Study notes on game theory (ii) Learning to think in a different position

Source: Internet
Author: User

Three elements of a game

    • Participant player
    • Strategy strategy
    • Interest payoffs

Strategies for SI i participants
S Policy Collection
Ui Part I participant selection Strategy SI benefits

We assume that there are now two participants, 1 and 2, for Player1
We say Si ' is a disadvantage strategy for SI, when and only if Player2 chooses whatever strategy sj,u1 (SI,SJ) >u1 (SI ', SJ).
We say Si ' is the weak disadvantage strategy of SI, when and only if Player2 chooses what strategy sj,u1 (SI,SJ) >=u1 (SI ', SJ).


About Third century BC, the elephant-ridden general Hannibal wants to invade Rome, there are two ways to choose: a rugged road, need to climb the Alpen, Die Mountain, the other flat, just follow the coastline. If the aggressor chooses the rugged road, it will lose a battalion's strength only over the course of the climb; if he encounters the force that you are stationed in, no matter where he goes, he will have to lose another battalion's strength. An intruder can only choose one of these routes for intrusion, and the defender can only choose one route to defend it. Which route should I choose to defend.

Alpha Beta
Alpha 2,0 0,2
Beta 0,1 The
Here it is assumed that alpha means a rough road, and β is a flat road. On the left is the number of battalions I can destroy, and on the right is the number of battalions the general Hannibal can keep (assuming he has only two battalions and loses two battalions he will be annihilated). Obviously for general Hannibal, the strategy beta is weaker than the strategy alpha, so general Hannibal will choose Strategy Beta. After General Hannibal chose Beta, I was able to get a better yield on beta. (In fact, General Hannibal had chosen to climb Alpen, Die Mountain.) )

The topic of the last lesson
The whole class chooses a number between 1 and 100, and whoever chooses the number closer to the average of two-thirds does not tell anyone, who wins. What's the number you chose?

Common knowledge common knowledge so if everyone is rational, then the optimal strategy is 1. But the average of all the numbers in the final statistic is 13 and 1/3, and the nearest 2/3 is 9, which is more than 1. Because in fact not everyone is rational.

When we go through this game again, the number of people who choose is generally smaller than before, because everyone has become sophisticated.

Because not only do we play this game ourselves better, we also know that the people around us play this game better. The analysis of this game not only makes everyone more sophisticated, but also gives you a better understanding of the sophistication of others, and you know that others know you know how to play this game. We come to an important conclusion: not only do you have to stand in the position of others to think about the benefits of others, you have to stand in the position of others to think about how sophisticated they are in the game, and you have to consider how sophisticated they think you are, and consider how sophisticated they think you think they are.

Study notes on game theory (ii) Learning to think in a different position

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.