Dear Northwestern Economics community. I was among the first to submit my bracket and I have already chosen all 16 teams seeded #1 through #4 to be eliminated in the first round of the NCAA tournament. In case you don’t believe me:
Now that i got that out of the way, consider the following complete information strategic-form game. Someone will throw a biased coin which comes up heads with probability 5/8. Two people simultaneously make guesses. A pot of money will be divided equally among those who correctly guessed how the coin would land. (Somebody else gets the money if both guess incorrectly.)
In a symmetric equilibrium of this game the two players will randomize their guesses in such a way that each earns the same expected payoff. But now suppose that player 1 can publicly announce his guess before player 2 moves. Player 1 will choose heads and player 2’s best reply is to choose tails. By making this announcement, player 1 has increased his payoff to a 5/8 chance of winning the pot of money.
This principle applies to just about any variety of bracket-picking game, hence my announcement. In fact in the psychotic version we play in our department, the twisted-brain child of Scott Ogawa, each matchup in the bracket is worth 1000 points to be divided among all who correctly guess the winner, and the overall winner is the one with the most points. Now that all of my colleagues know that the upsets enumerated above have already been taken by me their best responses are to pick the favorites and sure they will be correct with high probability on each, but they will split the 1000 points with everyone else and I will get the full 1000 on the inevitable one or two upsets that will come from that group.
Cheap Talk 
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March 20, 2013 at 12:20 am
afinetheorem
We talked about some extensions with Scott today. One thing to note that there is it is difficult ex-ante way to know whether to take the favorite or the dog if you pick first. (Take a one game tournament, three “bidders”, with the favorite winning with p=5/8. The final bidder with pick the underdog if no one has picked it, or the favorite if only one person has. The middle bidder, knowing this, will pick whatever the first bidder doesn’t pick. Hence the first bidder takes the dog. With two “bidders”, the first bidder takes the favorite. With eight bidders, it doesn’t matter as we all get the same payout in equilibrium.)
The above shows the worry with your strategy here. Imagine we are in the one-game, three-bidder, p=5/8 case. In simultaneous bidding, you (using the appropriate mixed strategy) can guarantee 1/3 of the payout in expectation. If you move first and choose the favorite, then if 2 and 3 bid sequentially, you will get 5/16<1/3 of the payoff. If, alternatively, 2 and 3 move simultaneously after your announcement, they will mix symmetrically such that the payoff from taking the underdog and the favorite are identical; therefore if there is any mixing, the payoff from taking the favorite and the dog are equal, and since it is easy to show that mixing is optimal, all players earn payoff 1/3, giving no advantage to moving first.
March 20, 2013 at 11:01 am
Scott
Suppose player 1 does not PUBLICLY declare his picks, but instead privately shows them to the other two players — AND is able to hide the fact that he has done so. I think this is how a single player can really increase the chances of winning.
Pulling off such information manipulation may be difficult. However, player 1 could also show ONLY player 2 his picks, and not tell player 3 about any of this. I think this too would help player 1.
So Jeff, who is the sucker now?
March 20, 2013 at 1:20 pm
Enrique
Great post, but I have a question: if Jeff’s department’s tournament were not a play-money one but a real-money competition (pennies instead of points, or better yet, dollars instead of pennies), that is, if one could stand to gain up to $1000 USD, would this change Jeff’s strategy of play? (I am not asking Jeff himself, since he will say “no” — I am asking everyone else.) As I see it, Jeff has chosen this unorthodox strategy not because he really wants to win his dept’s tournament, but because he wants to signal his problem-solving skills of his level of cleverness, which is fine, and since real money is not on the line, his strategy is certainly worth a try.
March 22, 2013 at 8:43 pm
Noto
I don’t think Jeff would do something elaborate just to signal his cleverness 🙂
March 22, 2013 at 11:42 am
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March 22, 2013 at 8:48 pm
Noto
Are you winning right now? LaSalle, Harvard, Ole Miss, and FGCU must have all given you a lot of points. Okla, AZ, and Memphis all look like they have decent chance at Elite Eight, which would give you even more points. And then at that point I assume you’re rooting for a #1 seed to win it all.
March 22, 2013 at 11:18 pm
jeff
I believe I am far ahead of the field, there should be an update tonight when this round is over. I was the only one to pick LaSalle, Harvard and FGCU.
March 22, 2013 at 11:51 pm
Scott
This pains me: https://docs.google.com/spreadsheet/ccc?key=0AhCDXfeTJUvWdFFNa3FMNlh0LTIyUnBicmItWjJQSEE#gid=6
Should have had a friend enter a shill bracket.