Source: Some Basic Game theory books
Problem:
Pick a number from 0 to 100. The winner is the person who chooses the number closest to 2/3rds of the group's average response.
What is the rational answer?
Problem:
Pick a number from 0 to 100. The winner is the person who chooses the number closest to 2/3rds of the group's average response.
What is the rational answer?
Suppose there are total n people who have to chose number.
ReplyDeleteI have divided n into sets such that n1+n2+n3+……= n
Now let’s assume avg. of set n1 is x. set n2 should chose a value y = 2/3 * x such that 0<y<x<100
Next set of people chose z=(2/3)*(avg. of n1 and n2)
Here ,we see that the avg. value keeps diminishing and approaches zero.
So, 0 is most apt choice.
This applies to every player, and so the iterated value of x keeps reducing till we reach zero, where if every other player plays zero, even I would want to play zero.
This is referred to as a Nash equilibrium in Game theory.