DSE 2012 Question 24: Game theory and strategic behaviour

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.