SOLUTION: Three players A, B, C play the following game. First, A picks a real number between 0 and 1 (both inclusive), then B picks a number in the same range (different from A’s choice) an

Algebra ->  Probability-and-statistics -> SOLUTION: Three players A, B, C play the following game. First, A picks a real number between 0 and 1 (both inclusive), then B picks a number in the same range (different from A’s choice) an      Log On


   

Question 1118562: Three players A, B, C play the following game. First, A picks a real number between 0 and 1 (both inclusive), then B picks a number in the same range (different from A’s choice) and finally C picks a number, also in the same range, (different from the two chosen numbers). We then pick a number in the range uniformly randomly. Whoever’s number is closest to this random number wins the game. Assume that A, B and C all play optimally and their sole goal is to maximise their chances of winning. Also assume that if one of them has several optimal choices, then that player will randomly pick one of the optimal choices.
Questions:
a) If A chooses 0, then what is the best choice for B?
b) What is the best choice for A?
c) What is the best choice for the first player when the game is played among four players?
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.

Notice that the mathematical expectation for the random variable that  "we then pick"  is   1%2F2 = 0.5. 

    It does not require special explanations, since it is OBVIOUS.


Therefore, 

(a)  If A chooses 0, then the best choice for B is to choose  1%2F2 = 0.5.


(b)  The best choice for A (who starts each tour) is to choose  1%2F2 = 0.5.


(c)  What is the best choice for the first player when the game is played among four players ?


     - Same as in n (b):  to choose 1%2F2 = 0.5.