Answers.Body: <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>
  
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Answers.UserDisplayName: Jim Ratliff
Answers.Body: <p>Ok actually reading about the <a href="https://chess.stackexchange.com/questions/41579/is-armageddon-more-fair-in-vickrey-auction-eg-magnus-hikaru-bid-858-vs-859">Vickrey auction</a> made me think of the Jim Ratliff's answer made me think it's LESS fair:</p>
  <p>If Hikaru wants to go for as low as 9 minutes, but Magnus wants to go for as low as 6 minutes, then maybe we'd just end up with that the final bid is - let's say there's a minimum of a 10 second difference between bids - Magnus with 8:50. Hikaru won't go lower, and then Magnus has a 3 minute advantage.</p>
  
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Body: <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>
  
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Comments.Text: What is your mathematical definition of "_fair_"?
Comments.UserDisplayName: SecretAgentMan
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Comments.Text: @SecretAgentMan same as GeneM...?
Comments.UserDisplayName: BCLC
Tags: <statistics><time-control><mathematics><armageddon>
Title: Is armageddon more fair if bids aren't 1-time only?
ThreadText: # Is armageddon more fair if bids aren't 1-time only?
  
  (Asked by: username_0 on 2023-02-09)
  
  As pointed out by GeneM [here](https://chess.stackexchange.com/questions/7962/which-side-has-the-advantage-in-an-armageddon-tiebreak-game/8269#8269)
  
  > 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](https://en.wikipedia.org/wiki/English_auction) instead of [1-time only](https://en.wikipedia.org/wiki/First-price_sealed-bid_auction)?
  
  My guess is yes but they do 1-time only bids for practical reasons like with [plurality voting](https://politics.stackexchange.com/questions/69965/plurality-voting-advantages). 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](https://www.youtube.com/watch?v=gd0Ih0WdY2E), where the bids were Hikaru 8:59 and Magnus 8:58.
  
  2 ways to look at it:
  
  1. 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.
  2. 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:
  
  3. 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](https://en.wikipedia.org/wiki/Vickrey_auction) as pointed out [actually by Jim username_2 in the same](https://chess.stackexchange.com/questions/7962/which-side-has-the-advantage-in-an-armageddon-tiebreak-game/32583#32583) thread with GeneM.
  
  **Tags:** statistics, time-control, mathematics, armageddon
  
  > **Comments:**
  > **username_1**: What is your mathematical definition of "_fair_"?  
  > **username_0**: @username_1 same as GeneM...?  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2023-02-10. Score: 1
  
  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](https://www.econport.org/econport/request?page=man_auctions_revequiv), EconPort. See also [the discussion in Math Stack Exchange](https://math.stackexchange.com/questions/3987876/revenue-equivalence-in-auction-theory-how-does-an-english-auction-generate-the).)
  
  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.
  
  
  ---
  
  ### Answer by username_0 on 2023-02-09. Score: 0
  
  Ok actually reading about the [Vickrey auction](https://chess.stackexchange.com/questions/41579/is-armageddon-more-fair-in-vickrey-auction-eg-magnus-hikaru-bid-858-vs-859) made me think of the Jim username_2's answer made me think it's LESS fair:
  
  If Hikaru wants to go for as low as 9 minutes, but Magnus wants to go for as low as 6 minutes, then maybe we'd just end up with that the final bid is - let's say there's a minimum of a 10 second difference between bids - Magnus with 8:50. Hikaru won't go lower, and then Magnus has a 3 minute advantage.
  
  
  ---
  
  