Suppose you hire a real-estate agent to sell your house. You have to leave town so you give him the authority to negotiate with buyers on your behalf. The agent is honest and hard working. He'll work as hard to get a good price for your house as if he's selling his own house. But unfortunately, he's not very good at keeping secrets. He wants to know what is the minimum amount you're willing to sell the house for so he can do the negotiations for you. But you know that if you answer him truthfully, he's liable to leak that information to buyers, giving them a bargaining advantage and driving down the expected closing price. What should you do? Presumably most of you in this situation would give the agent a figure that's higher than the actual minimum. (How much higher involves optimizing a tradeoff between the extra money you get if the house sells, versus the probability that you can't find a buyer at the higher fictional minimum.)

Now here's the kicker: that agent is actually your future self. Would you tell yourself a lie, if you could believe it (perhaps with the help of future memory modification technologies), and if you could profit from it?

Edit: Some commenters have pointed out that this change in "minimum acceptable price" may not be exactly a lie. I should have made the example a bit clearer. Let's say if you fail to sell the house by a certain date, it will be reposessed by the bank, so the minimum acceptable price is the amount left on your mortgage, since you're better off selling the house for any amount above that than not selling it. But if buyers know that, they can just offer you slightly above the minimum acceptable price. It will help you get a better bargain if you can make yourself believe that the amount left on your mortgage is higher than it really is. This should be unambigously a lie.