  This paper introduces a strategy in the two envelopes problem that utilizes
the prior beliefs of two players about the amount of money that their envelopes
can contain. This strategy gives them more information about the decision of
switching they have to make when one of the envelopes is opened and the amount
it contains is revealed. The player who implements this strategy can predict
which amount is larger with a probability greater than 1/2 so that he will have
a greater expected return from the game than that of the other player who will
not use the same strategy. The symmetrical case in which both players implement
the same strategy is also analyzed.
