Talk:Dollar auction

The article is completely wrong since its missing Formal Precommitment Mechanism
According to Dr. Martin Shubik the formal precommitment mechanism in 1971, needed to know that there was atleast 2 or more precommitted bidders in the auction event before the decision to initiate the bidding phase was made.

In 2012, the formal precommitment mechanism was converted into a computer algorithm, also known as the prefunding algorithm.

Dr. Martin Shubik has formally admitted that prefunding algorithm can be considered as the original way of doing business in 1971.

It was considered commonsense knowledge in 1971 that auction needed to have atleast 2 or more precommitted bidders before the decision to initiate an auction was made.

Bids were sold under "use them or lose them" contract.

A dollar auction does not induce rational players to overpay for the dollar. It is trivially easy to understand this. All players have the option to earn $0 by never bidding. Thus, each player's expected payoff must be at least 0. Further, the game has a clean solution found here: http://www.math.toronto.edu/mpugh/Teaching/Sci199_03/dollar_auction_2.pdf

The article needs to be rewritten and framed using the above article. As is, the article is wrong. — Preceding unsigned comment added by 75.84.163.162 (talk) 02:40, 24 December 2014 (UTC)


 * I would add that the original paper (by Shubik) in *no* way claims that the series of choices that lead to the loss are 'rational'. Shubik agrees that there are rational game theoretic solutions that don't lead to losses. Rather, his explicit point is that the game theoretic (rational) solution isn't a good model for actual human behavior. In Shubik's words: "the game theory model alone does not appear to be adequate." The idea that the actions that lead to losses are 'rational,' or even consistent with some traditional economic model of rationality is totally unsubstantiated by, and somewhat inconsistent with, the sources cited. Shubik's paper *is* a critique of rational choice theory to an extent - in that he holds this game up as an example of a case where human behavior is irrational. But it is totally untrue that this game shows rational choices leading to an ultimately irrational decision.98.245.84.83 (talk) 02:56, 30 December 2014 (UTC)


 * I don't quite agree with the claim that this example show that human behaviour is irrational. The very fact that at some point when the bid is x > 1 the players will definitely stop playing the game, knowing that it is better to accept the loss x than to continue since the other player might push the bid to more than x+1 and then stop, resulting in the loss being more than x. This shows clearly that the players who start playing are not irrational but merely foolish or rash, and that players who realize their foolishness but continue playing are merely suppressing their better judgement in the hope that the other players will stop soon enough. In the latter case, they are consciously suppressing their own knowledge that continuing can lead to greater loss, though if they even stopped one moment to think about it, they would realize that the only way they can reduce their loss is if other players are not like them. So while one can argue that the observed behaviour during the game is irrational, the underlying reason for the behaviour is not due to irrationality but rashness and perhaps some ego (preventing backing out of the challenge). In other words, it is not like the players sincerely believed that their strategy is correct after playing the game, which shows that they would consider playing to be an error! — Preceding unsigned comment added by 137.132.219.48 (talk) 07:06, 18 July 2016 (UTC)


 * The game is rational to the auction keeper and to the players, since amongs the players the winner will receive the best deal and gets to maintain his reputation and the other participants (losers) pays for the winners prize. all-pay_auction

There is a "2 or more precommitted bidders" auction initiation criteria that has been ignored for quite some time. — Preceding unsigned comment added by MikoFilppula (talk • contribs) 12:06, 30 October 2016 (UTC)


 * It says in O'Neill, International escalation and the dollar auction, p35 "Assume that by some arbitrary mechanism one of the players acquires the ability to make the first bid." Do the players know something about this mechanism, e.g. whether it is random or constant? Polskiblues (talk) 13:02, 9 April 2019 (UTC)

Adding material and possible error in formulation
I've expanded the Setup section, as without my additions, the description was insufficiently detailed and it did not explain clearly enough what happens to anyone unfamiliar with the topic. I used my own lecture notes which were based on the Colman reference as a guide, and added a reference to that book in an appropriate place later on. I hope that doesn't upset anyone here. DDStretch   (talk)  12:44, 27 July 2007 (UTC)

I am a professional mathematician but I do not understand this article at all...Why would the initial 1 cent bidder lose his 1 cent?? The rules said that only the second highest bidder would pay. Now there are three bids (1, 2, and 3 cents) from three different bidders. Then the first guy should not be obliged to pay?????


