The Applause Auction
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As I finished a series of game theory lectures I’ve been giving to my pupils, I left them with the Applause Auction.
The basic idea is a round of applause begins, and the prize money of £20 is up for grabs for the pupil who can continuously applaud for the longest period of time and out do all other pupils.
In other words, the pupil who applauds the longest and keeps applauding when all others have stopped gets the cash.
This is an “all-pay auction” - the students are bidding in kind, via their applause, and all bidders pay their bids, win or lose.
Play it with your groups and do let me know of any interesting dynamics - our auction had lots of great game theory talking points:
- A few students left a polite 20 secs into the applause
- After about 15 minutes some of the others got bored and left
- Now there were a small enough group to start to think about collusion. A few people made first attempts (between 9 of them) at a collusive agreement, but the majority were not even willing to sit down at the table to negotiate (all the while applauding away!) - the cartel group was simply too big to come to any agreement (e.g. WTO Doha round?)
- After about 22 minutes, a few more fell away, as they got phone calls from friends etc (opportunity cost of playing the game)
- Now there were only 5. The cartel was now small enough to agree to a collusive agreement. It was fascinating seeing them come with different agreements until one was finally accepted. They agreed that they would stop on the count of 3. Alas, the count of 3 came, and 2 of the cartel stuck to their agreement, but 3 cheated and carried on clapping. A classic error on the part of those who stuck to a cartel agreement where the dominant strategy is to cheat in the Prisoners’ Dilemma.
- (The 2 who got kicked out in this manner managed to use (non-violent!) force to stop one of the remaining 3 to stop clapping) - a link to a tit-for-tat punishment strategy?
- The final 2 (now we are around 30 minutes in) tried varying degrees of interesting collusive agreements but one party would always reject the proposal - the most innovate proposal involved getting a 3rd party to take a £10 note out of one of the applauder’s wallet and put it into the other’s pocket - in this way to create a binding credible strategy to split the £20 winnings - if he let him win. But he imposed a condition - namely that if Mr. Tanweer did not pay out the £20, he would want his £10 back from the other applauder. This was rejected on the grounds that there was no upside for the applauder, since he was confident he would win. Indeed the proposer had already signalled that he was weakening, simply by proposing such an agreement.
- After 35 minutes, the idea of a war of attrition was firmly bedded down, but the idea of sunk costs and not making the decision to carry on with the applause, just because you have been applauding for 30 mins so far (tantamount to keeping a loss-making business open simply because you have incurred past losses) wasn’t quite there yet.
- Finally the agreement was reached after around 37 minutes, which was player 1 was to give player 2 two kit kats and two coke cans, in return for being allowed to win the game. He also added, “I don’t actually care if I get paid now, I just want to win”. The binding part of the agreement was that “I swear if I don’t give the food to you, you can beat me up”.
- The deal was settled and the game ended.
- Congratulations to George Salisbury... but I then reminded the two players that this was a one-shot game, and they had forgotten about the most important player in the game - namely me - my dominant strategy in this game was always to cheat and thus I promptly left the building without paying. 
And for 37 minutes I felt like a very popular lecturer
Try it out and do let me know how the dynamic works!
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