Question

Consider the following version of the p-beauty contest. There are n players, each player can choose a number from {0,1,2}. Players whose choice is closest to 3/4 of the average split $1 between themselves.

(a) Let n = 2. Which of the players' strategies are rationalizable?

(b) Let n = 3. Which of the players' strategies are rationalizable?

Answer 1

A.In p-beauty contest game ( where p differs from 1 players exhibit distinct.

Here we assume the level of players to easily find out its solution...so firstly we start from the lowest i.e.

''Level 0''players, choose numbers randomly from the interval (0,100) .

the next higher level i.e. ''Level 1'' players believe that all other players are Level 0. These Level 1 players therefore reason that the average of all numbers submitted should be around 50.For example if p= 2/3 then these level 1 players choose as their number ,2/3 of 50 i.e. 33 like as in question;-

a)when n=2 and p=2/4 then these Level 2 players choose as their number 2/4 of 33 i.e. 16.5 As the n increases the players strategies level decreases... as compared to Level 1 ...level 1 strategies are rationalizable.

b) when n=3 and p=3/4 then these Level 3 players choose as their number 3/4 of 16.5 i.e. 12.375 and similarly in this Level 2 strategies are rationalizable.