博弈论(一)--yale

@(study)[大学生活, markdown_study, LaTex_study, English_study]
课程地址

why change the course

the reason why i change the game theory is simple :

for studying english
the Yale course is more theoretical

game 1

开玩笑的,怎么可能只写英文,下面是第一个博弈

game_1

AD转换一下(量化收益(payoff)):

game_1_payoff

Obviously,strategy A is always better than B !
不妨先定义一个术语:
We say that my strategy a strictly dominates my strategy b r(严格优势策咯) if my payoff from a is strictly greater than that from b regardless of what others do

It is crystal clear that:

lesson 1 : Do not play a strictly dominated strategy (被动态,表严格劣势策略)

the question is in what situation that we need to choose B ?
Unless all the people want to get a better score , but that is some wrong with this reasoning :

it bases on the magical reasoning aspect , my choice can affect others
even if everyone choose b ,I choose a is still better

so is does not exist a situation to choose B....

But in the same time ,it explains that

lesson 2 : rational choice in this case , can lead to outcome inefficient

在这个时候我们回观几乎所有人都知道的博弈论典型非零和博弈模型:
囚徒困境

在囚徒困境中,假设你的对手是其它狱友,明显严格优势策略是坦白,但实际上,坦白带来的并不是最优解,因为一定情况下你的对手并不是你的狱友.

but how about we change the payoff :

game1_payoff2
in the time , a is not the strictly dominates strategy
this kind of game is called a "Coordination problem"(协和谬论 )

So,the payoff is matter ,in other words :

you can't get what you want unless you know what you want

think about another payoff:

game_1_payoff_3

in this way , for me ,it does not exist the strictly dominate strategy , but my opponent has strictly dominate strategy is a . On the basis of lesson 1 , he/she will choose a .
Therefore ,our best choice is a .

lesson 4 : put yourself in other's shoes and try to figure out what they will do

lesson 5 : Yale students are evil .......

跟之前课程很相似的一个game2:

"Pick a number"
Without showing your neighbor what you are doing,put in the box below a whole number between 1 and a 100.We will calculate the average number chosen in the class .
The winner in this game is the person whose number is closest to two-thirds times the average in the class
The winner will win $5 minus the difference in pennies between her choice and that two-thirds of the average