 * The original paper, and many other sources primarily discuss the two-player version of the game. As it is, the article is clearly assuming the two player version without stating that explicitly. That should probably be fixed. 98.245.84.83 (talk) 15:43, 30 December 2014 (UTC)

Winning strategy
Isn’t it a winning strategy not to play? Roman V. Odaisky 20:40, 28 July 2007 (UTC)


 * In addition it would seem that if the first bidder bids 99 cent noone has a motive to bid higher, so that the best one can do, would be to gain 1 cent 87.66.222.129 18:24, 3 October 2007 (UTC)


 * I agree. putting in one cent is provably irrational if one looks ahead. A 99 cent bid would be optimal if no one in the room is a jerk; otherwise no bid is the best choice. Cute paradox, probably worthy of an article, but a low-tier one IMO. --Headcase (talk) 23:21, 27 May 2009 (UTC)

moved from article
"Additionally, this game is not an auction, per say, but gambling. As gambling, the choice to enter into it with more money than one is willing to lose is an irrational decision. The claim is perfect information, but calling gambling an auction confuses people and distorts one's perception of how to calculate returns, resulting in actions consistent with auctions prior to the $1.00 bid, and actions consistent with gambling after that point." contributed by 70.152.255.102. Pete.Hurd 15:25, 24 September 2007 (UTC)

If this was "re"moved, why, or if it was simply moved, where can I find it? --the person who added this notation. —Preceding unsigned comment added by 132.170.49.6 (talk) 19:07, 11 October 2007 (UTC)


 * It was moved from article to here, because
 * it's wrong: the dollar auction is most certainly an auction.
 * any claim otherwise ought to be supported by verfiable reliable sources, per WP:V and WP:RS, otherwise the claim amounts to original research.
 * the writing was poor, in an inappropriate tone among other things, which confused the points. What is "The claim is perfect information, but calling gambling an auction confuses people and distorts one's perception of how to calculate returns, ..." supposed to mean?  How does perfect information (which is the case in this game) play into the point you are trying to make about gambling?
 * Pete.Hurd 19:24, 11 October 2007 (UTC)

All auctions, on some level, relate to gambling: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=905606 This auction is more closely related to gambling because of the additional requirement that the losing bidder must also pay: http://en.wikipedia.org/wiki/Betting_(poker) VS http://en.wikipedia.org/wiki/Auction It could be considered a type of "all-pay" auction, which is generally used in charity cases, where all bidders are not in it so much for the prize as much as wanting to help the charity. So yes, it is an auction, but not one in the traditional sense. Tone: If your claim is that my writing had a tone (which was certainly not my intent) then how can you argue that using a certain 'tone' of words in describing the game would not change anything? Perfect Information and Gambling? http://links.jstor.org/sici?sici=0363-7425(198604)11%3A2%3C311%3AECTACO%3E2.0.CO%3B2-U Escalation of Commitment is extremely rare in cases of Perfect Information. The most obvious case where it does occur, is gambling. That was what I was trying to explain.20:09, 19 November 2007 (UTC)

Why is there a picture of a dollar here?
Just out of curiosity, why is there a picture of a dollar in here?

The dollar's not in the act of being auctioned, most people who read this article are going to know what a dollar looks like, and in any case, dollar auctions (or, I suppose, currency auctions) can just as easily use any currency.

Anybody care to defend the image? superlusertc 2007 December 23, 15:30 (UTC)

Hello,

Though personally I don't really care that much and the pictureless article is fine to me, but I must note that I'm a visual thinker and an illustrative addition does help me in my mental processes. I just came here from an article about this sunject in another language where a dollar picture was present, and I've found myself to focus on the image while organizing and musing about the procedures in my head, so it basically served as an external anchor. Since it is a very simple subject I didn't really need this anchor, all the visualising is done is my head, but in more complex articles- pictures are a must. Shame that the wiki format can't contain videos, since the easiest way to learn for me are those videos you see on History/Discovery channel...

