@tcpolymath suggested I write something up about bidbots and how the current auction method they use sucks for everybody involved.

## Bidbots

The majority of active bidbots operate on a 2.4-hour or 1.2-hour cycle, collect bids during each cycle, and then apportion their upvote proportional to bid amounts.  See https://steembottracker.com/ for a bidbot dashboard.

For example, suppose a bidbot's full vote is worth 100 STEEM, and it receives bids of 2 SBD, 2 SBD, 6 SBD, 10 SBD, and 30 SBD.  Then the bidders will receive 4%, 4%, 12%, 20%, and 60% of the vote at the end of the cycle.  The high bidder has paid 30 SBD for an upvote expected to be worth 60 STEEM.  Note that every bidder receives the same return on investment.

This auction mechanism is similar to a "penny auction" in that proper bid strategy is very much dependent upon the number of participants, and upon bid timing and signalling.  While no bidder goes away empty-handed, there is both the possibility of negative return, as well as the opportunity cost of not identifying the highest-return bid.  The sources of economic inefficiency in a bidbot auction come mainly from a lack of information:

* Early bidders must predict how many subsequent bids will arrive, in order to calculate their expected return.  Or, they must capture "nearly all" of the upvote value in order to discourage later bidders, possibly lowering their own ROI.
* Bidders who wait until later in the cycle may accidentally push the bid total over the value of the upvote due to simultaneous bids.
* Every bidder receives the same ROI, even if they would be willing to accept less.
* Price discovery is indirect; bidders can look at the history but the auction provides no way to match buyers and sellers in a predictable fashion.  (It would also not be surprising to me if rates varied, unnecessarily, according to time of day.)

Bidbot votes are not 100% fungible. Even if every upvote from a particular bot is worth the same amount, a bidder cannot split their bids across two different rounds for the same bidbot, for the same post.  This means they may be less willing to reduce bid size if necessary.  Similarly, some bidders may choose to bid close to the end of the upvote window (though some bots prohibit this.)  They cannot afford to wait until the next round.  Those effects can be mitigated by having multiple discussions that are eligible for upvotes.

The inefficiencies obviously affect bidders, but they also harm sellers.  Uncertainty about returns causes bidders to be conservative rather than revealing their true price information, or to decline to bid and wait for a more favorable situation.  Uniform outcomes mean sellers can't extract the most value from bidders.  As a result, bidbots could achieve better returns by adopting a more sophisticated auction model.

## Multi-unit Auctions

There is an existing field of study on auctions and mechanism design which has already looked at similar problems.  We don't even need the full power of [Combinatorial Auctions](https://en.wikipedia.org/wiki/Combinatorial_auction) to improve efficiency, since the goods being sold are "substitutes": every fraction of the upvote is as good as any other.

One possible mechanism is a ["clearing price" auction](https://en.wikipedia.org/wiki/Multiunit_auction) in which each bidder gives a desired allocation (% of vote, or STEEM value) and the price they are willing to pay per unit.  The seller sets a price that lets them sell the entire inventory, and each bidder who exceeds that pays only the "clearing" price.

The downside of this as a bidbot auction is that the bids are currently public rather than sealed. The uniform pricing also does not give bidders an incentive to bid truthfully.  Still, this mechanism would be more economically efficient.

### Example clearing price auction vs. all-bids-accepted auction

Suppose we have eight bidders 'A' willing to pay 2 SBD for 10% upvote, a single bidder 'B" with 11 SBD for 50% upvote, and another bidder 'C" only willing to pay 9 SBD for 50% upvote.  In the current auction mechanism, the outcome is difficult to predict.

If all bids are honest, the clearing price auction results in 20 SBD for the bidbot; it accepts the 'B' bid and five 'A' bids, for a clearing price of 2BD per 10%.

The bidbot cannot guarantee it does that well in all situations with the current mechanism.  If ‘B’ bids first with 11 SBD, then enough ‘A’ bidders are willing to enter to bring the price up to 19 SBD, but only if fifth bidder is willing to split their bid can we get to 20 SBD.

If all the ‘A’ bidders are first with their 2 SBD bids, bringing the total to 16 SBD, then neither ‘B’ nor ‘C’ can achieve their desired vote share, and again achieving 20 SBD is dependent upon their willingness to make a less than full bid.  ‘C’ in particular is a difficult spot because he must bid no more than about 3.5  to meet his price goal, which assuming no further bids results in 19.5 SBD for the bidbot.  More likely ‘B’ and ‘C’ will just wait for the next round or use a different bot, resulting in 4SBD in lost opportunity.

