DSE 2012 Game theory question

[MohitG]

QUESTION 24. 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

[Aranya]

It is d)0. As both the players know that the other player will choose "SWAP" it he gets sufficiently small amount both will not choose "SWAP" as it will give him a low amount always.

[MohitG]

Hey thanks a ton Aranya

[Aranya]