Suppose there is a big pig and a little pig in the pigsty.
One end of the pigsty has a pig trough (both pigs are at the trough end), and the other end is equipped with a button to control the supply of pig food. When you press the button, 65,438+00 units of pig food will enter the trough, but on the way to the trough, there will be two units of pig food consumed in kind. If the big pig reaches the trough first, the profit ratio of the big pig to the food is 6: 4; At the same time (press the button), the income ratio is 7: 3; Piglets reach the trough first, and the income ratio is 9: 1.
Then, under the premise that both pigs are wise, the final result is that the little pig chooses to wait.
"Intelligent pig game" was put forward by Nash in 1950.
In fact, the pig chooses to wait and let the big pig press the control button, and the reason why he chooses to "take a boat" (or hitchhike) is very simple: on the premise that the big pig chooses to act, if the pig chooses to wait, the pig can get four units of net income, while if the pig acts, it can only get 1 unit of net income left by the big pig, so waiting is better than acting.
On the premise that the big pig chooses to wait, if the little pig acts, the income of the little pig will not cover the cost, and the net income is-1 unit. If the pig also chooses to wait, the benefit of the pig is zero and the cost is zero. In a word, waiting is better than action.
When the big pig chooses to act, if the little pig acts, its income is 1, and if the little pig waits, its income is 4, so the little pig chooses to wait; When the big pig chooses to wait, if the little pig acts, its income is-1, and if the little pig waits, its income is 0, so the little pig also chooses to wait.
On the whole, whether the big pig chooses to act or wait, the choice of the little pig will be waiting, that is, waiting is the dominant strategy of the little pig.
2. Cooperative attack problem
The two generals led their troops to ambush on two mountains at a certain distance, waiting for the enemy. General A has received reliable information that the enemy has just arrived and the situation is unstable. If the enemy is unguarded and the two armies attack together, they can win; And if only one side attacks, the attacker will fail. This is known to both generals.
A encountered a difficult problem: how to cooperate with General B's attack? At that time, there were no communication tools such as telephones, so we had to send intelligence agents to deliver messages. General A sent an agent to find General B, telling General B that the enemy was unguarded and the two armies attacked together at dawn.
However, what may happen is that the agent is missing or captured by the enemy. That is, although General A sent an intelligence agent to convey the message of "attack together at dawn" to General B, he was not sure whether General B had received his message.
Actually, the agent is back. General A was lost again: How did General B know that the agent must have come back? General b won't attack rashly without being sure that the agent will come back. So general a sent agents to B. However, he can't guarantee that the agent will arrive at General B this time. ...
This is the "cooperative attack puzzle" put forward by J. Gray in 1978. To make matters worse, some scholars have proved that no matter how many times the agent successfully ran back and forth, he could not let the two generals attack together.
Extended data
1928, von Neumann proved the basic principles of game theory, thus announcing the formal birth of game theory. 1944, the epoch-making masterpiece Game Theory and Economic Behavior written by von Neumann and Morgenstein extended the two-player game structure to the n-player game structure, and systematically applied the game theory to the economic field, thus laying the foundation and theoretical system of this discipline.
In 1950 ~ 195 1, John Forbes Nash proved the existence of equilibrium by using the fixed point theorem, which laid a solid foundation for the popularization of game theory. Nash's groundbreaking papers such as Equilibrium Point of N-person Game (1950) and Non-cooperative Game (195 1) give the concept of Nash equilibrium and the existence theorem of equilibrium.
In addition, the research of Reinhard Zelten and John Hasani also promoted the development of game theory. Today, game theory has developed into a relatively perfect discipline. Widely used in finance, securities, biology, economics, international relations, computer science, political science, military strategy and many other disciplines.
Baidu Encyclopedia-Game Theory