Consider the following decision process : choose between
+ playing the following game : bet on one of the 37 numbers {0,…,37} (probability of winning = 1/37) and gain 36 euros if you win (and nothing otherwise).
+ not playing the game and instead receive 1 Euro for sure.
What is the expected (financial ) gain of playing ? of not playing ? Consider an agent who decides to play. Can his/her utility function be identical to the financial gain ? What can this utility function be ?
Example 2 :
Consider the following decision process : choose between
+ taking an insurance policy (price : 100 Euros) and do not pay anything if there is a fire;
+ not taking the insurance policy and in that case, pay 50 000 Euros if there is a fire, otherwise pay nothing. The probability of there being a fire is 1/1000.
What is the expected (financial ) gain of taking the insurance ? of not taking it ? Consider an agent who decides to take an insurance. Can his/her utility function be identical to the financial gain(with the convention that loss = negative gain) ? What can this utility function be ?
Example 3 :
Consider the following 4 lotteries l1, l2, l3, l4
+ l1 = <0.9, 30000 euros ; 0 Euros>
+ l2 = 20.000 euros (with probability 1)
+ l3 = <0.9, 30000 euros ; 0 Euros>
+ l4 = <0.1, 20000 euros ; 0 Euros>
What do you chose between l1 and l2 ?
What do you chose between l3 and l4 ?
Show that an agent who prefers l1 to l2 and who prefers l4 to l3 is not rational according to von Neumann and Morgenstern ?
Theo cảm tính của em thì trong ví dụ 1 em sẽ chọn là chơi, trong ví dụ 2 em sẽ chọn ko đóng bảo hiểm, còn trong ví dụ 3 thì em sẽ chọn l2, và l3 chứ ko chọn l1 và l4 nhưng em ko biết dùng toán học để giải thích như thế nào, vì em ko phải là dân toán mà. Mong các bạn giúp đỡ, mình xin cám ơn rất nhiều.
Bài viết đã được chỉnh sửa nội dung bởi NATaLIa: 04-08-2007 - 00:19
