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.
a computer capable of flawless logical play facing a second flawless computer will result in equilibrium.
ReplyDeleteIntroduction of imperfection will lead to its disruption either through loss to the player who makes the mistake, or through negation of the common knowledge criterion leading to possible victory for the player.