Unique bid auction

If an investigating authority were to determine that randomness or chance plays too large a role in the outcome, the auction may be considered a type of lottery.

If, on the other hand, the investigating authority found strategy and skill played a sufficient role in the outcome, they may find the auction to be legal.

Worldwide, there are no reported cases or statutes specifically outlawing the lowest-unique bid auction model.

[2] An English case held that "there will seemingly be never any finality on the question what is a lottery" because “attempts to do so may indeed be counter-productive, since each added precision merely provides an incentive to devise a variant which eludes it”.

[3] Legislatures tend to leave the definition open in order to encompass lotteries that were not envisaged at the time of the enactment of the legislation.

Under English common law, a lottery includes any game, method, device, scheme or competition whereby money or money’s worth is distributed or allotted in any manner depending upon or to be determined by chance or lot, whether the same is held, drawn, exercised or managed within or without the jurisdiction.

Unique bid auction companies typically avoid calling the payment by the bidder an outright fee for the chance of winning an item, applying synonyms to elude the purpose of raising revenue from a collective pool of bidders that covers the cost of the auction item.

In the New Zealand case Department of Internal Affairs v Hayes [2007],[4] customers offered bids costing 99 cents for the chance to win a Peugot car.

Although customers received an item of value, the bids were sent for the purpose of winning a car, and the refund was not identical to what had been offered, the auction was held to be a lottery.

[6] "The exercise of any skill, greater than a mere scintilla, which, looking at the scheme as a whole, has contributed to the successful result, will be sufficient to take the case out of the (English) Act.

"[7] An example where a scheme was permitted to run despite the role of chance was when the individual "used his knowledge and experience of the football world in choosing the pools to be entered into and the method of completing them".

[6] Sports wagering is legal in only a few US locales that typically also allow other forms of gambling—Las Vegas for instance.

A distinguishing difference between unique bid auctions and traditional lotteries, games of chance, and sporting events (gambling) is the absence of an external randomizing device.

In sporting events, the participants in the competition (football players for instance) represent the element of chance since their behavior is outside the control of those wagering on the outcome.

The unique bid auction model's attractiveness is the possibility of obtaining an item at significantly lower cost than the retail price.

[10] Further work by Bruss et al.[11] and a number of other researchers including Gallice,[12] and Rapoport and Otsubo[13] has continued to develop the theory on this subject.

In a 2012 study Pigolotti et al. conducted a thorough study of the unique bid auction in the grand canonical ensemble, finding a theoretical expression for the Nash equilibrium distribution and showing that real-world players play according to this distribution when the number of players in the auction is low.

[14] Closely related is the Lowest Unique Positive Integer (LUPI) game, studied by Östling et al (2011).

[15] Östling et al give a method for calculating the Nash equilibrium distribution for the game,[15] shown on the right for the case of N=100 independent entries.

Below this threshold the Nash distribution is constructed to give each player the same chance of winning, regardless of which number they choose.

[17] Considering data from the Swedish "Limbo" game, Östling et al found that players had rapidly adapted to avoid high numbers, above the Nash cut-off, when these did not win.

However, the range of numbers backed by most players did not extend quite as high as the Nash equilibrium would predict.

Östling et al found that a model based on a mixture of iterative solutions of increasing depth was able to reproduce the observed distribution quite well.

) to be in "striking" agreement with the predicted Nash distribution, in particular accurately matching the position of the sharp cut-off.

[14] Östling et al found similarly in a LUPI game recreated for the study with an average of 27 players.

[14] In both cases the researchers found typical psychological patterns in the finer structure of the numbers chosen.