Two envelopes, given one each to you and a friend, contain an amount of money between $5 and $160 inclusive, and one amount is twice the other amount. You look inside your envelope to see the amount you have received, but you do not disclose the amount. Your friend does the same. You see that you have received $x.
You may suggest a swap (a one-time exchange of envelopes) but you don't converse directly with your friend. Instead, a facilitator comes to each of you, in turn, and asks what you want to do. If and only if you both ask for a swap the envelopes are exchanged. You and your friend make your decisions independently and in ignorance of the decision made by the other. For what values of x will you favor swapping envelopes? Assume your friend acts reasonably and in his/her own best interest.