user4399: As pointed out by GeneM here

Armageddon Chess is a fair tie-break system only if the two players bid for how much time Black should have.

Question: But is it actually more fair if the bids are the usual English auction instead of 1-time only?
My guess is yes but they do 1-time only bids for practical reasons like with plurality voting. Of course it could be that either 1-time only is actually more fair than bid or somehow, the results will end up the same regardless of the kind of auction.
Consider recently in 2023 champions chess tour Airthings Masters magnus vs hikaru, where the bids were Hikaru 8:59 and Magnus 8:58.
2 ways to look at it:

I think with 1-time only, they're bidding far lower than what they normally would bid in an English auction - something like they're bidding not how much they want black (or white, if you can choose colour) but how much they don't want their opponent to get black. I think if they did an English auction, then black would end up with maybe 10-12 minutes.

But here, there's only a 1 second difference. Maybe they'd bid even lower. If the bids would continue - let's say the next bid must be at least 10 seconds lower than your opponent's bid - then the might go as low as 6 minutes.


Consider also:

If I were to bid exactly 15 minutes because my opponent thinks I'd go as low as 9 minutes. Then I'd trick my opponent to do like 8:30 whereas my opponent wouldn't even have gone lower than 10 minutes otherwise. I think this can be fixed with Vickrey auction as pointed out actually by Jim Ratliff in the same thread with GeneM.


user17203: Auction theory says that, under pretty general conditions:

[A]ll four of the standard single unit auctions have the same expected
sales price (or seller's revenue).The four standard single unit
auctions are the English auction, the Dutch auction, first-price
sealed-bid auction, and the second-price sealed-bid auction.

(See Revenue Equivalence for One-sided Markets, EconPort. See also the discussion in Math Stack Exchange.)
Here, the “sales price” corresponds to the amount of time on the clock a player is willing to sacrifice to obtain draw odds with the Black pieces rather than full time with the White pieces.
The reason this is achievable in a single round of sealed bids (as is the typical mechanism in Armageddon bidding) is that “truthful revelation” is the equilibrium, and the winner gets the loser’s bid.

4399: <p>As pointed out by GeneM <a href="https://chess.stackexchange.com/questions/7962/which-side-has-the-advantage-in-an-armageddon-tiebreak-game/8269#8269">here</a></p>
<blockquote>
<p>Armageddon Chess is a <em>fair</em> tie-break system only if the two players <em>bid</em> for how much time Black should have.</p>
</blockquote>
<p><strong>Question</strong>: But is it actually more fair if the bids are the usual <a href="https://en.wikipedia.org/wiki/English_auction" rel="nofollow noreferrer">English auction</a> instead of <a href="https://en.wikipedia.org/wiki/First-price_sealed-bid_auction" rel="nofollow noreferrer">1-time only</a>?</p>
<p>My guess is yes but they do 1-time only bids for practical reasons like with <a href="https://politics.stackexchange.com/questions/69965/plurality-voting-advantages">plurality voting</a>. Of course it could be that either 1-time only is actually more fair than bid or somehow, the results will end up the same regardless of the kind of auction.</p>
<p>Consider recently in <a href="https://www.youtube.com/watch?v=gd0Ih0WdY2E" rel="nofollow noreferrer">2023 champions chess tour Airthings Masters magnus vs hikaru</a>, where the bids were Hikaru 8:59 and Magnus 8:58.</p>
<p>2 ways to look at it:</p>
<ol>
<li><p>I think with 1-time only, they're bidding far lower than what they normally would bid in an English auction - something like they're bidding not <em>how much they want black</em> (or white, if you can choose colour) but <em>how much they don't want their opponent to get black</em>. I think if they did an English auction, then black would end up with maybe 10-12 minutes.</p>
</li>
<li><p>But here, there's only a 1 second difference. Maybe they'd bid even lower. If the bids would continue - let's say the next bid must be at least 10 seconds lower than your opponent's bid - then the might go as low as 6 minutes.</p>
</li>
</ol>
<p>Consider also:</p>
<ol start="3">
<li>If I were to bid exactly 15 minutes because my opponent thinks I'd go as low as 9 minutes. Then I'd trick my opponent to do like 8:30 whereas my opponent wouldn't even have gone lower than 10 minutes otherwise. I think this can be fixed with <a href="https://en.wikipedia.org/wiki/Vickrey_auction" rel="nofollow noreferrer">Vickrey auction</a> as pointed out <a href="https://chess.stackexchange.com/questions/7962/which-side-has-the-advantage-in-an-armageddon-tiebreak-game/32583#32583">actually by Jim Ratliff in the same</a> thread with GeneM.</li>
</ol>
 17203: <p>Auction theory says that, under pretty general conditions:</p>
<blockquote>
<p>[A]ll four of the standard single unit auctions have the same expected
sales price (or seller's revenue).The four standard single unit
auctions are the English auction, the Dutch auction, first-price
sealed-bid auction, and the second-price sealed-bid auction.</p>
</blockquote>
<p>(See <a href="https://www.econport.org/econport/request?page=man_auctions_revequiv" rel="nofollow noreferrer">Revenue Equivalence for One-sided Markets</a>, EconPort. See also <a href="https://math.stackexchange.com/questions/3987876/revenue-equivalence-in-auction-theory-how-does-an-english-auction-generate-the">the discussion in Math Stack Exchange</a>.)</p>
<p>Here, the “sales price” corresponds to the amount of time on the clock a player is willing to sacrifice to obtain draw odds with the Black pieces rather than full time with the White pieces.</p>
<p>The reason this is achievable in a single round of sealed bids (as is the typical mechanism in Armageddon bidding) is that “truthful revelation” is the equilibrium, and the winner gets the loser’s bid.</p>
