Auctions, Bidding Syndicates, and Bidding Strategies

Hi Everyone,

This past week opened at $600/BTC before jumping to $640/BTC-$660/BTC before ending at $634/BTC.  Much of the early action from $600/BTC to $640/BTC was likely due to US Marshal auction insiders buying up to at least their bid, possibly a little more based on their expectation of the winning bidder's bid conditional on their own information set (their bid price and the fact that they didn't win).  The market seems to agree that the winning bid is somewhere between $640/BTC and $660/BTC.  On a side note, it's interesting that the US Marshal sent the 30k BTC to the winner (Tim Draper) with no network fee (coin age likely helped speed up the inclusion of this transaction into a block).

Had an interesting thought the other day on why syndicates (e.g. SecondMarket's syndicate) don't win auctions like the US Marshal bitcoin auction.  One common reason a person might join a syndicate instead of become a bidder himself (herself) is that he might not have the capital or desire to buy a full 3k BTC block.  In either case, his slippage from buying through the market would be significantly smaller than slippage incurred by someone buying a full 3k BTC through the market.  Therefore, his "soft" upper bound on what he is willing to bid is much lower than a full-block bidder's upper bound.  So long as there are enough real bidders (and assuming some bell-esque distribution of willingnesses to pay), there will likely be at least one bidder who is willing to bid above the syndicate's highest bidder's upper bound (as proxied by slippage) which means the syndicate will not win.  By the same reasoning, it makes sense that one bidder swept all the blocks since, if his intention was to buy 30k BTC, his market slippage would have been the greatest compared to bidders who wanted fewer than 30k BTC and thus his upper bound on willingness to pay would be the greatest.  Conditional on a person being the highest bidder of this group (those who want all $30k BTC) he is very likely to be the highest bidder overall as well (once again assuming some bell-shaped distribution of willingnesses to pay).

Another interesting thing to consider is the bidding strategy for the syndicate.  At the lower limit, the syndicate will take the top bids which total a quantity of 30k BTC and do a weighted-average to get the syndicate's bid price and then bid on all blocks at that price (assuming the syndicate does not purposely bid below this to net itself some profits on a win).  If the syndicate wins, almost everyone (besides the bottom bidders) gets what they bid for and everyone is happy.  At the upper limit, the syndicate will take the top bids which total a quantity of 3k BTC and do a weighted-average to get the syndicate's bid price and then bid on one block at that price.  If the syndicate wins, only the top bidders get what they bid for and everyone else gets cash returned.  There are also intermediate strategies involving bidding on 2-9 blocks but considering the edge cases reveal the some insight.  In the first case of taking the grand average of all bids summing up to a quantity of 30k BTC, there are reflexive effects.  Those syndicate members who bid less also pay less and thus free-ride on the higher bidders' willingnesses to pay.  So optimum bidding strategy for syndicate members involves shading bids down because the marginal effect of an individual's lower bid on his own profits is positive and stronger than the marginal effect his lower bid has on reducing the average syndicate bid and subsequently the probability the syndicate actually wins.  In other words, if you are a syndicate member, your maximum payoff is achieved when you bid the lowest possible bid that still puts you in the the top 30k BTC bidded for (so you still qualify).  This essentially turns into a multi-player Prisoner Dilemma situation, the end result being an aggregate syndicate bid which is much too low to have a reasonable chance to win the auction.  Strategy effectiveness increases monotonically as the syndicate's bidding strategy moves toward securing fewer and fewer blocks.  In the limit case of the syndicate bidding on one block, their chance of success is highest as both the average price bidded by qualified members is naturally higher and due to less moral hazard of qualified members shading down their bids (though there is still some of this so long as it takes more than one syndicate member to clear one 3k BTC block).  Also it's worth noting that higher homogeneity in syndicate members' willingnesses to pay implies lower moral hazard since the low-bidding free-riders extract less value from the high-bidding members.

Finally, it's worth noting that a syndicate benefits directly from the flow information it receives from its bidders.  First, if we ignore all bids under market value (there's some ambiguity here on what market value means e.g. market value before the start of the auction or market value right before the end of the auction or somewhere in between), the syndicate gains information on how many coins are demanded above market price and at which specific prices.  Going further, the syndicate also knows at what times it's members bidded what price and how that compared to market price at that exact time.  In the event of losing the auction, the syndicate can estimate how much unsatisfied demand exists in the market from its own members which gives a lower bound on unsatisfied demand in the entire market.  Second, the syndicate can buy on the market up to it's own final aggregate bid and gain positive expected value.  If they win, they get coins at cheaper than their bid.  If they lose, they get coins at cheaper than the winner.

To conclude, bidding syndicates make the most sense where the average price of the auctioned asset on the market decreases with respect to quantity bidded for (similar to many commodities e.g. a 100 kilos of wheat will be cheaper per kilo than 10 kilos of wheat).  This is true for angel syndicates as well where it is less hassle for a startup to deal with a syndicate than its individual members so it can offer a better deal to the syndicate.  There and in normal commodity markets there are direct synergies and efficiency gains of a syndicate banding together to get a cheaper price.  In the case of the US Marshal bitcoin auction, the opposite is true where the average price of the auctioned asset on the market increases with respect to quantity bidded for due to the way slippage works (e.g. 100 bitcoins will be more expensive per bitcoin than 10 bitcoins).  This combined with inherent moral hazard between low-bidding members and high-bidding members makes it very unlikely for a syndicate to win this type of auction.

Other news this week:
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