Nash Game and Examples

Nash equilibrium is the Nash equilibrium solution of the game. So neither of your two questions is a typo.

One of the most famous examples is the "Prisoner's Dilemma". You can find a lot of them just by searching, so I won’t go into details here. Let me give you a recent example to help you understand.

Not long ago, a cargo ship of my country's Ocean Shipping Group was hijacked by pirates in Somalia, which triggered a discussion on maritime security issues. Maritime security issues are actually a typical Nash game, and every country is in a prisoner's dilemma. middle.

Maritime security can be regarded as a public good. For example, if a country establishes a maritime guard to protect its own ships, other countries can enjoy it "by the way" without paying, which is called "Hitchhiking". In this way, every country has no incentive to provide maritime security. They all hope that other countries will provide it, and they will directly enjoy the benefits without paying the relevant costs. In this game, the dominant strategy of each country is not to provide it but to be provided by other countries. In this way, the Nash equilibrium is that all countries do not provide it. This ultimately resulted in an insufficient supply of maritime safety products.

After giving examples, let’s talk about what Nash equilibrium is. The Nash equilibrium is: given A's choice, B's choice is optimal. If B's ??choice is given, A's choice is optimal. In other words, no one is willing to change unilaterally given an opponent's actions. Then a problem arises. When any one has to choose his own strategy, he does not know what strategy the other person will have, so each person will make an expectation of the choice that the other person will make. In short, that is When a person makes a choice, he will guess what his opponent will do, and then make the choice that is most beneficial to him. To simplify the example I gave you before, if there are only two countries in the world, the United States and China, and there are trade exchanges between the two countries, if a maritime guard is not established, Chinese and American ships may be hijacked, causing losses to both parties. If the United States establishes a maritime guard force, China can enjoy it without paying any cost, which is more effective than spending a lot of money on it (just imagine, if you can get what you want without spending money, it will definitely be better than if you pay a lot of money to get it. get more satisfied). vice versa. Therefore, in this game, neither China nor the United States is willing to take the initiative to provide it, but hopes that the other party will provide it. The best way to solve this dilemma is to clarify property rights, such as the zoning escort proposed by China.