutes. 2000/100 + 45 == 2000/100 + 45.

Changes

Let's try to do something that seems to shorten the travel time. We are adding a new street 1 > 3, for the sake of simplicity we assume that the travel time for a new street is 0.
What are possible equilibrium states? Still we can choose previous one from the model without 1 > 3 street, but also we can pick new one 4 > 1 > 3 > 2 but this state is worse. Simple math 4000/100 + 4000/100=80 and we see that in new equilibrium state travel time has increased to 80 minutes what is contrary to intuition.

Braess's paradox

Such impossible situation really happens and we call them Braess' paradoxes. Such case was described in the New York Times In 1990 New York City's Transportation Commissioner decided to close 42d Street this has improved the driving conditions in the city. It is worth noting that similar situations may occur on the Internet when choosing the best path for packets. Game theory is interesting, biologists use it to describe the behavior of animals in the flock and economists describe the behavior of companies and consumers.