Refutations
The first paragraph of the "Refutations" section should be removed. The sort of collaborations it describes violate the premise of a game in game theory. —Preceding unsigned comment added by Emperor Will (talk • contribs) 21:09, 26 August 2008 (UTC)

Equilibrium
I think the equilibrium reversions are kinda missing the point. First, to the editor who's saying there is a unique equilibrium--unfortunately, offering your own proof probably isn't good enough for Wikipedia. WP:OR generally means you need to cite someone else's proof. (I personally would be interested in seeing your proof on my talk page, if you can't point toward one in the literature.) On the other hand, the "no equilibrium" bit that's there isn't cited either right now, so I don't know that we should be very enthusiastic to revert your change. I'm hoping to look this stuff up later today and see if I can flesh it out. C RETOG 8(t/c) 17:34, 10 September 2008 (UTC)
 * In retrospect, my reversion looks far more terse than I had intended. 152.2.122.191, you have my apologies.  Personally, I'd like to see a proof (even if it fails WP:OR) just because I'm interested in the topic.  Post it here on the talk page if you wish.  There's a literature out there on this topic, it was my understanding that there wasn't an analytic solution... I could be mistaken, afterall I make mistakes for a living, I'm a scientist. Cheers, Pete.Hurd (talk) 17:53, 10 September 2008 (UTC)
 * Well, Shubik points out one equilibrium, which has the first bidder bidding $1, and the second bidder staying out. But obviously that's not what he focuses on. Can this be shown to *not* be an equilibrium? Looks good to me offhand. For this game, it's also important to keep clear the difference between Nash equilibrium and dynamic solution concepts, because if the first bidder could make a credible threat, they could bid $0.01 and promise to retaliate against any response with a bid of $10 or some such. C RETOG 8(t/c) 21:22, 10 September 2008 (UTC)
 * Note to Ddstretch, I think Cretog8's point above was the the version you just reverted to is just as unsupported by any reliable source as the version you reverted away from... Given that state of affairs I'm unwilling to revert anything until someone comes up with a source. I'm not going to revert it back, but I see no reason anyone should view the current version as more likely to be true than the other. Pete.Hurd (talk) 22:04, 10 September 2008 (UTC)
 * I just pulled the section out. Given what I say above (technicality about dynamic vs. simultaneous solution concepts, plus Shubik's explained equilibrium) I think the original was wrong as well as unreferenced. Might as well try to clear it up first here. C RETOG 8(t/c) 22:09, 10 September 2008 (UTC)


 * Actually, yes, you are both right in your actions here. It is better with nothing in until and unless it can be verified. There's too much unverified stuff around as it is without fighting a pointless battle over which one of two such unverified claims should "hold sway" temporarily.  DDStretch    (talk)  22:14, 10 September 2008 (UTC)