If 'C' is the first bidder in a new round with 9 SBD, then whether the bidbot receives only 19 SBD or the full 20 SBD, ‘C’ will fail meet his target price.  ‘C’ could try bidding twice as much to achieve his desired ROI; an early bid of 17.9 might discourage all the ‘A’ bidders from risking a later bid, again leading to lost revenue for the bidbot. Even if an ‘A’ bidder does jump in, the bidbot is still 0.1 SBD short of the efficient outcome.

## Auction design to encourage truthful bidding

In a clearing price auction, a bidder who is close to the expected clearing price might be tempted to underbid a little bit; after all, if she is the cheapest of the winning bidder then her price will determine the outcome.  This is particularly a risk when the bids are publicly visible for everyone to see.

The theoretically best mechanism for extracting honest bids is the [Vickrey-Clarke-Groves auction](https://en.wikipedia.org/wiki/Vickrey%E2%80%93Clarke%E2%80%93Groves_auction), which reduces to a “second-price” auction in the case of a single item.  In a VCG auction, each bidder pays the “marginal harm” they have caused to other bidders. What this means is that for each winner W, the value of the “second-best” auction without W’s bid is calculated, minus the bids of the other winners.  The result is the price that W pays.

Unfortunately, VCG can lead to lower payouts for the seller, and that payout can be reduced further by use of psuedonymous bidding.  Fortunately, in the bidbot use case, there is only one good for sale (the vote), so some of the weirder possible outcomes are avoided.

### Example VCG auction

As before, suppose we have bids:
* A1-A8, 2 SBD for 10% upvote
* B, 11 SBD for 50% upvote
* C, 9 SBD for 50% upvote

The auctioneer calculates the maximum-value outcome, which is to accept B’s bid and C’s bid for 20 SBD total.

Without B’s bid, the second-best outcome is 19SBD (C plus A1-A5).  Thus, B should pay 19 - 9 (C’s bid) = 10 SBD.

Without C’s bid, the second-best outcome is still 19SBD (B plus A1-A4).  Thus, C should pay 19 - 10 (B’s bid) = 9 SBD.

Thus, VCG nets only 19 SBD for the bidbot.

In cases where there is no second-best bid (say only B and C bid at all), the VCG revenue would be 0 SBD, This outcome can be avoided if the auctioneer places a reserve bid on their own item. Unsealed (public) bids increase the chances that there is no second-best bid, as participants would simply decline to bid if they determined they were not going to be part of a winning set of bidders.  But, those losing bids are crucial to establishing a fair price.

## Other auction designs

There are good designs which do not require up-front revelation of prices, and instead use an iterative bidding process. Unfortunately this does not seem feasible without the use of automated bidding proxies--- far too much infrastructure.  ~~Sealed bids are also a problem for Steem bidbots, as there is no built-in public-key infrastructure by which bids may be secretly delivered.~~ (EDIT: Steem does provide encrypted memo fields, so perhaps sealed bids are not a problem after all.)

For example, in an “ascending price auction”, the seller broadcasts a price per unit (say, SBD per 1% vote) and the bidders indicate how many units they are willing to purchase at that price, which must be strictly less than their previous bid.  The auction increases the price in increments until all units can be sold.  This allows the bidders to keep their true valuations secret, yet achieves the same outcome as the clearing price auction.

This mechanism, like all auction methods, suffers if there is collusion between the bidders.  If bidders can agree ahead of time on the winning bids, they could submit low values to the bidbot and transfer the excess value to losing bidders.  For example, if a coalition of bidders determined the winning value would be 20 SBD in a fair auction, the winners of the “pre-auction” could submit bids worth 10 SBD, and distribute 5 SBD to the losing bidders if they refrained from outbidding.  Fortunately, on Steem, there is a large pool of bidders making coalition-building difficult.

## Conclusion 

There’s no simple answer that both encourages honest bidding and maximizes revenue for the seller. However, I feel confident that the current bidbot auction can be substantially improved, by asking bidders to include a target allocation along with their bid. This would allow either a straightforward “first-price” auction in which the bidbot accepts a collection of bids maximizing its revenue, or a “price-clearing” auction in which all winners receive the same price to encourage honest bidding.  Both of these options would significantly reduce the risk to bidders, which will lead to better price discovery and more consistent outcomes.

## Further Reading

My slides from a talk on Combinatorial Auctions: https://github.com/mgritter/minnebar-talks/blob/master/Minnebar%202016%20-%20Combinatorial%20Auctions.pdf

Peter Cramton, Yoav Shoham, Richard Steinberg, “Combinatorial Auctions”, MIT Press, 2006