In this question on math the situation was given
A Tv Shows organize a lottery with two cars as prizes. Any watcher may send an SMS for participating independently of other watchers. If there are only one or two participants then they get a car. Otherwise, no one wins.
If you assume that all the other viewers will behave as you do, what should you do to maximize your expected winnings?
Added: Douglas Hofstadter had a piece "Dilemmas for Superrational Thinkers, Leading Up to a Luring Lottery" in the June 1983 Metamagical Themas (free download) like this with just one prize, which was a million dollars divided by the number of entries. It is an interesting essay.