 * I am the guy who posted the mixed strategy equilibrium claim. I would also like to apologize for rude comment insinuating that my being an economics prof gives me authority. I have never seen a published proof of the existence of the mixed strategy equilibrium, but I will sketch a simplified version of it below. Also, I want to say that this is not the unique equilibrium, of course (bid a dollar, no other bid is an alternative, as are nash equilibria that aren't subgame perfect as described above). This equilibrium is, I believe, the unique mixed strategy equilibrium, but I haven't proved uniqueness. Let the bid increment be B and the amount to be auctioned be NB, with N an integer greater than 1. Let t denote the period. Player 1 bids in odd periods and player 2 bids in even periods. For simplicity, if player 1 does not bid in period 1, player 2 receives the prize (this assumption isn't necessary, but it makes the sketch below complete). Let Vi(t) be the expected payoff to type i in period t, assuming the game has reached that point. We search for mixed strategy equilibria. This implies that the payoff from bidding and not bidding must be equal. Let the probability of a bid at time t be Pt. Let's say that t is odd and greater than 1, so that it is player 1's turn to bid and there are already bids on the table. The current bid is (t-1)*B.  Therefore, if t is odd, the payoff to player 1 not bidding is -(t-2)B (she loses her current bid). Payoff to bidding must equal that amount for her to be willing to randomize.  Therefore, for t odd, V1(t)=-(t-2)B. Now let t+1 be even. Then player 1's payoff at time t+1 depends on whether player 2 bids. Her expected payoff is the probability of no bid times her payoff net of her bid plus the probability of a bid times her continuation payoff at time t+2: V1(t+1)=(1-Pt+1)(N-t)B+(Pt+1)*V1(t+2).  Plugging in for above, we get V1(t+1)=(1-Pt+1)(N-t)B+(Pt+1)*V1(t+2)=(1-Pt+1)(N-t)B-(Pt+1)*(t+2-2)B. The payoff from continuing the game for player 1 if t is odd equals -(t-2)B whether or not she bids, so we can set V1(t+1)=-(t-2)B.  Then we get (1-Pt+1)(N-t)B-(Pt+1)*(t+2-2)B=-(t-2)B. Rearranging yields Pt+1=(N-2)/N for all t. This argument works for player 2 as well. The randomization probability at any time t is (N-2)/N. This argument follows for every t except t=1, since the assumption above is that by not bidding the amount (t-2)B is lost for good. In period 1 this doesn't follow, obviously. Dealing with the initial bid is a hassle I won't get into here, but I'm sure any of you could adapt this argument to period t=1.  —Preceding unsigned comment added by 66.57.254.60 (talk) 13:52, 11 September 2008 (UTC)


 * I don't think any apology is needed, I assumed you were new or newish to editing WP, and so didn't know the details of WP:OR. Unfortunately, if your proof is novel, I don't think it's legit to use here. I'm looking forward to looking it over when I have time to concentrate (proofs always take me some time.) C RETOG 8(t/c) 17:58, 11 September 2008 (UTC)


 * Sorry it's taken so long to respond. I seem to be pretty thick-headed lately and when I can focus I need to focus on other things. Your proof leaves me uncomfortable, but that's probably just my thick-headedness. Any proof leaves me uncomfortable until I've grokked it. I haven't grokked yours, but it does look good. There's a big assumption you've built in which isn't in the standard game description though. You have all bids be strictly incremental, while Shubik's game has freer bidding. Your setup, for instance, would disallow the "bid a dollar" equilibrium. I'm not sure how important that is.


 * In any case, when I'm a little less thick-headed, I need to poke more at this article. It seems as thought the Dollar auction is more a behavioral matter than an equilibrium matter. C RETOG 8(t/c) 05:33, 18 September 2008 (UTC)


 * Actually the problem here is that the concept of equilibrium is not well defined, or perhaps more precisely there is no equilibrium (including no eq in mixed strategies) (though one could come up with a definition of equilibrium which differs from normal Nash) because the strategy space of each player is infinite (note that the editor above is artificially restricting the possible number of strategies to get his result), which violates one of Nash's assumptions. In that respect it's similar to the game of "pick an integer and write it down on a piece of paper. Whoever picks the highest wins." <- no eq. in mixed strategies either, basically for the same reason. If you want a source/proof for this assertion then I believe there is one in Kreps' "Game Theory and Economic Modelling" though last time I looked at that book was in grad school, right before I loaned it to someone and never saw it again.radek (talk) 02:38, 1 November 2008 (UTC)

The equilibrium that exists is the same as balance of power between global powers and the world order.

The ones in power will force the players to a contract, ie. Power Elites forced European leaders to form EU under contract or Europe would face another war.

The power elites would start the war unless all EU country leaders agree to contract terms unitedly.

In other words the citizens and players were forced to agree to a united contract since the "bids" were sold in advance and "bids" were sold on use them, or lose them terms. — Preceding unsigned comment added by MikoFilppula (talk • contribs) 09:36, 30 October 2016 (UTC)

Game presentation
I have two questions about the current presentation of the game in the article (and in general). First, Shubik presented the game as having a $0.05 bid increment. I would lean toward following him, but I haven't read the other sources yet, and $0.01 increments work to. Thoughts?

