You may have seen in the news that Ashton Kutcher was trying to sign up 1,000,000 Twitter followers and in order to make that goal he offered the 1,000,000th follower a copy of the game Guitar Hero. This is not a very good mechanism because the optimal strategy it induces is not to sign up (until 999,999 others do, which will not happen because they are also waiting.) Here is a story about the Kutcher mechanism. (thanks to Joe Spanier and Toomas Hinnosaar for the pointer.)
A better mechanism is the following. Set a deadline, say midnight. If at midnight there are fewer than 1,000,000 followers then each of the existing followers wins a prize and the prize that the nth follower wins is decreasing in n. Thus, the 1st follower gets a larger prize than the 2nd which is larger than the 3rd, etc. On the other hand, if before midnight the number of followers reaches 1,000,000, then give only the 1,000,000th follower a prize. And it can be a very small prize.
In this mechanism, there is no incentive to wait to sign up and as a result the goal is guaranteed to be reached and the beautiful twist is that the only prize given out is the small prize to the 1,000,00th.
Coincidentally, just last week (before the Kutcher thing) I played this game with my intermediate microeconomics students where my goal was to sign up 150 followers in 2 days. I offered prizes ranging from $40 for the first follower down to $10 for the 149th follower and $1 to the 150th follower if I made my goal. If you look at the sidebar to this blog (scroll down on the left) and click through to my twitter page, you can see how I did.
Cheap Talk 
12 comments
Comments feed for this article
April 17, 2009 at 3:39 pm
tom s.
Nice, but I don’t think your approach scales to 1 million. That’s a lot of envelopes to lick, and the first signer-up will get a mighty big prize if the size of prize is to decrease all the way to a million.
April 18, 2009 at 6:59 am
Anonymous
Kutcher won the bid! So, how do you explain that? Unobserved factors?
April 19, 2009 at 10:46 pm
jeff
Getting to 1,000,000 is easy for Ashton Kutcher. I signed up 150 out of 250 students in my class. I am sure that many more than 5,000,000/3 people knew about the Kutcher contest.
April 19, 2009 at 1:31 pm
Anush
What about ‘externalities’? If you run a competition your way, it’s a better mechanism, but everyone who was supposed to get a prize and then doesn’t because of the 1,000,000th follower feels cheated. Besides, Kutcher doesn’t just want people to sign up. He wants them to keep consuming his internet thoughts. So he needs to come up with a system that gives consistent rewards that don’t cause resentment.
I think the actual Kutcher mechanism — donating to charity if a reward is reached — is the best incentive. Every follower gets something (warm fuzzies) that does not diminish when shared.
April 19, 2009 at 10:06 pm
Ana Andjelic
hey, your model may be slightly better, but doesn’t the incentive also diminishes here as time approaches midnight and the number approaches the limit? if it’s 11:50 and there are 999,998 people signed up, i would not have the incentive to sign up for a prize because i would know that the chances are great that someone will show up and sweep the prize. your model works until the very end, and then it doesn’t, it seems.
isn’t the better solution to say ‘there are going to be 2o prizes, raffle style, IF and ONLY IF there is a million people who play’. in this way, people collaborate to reach the goal because they hope they will get the prize afterwards.
April 19, 2009 at 10:48 pm
jeff
the problem with that mechanism is that there is an equilibrium in which nobody believes that 1,000,000 will sign up and then nobody has an incentive to sign up.
April 20, 2009 at 7:16 am
Ana Andjelic
Hm, perhaps. But — isn’t a common goal an incentive?
Also: do you think, and/or have you noticed that the incentive in your model reaches plateau as the time goes on & the number of people reaches the set limit? I may be wrong, but it seems to me that the activity grows exponentially and then stalls.
April 20, 2009 at 11:36 am
jeff
you are probably right that even if i think that the goal will not be met i have an incentive to contribute just to feel good that i tried to help.
from that kind of marketing perspective i would guess that my mechanism on a larger scale would also have some extra-monetary incentives. because the scheme is so crazy, it would take on a viral aspect which would attract attention.
in answer to your second question, yes. if you look at the timing of signups, there was a big burst at the beginning followed by a slow but steady increase and then a huge flurry at the end.
April 21, 2009 at 7:33 am
Ana Andjelic
Right.
What I still fail to understand is a huge flurry at the end. What kind of rational incentive the participant have as the time nears midnight and the number reaches the limit? In terms of probability, the chances that none of them (except the last one) is going to get the prize increase – and they are aware of that. Simply put, it seems like they are digging their own grave, and rushing to do so.
April 21, 2009 at 9:03 am
jeff
The logic is surprisingly simple. If you think the threshold will not be met then you should sign up. Thus, the threshold will be met.
Toward the end the choice turns into one of whether to sign up now in hopes that the threshold won’t be met or wait and be the last to sign up and get the prize. The flurry comes from the fact that many are waiting and watching and once a few signups occur in rapid succession, everyone concludes that the threshold is just about to be met and they signup immediately to try and be the 150th.
I know what you are thinking now. Why such motivation over $1? I can think of two reasons. First, its just fun to play. Second, you would be surprised how much people are motivated by even small amounts of money.
Case in point: Ana you have yet to sign up to follow me on Twitter. I can only conclude that you are waiting for me to take my Twitter mechanism to a larger scale at which point you will sign up. 🙂
April 21, 2009 at 3:30 pm
Ana Andjelic
Hm. I understand. Still, I don’t think that I would choose to sign up if there are already 999,998 people. I think being 999,999 would make me a dumbest person in the world. But, then again – I do not know this number and hence I will sign up. Makes total sense, finally.
And ha – yes, waiting for scale. Makes no sense to rush now. 🙂
June 17, 2009 at 9:13 pm
My Intermediate Micro Course: Incentives and Game Theory « Cheap Talk
[…] This year I had just started using Twitter and I came up with a fun game to play on Twitter. I blogged about this game […]