Wikipedia:Reference desk/Archives/Mathematics/2017 March 2

= March 2 =

March Madness Auction
I've been invited to participate in an upcoming auction for the NCAA basketball tournament, in lieu of the typical fill-out-a-bracket, with rules roughly as follows:


 * Each team (final 64 only; play-in games are ignored) goes up for auction in a random order
 * Depending on the seed of the team, there's a minimum bid price (ranging from $1 to $20, but I don't know the specific distribution)
 * Each team must be sold
 * Payouts are based on the games that each team you own wins, as a percentage of the total pool of money spend buying teams, as follows: 1% for 1st round win; 1.5% for second; 2% for 3rd, 3% for 4th, 4% for 5th and 8% for winning the championship.
 * The total amount of the pool (and the number of players, though I think that's irrelevant) is, of course, unknown in advance.

With data for the likelihood that each team will reach each round in the tournament (which I can get from 538 or the like), I can calculate the expected percentage of the total pool that each team will win. What I don't know how to do is translate that info into an appropriate bid amount, since I won't know until the end what the total pool is.

To finally get to asking a question, any idea how I can get a plausible estimate for the "correct" amount to bid on each team? I could always just decide in advance what I think the total pool amount will be, but that's unlikely to be inaccurate and would lead to systematic over or under bidding, so I think I need some process (hopefully quick, since this'll be happening live) that could quickly update my total pool estimate (and thus my break even bid amount for each team) as each team is purchased. --Strohbot (talk) 23:03, 2 March 2017 (UTC)

EDIT: Should have googled first, but it turns out this is a thing with a name: Calcutta auction. So I guess my real question is, any information available for a bidding strategy for a Calcutta auction? --Strohbot (talk) 23:12, 2 March 2017 (UTC)


 * You should be able to estimate the number of total bidders there will be by the number who bid on earlier auctions. However, we get into game theory here, in that others may also take a wait-and-see approach to gauge the amount of bidders, too.  So, it could end up like an Ebay auction, where it's pointless to bid until the last few seconds, as doing so gives away too much info. StuRat (talk) 04:00, 3 March 2017 (UTC)


 * Then there's historical data. That is, how many bidders were there last year, and what was the total payout ?  Combining these two techniques, you could use the relative number of bids in last year's early auctions versus this year's.  The random nature of the auction order does throw a bit of a monkey wrench into the works, but if the first half of the auctions have 10 times as many bidders as last year, you could reasonably assume the total payout will be around 10X last year's. StuRat (talk) 19:37, 3 March 2017 (UTC)