Second, I'm a little stumped at the moment about the tie-breaking rules, which should be detailed for the game to be complete. Shubik's a little confusing on this point (to me). C RETOG 8(t/c) 22:13, 10 September 2008 (UTC)


 * On point 1: Donno, you would think that as just the best-known example of the concept of an All-pay auction that a solution would be phrased in terms of a continuous quantity. On two, there must be some general Econ solution to ties in auctions (I know what we do for biology models, but Econ's must be different, and actually usable in the Real World). Pete.Hurd (talk) 22:46, 10 September 2008 (UTC)
 * So far for this, I've seen discrete bid increments. I think that may well be important for the model. For ties, the standard in economics is to select the winner randomly in the case of a tie. Shubik says in the event of a tie, the winner is "the bidder closest to the auctioneer" (not an actual quote, I don't have the paper in front of me). That could be interpreted as random, but it could also be interpreted as meaning that the winner in the case of a tie is assigned at the beginning of the game, and so can be part of the strategy. C RETOG 8(t/c) 23:23, 10 September 2008 (UTC)


 * You should have discrete bid increments simply because it's the weaker assumption - "even if" bids must be discrete, there's still no equilibrium in this game (i.e. assuming discrete increments restricts the strategy space). Also if you have bid increments, then the only possible tie is nobody bid nothing, right?radek (talk) 02:45, 1 November 2008 (UTC)


 * Ah, ok, I'm wrong. The way it is presented here the discrete-vs-continuous does matter. Additionally, there's I believe another version of this game, where both players pay the second highest bid. This eliminates the "bid 99 cents" or "bid 1$" strategies as equilibria. Another way to get this is to assume that the bids actually DO have to be incremental. I.e., the first bid must be, say, 5c, the second 10c and so on.radek (talk) 02:55, 1 November 2008 (UTC)

Swoopo?
I don't think it should be linked here... Sure, the article explains that the dollar auction is irrational, but linking to the site still seems a lot like free advertising to me (especially since the site's relevance isn't explained, and since it isn't exactly the same game). sten for the win (talk) 00:56, 17 December 2008 (UTC)
 * I agree, and pulled it out. C RETOG 8(t/c) 01:11, 17 December 2008 (UTC)

Swoopo was mentioned here again, with a WARNING--There's a lot of bloggish reference to Swoopo and the dollar auction, but I haven't found a ref good enough to use in the article. I think a mention of it might be OK if well-referenced. C RETOG 8(t/c) 00:34, 15 September 2009 (UTC)

There's a bit from Richard Thaler in the NYT which makes the connection between the dollar auction and Swoopo.com. It's here. I think that's a good enough ref if someone wants to include it. C RETOG 8(t/c) 04:00, 15 November 2009 (UTC)

Refutations again
Some recent edits removed "fact" tags on some of the stuff in the "Refutations" section. Whether the stuff is obvious or not, the thing is that WP requires verifiability not truth. The important thing for this article is that we aren't coming up with our own refutations, but describing possible refutations that others have come up with. C RETOG 8(t/c) 18:28, 19 January 2009 (UTC)


 * Please discuss here rather than in edit summaries--they don't leave much room, and also make edit warring the only way to discuss. You commented, "How do you reference a logical statement? Would you need a reference for "2 + 2 == 4"?". You wouldn't need a reference for 2+2=4, but you would need a reference before saying that 2+2=4 argues against X. Otherwise, I could derive lots of my own logically valid arguments throughout game theory articles, but that would be WP:OR. The bit in question is talking about a specific alternative approach to the dollar auction--there could be infinite such approaches. It should only be in the article if it's notable--if an article or textbook or something proposes this approach. C RETOG 8(t/c) 22:22, 19 January 2009 (UTC)


