(1) each student submits a sealed bid
(2) they might as well include their money with the bid, because they pay their bid regardless of whether they win
(3) the student with the highest bid wins the $20 bid
(4) I repeat, everyone loses their bid, regardless of whether they win
(5) After the auction, shred the money in front of everyone
Potential Twist: Require each student to bid a minimum amount, say $1
They will enjoy this auction, and you may get bids greater than $20, depending on whether you use the twist or not. More importantly, the auction will teach them the social consequences of rent-seeking. Our government is currently doling out billions in bailout funds and stimulus packages. To obtain this "free money", one must hire lobbyists to lobby for the money, and lobbyists are not cheap.
This is how lobbying for free political money works: you hire lobbyists to fight for the money, and if you spend the most lobbying money you get the money, otherwise you do not receive the money. Either way, you still have to pay your lobbyists. So rent-seeking is just like the auction described above.
What is important to note is that it is very easy for the number of dollars seeking the free money to exceed the amount of free money, creating a loss for society. In many government programs to provide housing assistance, they do (see EconTalk.org, June 23, 2006). If I auction off twenty dollars and students in total pay $50, and if I burn the $50, society losses $30 in value. And money given to lobbyists really is like burning money for society as a whole. We take smart, valuable people who could be producing beneficial goods and services, and have them rent-seek instead.