GAME 5 All-Pay Acution of $10
Everyone plays. Show the students a $10 bill, and announce that it is the prize; the known value of the prize guarantees that there is no winer’s curse. Hand out cards. Ask each student to write his name and a bid (in whole quarters). Collect the cards. The highest positive bid wins $10; if two or more tie with the highest positive bids, they share the $10 equally.
All players pay the instructor what they bid, win or lose. Be sure to emphasize before bids are submitted that “This is for real money; you must pay your bid in cash on the spot. You can make sure of not losing money by writing $0.00. But of course if almost everyone does that, then someone can win with $0.25 and walk away with a tidy profit of $9.75.”
Once you have collected the cards, write the distributionof bids on the board. Hold a brief discussion about the distribution and the value of the optimal bid. This game usually leads to gross overbidding; a profit of $50 in a class or section of 20 is not uncommon. If that happens, you will have to find ways of returning the profit to the class; we have done this by having a party if the sum is large enough or by bringing cookies to the next meeting if the sum is small. Of course, do not announce this plan in advance.. If you play the game on the first day, you can lead up to at least some of the points made there, even though the analysis at this early stage cannot go anywhere close to that level. If you prefer to follow this game with a more in-depth discussion and, perhaps, the derivation of the formula for the optimal bid.