 * Please give a couple more examples of the "infinite varieties". The article would only need references if it claimed that those solutions were the only ones or if it claimed they were mentioned specifically.  Otherwise it is just trivial and there is nothing to reference.  The article does not say "2+2=4 argues against X" it says "2 + 2 = 4" argues for "2 + 2 > 3".  The arguments in that section are so basic nobody would bother to publish them for referencing.  Tu rk ey ph an t 00:23, 21 January 2009 (UTC)

An encyclopedia aims to document externally existing knowledge of a topic. A great deal has been written about the dollar auction, and that body of work comprises the subject of the encyclopedia article. Thought outside of that work is appropriate in other venues, but not appropriate for this venue. The prescription against reporting original thought WP:OR, or representing views out of proportion to their prominence in reliable sources WP:UNDUEWEIGHT, means that we only present that which is typically presented on a topic by secondary and tertiary sources, see WP:SECONDARY. Pete.Hurd (talk) 05:42, 21 January 2009 (UTC)
 * What's your point?  Tu rk ey ph an t 16:56, 22 January 2009 (UTC)

The expected value
I removed the reference to the expected value. The concept of expected value makes sense only in context of random variables. As there are no clearly defined random variables here, the reference to the expected value does not make sense. I assume this part of the article was original research as no citation was also provided.


 * Expected value can make sense, because in analyzing the game players are likely to play (or at least be allowed to play) mixed strategies, and that's where the random variables come in. Nonetheless, the material you removed was uncited and a muddle, so I think the removal was a good idea. C RETOG 8(t/c) 14:56, 5 February 2009 (UTC)

has anyone bothered to attempt this
seriously, im sure scholars and internet people can debate this to death and it has its implications for the definition of 'rational player' and such.... but is it that hard to find a 'generous benefactor' to put $1 up for auction. not as an undisputed answer to this paradox, that would be like experimentally testing Schrödinger cat. it would be a nice demonstration about how rational people can diverge from the 'perfectly rational' model and get a better outcome. just like the travelers dilemma. I predict that smart players would end up at a tie bid of either 50 cents or 1 dollar. at 50 cents they break even. if they dont have the foresight to stop at 50 cents then surely they would stop at 1 dollar because at that point it is no longer profitable to either player. —Preceding unsigned comment added by 96.234.107.175 (talk) 15:40, 10 July 2009 (UTC)
 * Purely anecdotal, but I have seen this carried out in real life, with a group of 4-6 people rather than two. The results were pretty mind-boggling: they kept bidding far beyond when it would have been rational to stop. I can't remember how much the dollar eventually went for, but I think it was at least $5. Goes to show that in real life, people are just not rational and don't think about the consequences of their actions. I'm just glad I had the good sense to stay out of it. Robofish (talk) 23:32, 21 April 2011 (UTC)
 * Also seen this done in real life. Yes, it happens the way the theory predicts, except with real money the players do eventually realize how pointless it is and stop - though way beyond 1$ bids.Volunteer Marek (talk) 05:34, 7 July 2011 (UTC)
 * Maybe it's a cultural difference or maybe because I introduced the game as "pretend" (because I was in a class-room setting and because I didn't want to have people burned and angry), but my Korean students easily beat the game immediately. One of 10 students bid, another bid; and then the first one said, 'Let's stop and share it.'  If it had been for real, I would have been

out 88% of the 10,000 weon note (roughly worth $10). Kdammers (talk) 07:03, 5 November 2013 (UTC)

Dollar-Dollar Auction
See my question here on the "Polish Auction" which is sometimes known as a "Dollar-Dollar Auction". While I doubt these are directly related to the main subject of this article I was wondering if anyone had run into any game theory research on the subject. I figure the similarity in names might have caused a serendipitous connection. :) 66.97.213.94 (talk) 19:49, 11 October 2010 (UTC)

Refutations
I removed the stuff about the cooperative outcome from the Refutations section as 1) it's OR, 2) it's not really a refutation since it involves a fundamentally different game, 3) is not even particularly insightful since with cooperative behavior essentially anything can happen.

