DSE 2012 QUE 24

[chandramouli]

 Consider the following two-player game. The players simultaneously draw one sample each from a continuous random variable X, which follows Uniform[0,100]. After observing the value of her own sample, which is private information (that is, opponent does not observe it), players simultaneously and independently choose one of the following: SWAP, RETAIN. If both the players choose SWAP then they exchange their initially drawn numbers. Otherwise, if at least one person chooses RETAIN, both of them retain their numbers. A player earns as many Rupees as the number she is holding at the end of the game. Find the probability that the players will exchange their initially drawn numbers
(a) 1
(b) 1/2
(c) 1/3
(d) 0
Answer: (d)
PLEASE SHARE THE  SOLUTION . I DONT KNOW WHY IT IS ZERO.

[dhruv]

Solve it using game theory. Consider two persons A and B. There are three possibilities either both get same number, or A get greater number than B or B get greater number than A. In case 1, they will have same payoffs if they swap or retain  but in other cases after swapping one person will be worse off and other would be better off. So, retain becomes the dominant strategy and hence there is ) probability that they will swap.