Thursday, January 26, 2012

Beauty Contest

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?

1 comment:

  1. Suppose there are total n people who have to chose number.
    I 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.

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