What I left in the section isn't particularly accurate either however. As mentioned above "don't play in the first place" is not an equilibrium either. If everyone else chooses "bid zero" then your best option is to "bid 1 cent" (or epsilon or whatever) since in that case you make 99 cent profit, as opposed to 0 profit if you also play "bid zero". Of course that means that someone else's best response is "bid 2 cents" and then the whole process begins. As I've stated above, this is essentially a game with no equilibrium (either in mixed or pure strategies) and that's what creates the paradox.Volunteer Marek (talk) 05:40, 7 July 2011 (UTC)


 * I have a general question about this "paradox": If all the bidders indeed have perfect information, they should be able to foresee how overbidding each other will lead to losses for the two highest bidders, should they not? As they try to maximaze their profits and losses are essentially negative profits, not bidding or cooperation are more succesfull strategies that should therefore be applied instead.
 * tl;dr: Why is it assumed the bidders engage in a bidding-war they must know they can't profit from in the first place? --89.12.17.178 (talk) 20:30, 7 October 2011 (UTC)

Either the paradox is moot, or the article does not explain it well
The article claims that the "Dollar Auction" contains a paradox, but it is not clear where the paradox lies. What does "complete information" mean in this context? Can the bidder assume that the other bidders (if any) are rational? Consider these cases:

1. There is only one bidder, Alice. She knows there are no other bidders. She bids 5c. She wins. Done.

The formal precommitment mechanism made sure there is atleast 2 or more precommitted bidders in the room before auction was initiated.

2. There are other bidders, but Alice gets to bid first (and she knows that). She bids 95c. The other bidders are rational and nobody bids 1$ because bidding is extra work for no gain. Alice wins. Done.

The formal precommitment mechanism made sure there is atleast 2 or more precommitted bidders in the room before auction was initiated.

So, again, where is the paradox?

So there was atleast 2 persons who had bought bids towards the auction.

'''Bids were sold on "use them or lose them" contract. '''

Luigi Semenzato — Preceding unsigned comment added by 2620:0:1000:3803:A800:1FF:FE00:54E8 (talk) 01:12, 1 June 2013 (UTC)


 * Very good point, Luigi. Maybe at 95 cents some-one might be "foolish" enough to jump in, but certainly at an initial bid of 99 cents, there is no normal (i.e., game theoretical) incentive to enter into the bidding: Alice wins one cent, and no-body else (except the auctioneer) loses, since the next possible bid would have to be $1 (break-even and hence a waste of effort) or above (loss for the bidding party (only some-one perverse or Alice's ex-boyfriend would be interested in doing this, and neither fits normal game-theoretical conditions).

As far as research goes, there is an academic article, but with the pay-wall, I can't say if it actually includes empirical research in spite of the statement about results on the first page: http://www.jstor.org/discover/10.2307/173254?uid=3738392&uid=2&uid=4&sid=21102869324217. The author "ignores" both co-operation and the 99 cent solution. Another article >is< a report of an actual experiment. the fact that it was done with MBA students might explain the extreme results: http://jme.sagepub.com/content/26/1/56.abstract .Kdammers (talk) 07:18, 5 November 2013 (UTC)

I don't understand, thanks to vandalism?
If the minimum bid is 5 cents how can the superrational guys bid 1 cent? Palosirkka (talk) 06:08, 30 April 2014 (UTC)

Formal Precommitment Mechanism
According to Dr. Martin Shubik the formal precommitment mechanism in 1971, needed to know that there was atleast 2 or more precommitted bidders in the auction event before the decision to initiate the bidding phase was made.

In 2012, the formal precommitment mechanism was converted into a computer algorithm, also known as the prefunding algorithm.

Dr. Martin Shubik has formally admitted that prefunding algorithm can be considered as the original way of doing business in 1971.

It was considered commonsense knowledge in 1971 that auction needed to have atleast 2 or more precommitted bidders before the decision to initiate an auction was made. — Preceding unsigned comment added by MikoFilppula (talk • contribs) 08:38, 30 October 2016 (UTC)


 * This is very interesting, as the original article be Shubik does not give enough information on how the game is actually defined. Can you please give us a source on this? Polskiblues (talk) 12:00, 7 April 2019 (UTC)