Vickrey's auction

Introduction

Out of all commonly described types of auction, Vickrey auction to be the one that sounds the weirdest, most complex and least useful. It is defined as type of auction using offers sealed in envelopes. As one would expect, the highest bid wins the auction, but the winner does not have to pay the price he offered, but only the price that has been offered in second highest bid.

While this is obviously not the most effective type of auction from the view of the seller, around 30 billion dollars were reassigned using this type of auction in the year 2010 and this sum is rising every year. The reason for this is the fact the Google, Yahoo and other mayor players at the field of internet advertising are using this type of action (or more specifically generalized Vickrey Auction). Thus, every time you browse internet, dozens of Vickrey actions happen to determine which specific advert you will see. Using modified Vickreys auction, Google claims to aim for win-win-win situation by reaching ideal ratio of the advertiser’s benefit, Google’s profit and thanks to some modifications to the auction also user’s experience.

Vickrey auction

Vickrey auction is often also called Second Price auction because of the above-mentioned fact that the not the highest, but second highest price is to be paid by the winner of the auction. The concept of this auction was first thoroughly described by the Canadian Economy Nobel Prize holder William Vickrey in 1961. It was however used much earlier, for example, it is used by stamp collectors since 1893.

Aside from its use in specific real-life scenarios, it is very interesting for theoretical research and demonstrating several matters commonly mentioned in Game Theory.

There are three main reason for Vickerey auction popularity in academic and other theoretic circles. First of all, this type of auction is known to be truth revealing, or more specifically, the equilibrium strategy for this auction is truth revealing. The equilibrium strategy for Vickerey auction is to offer the true value of the auction’s object, thus reveal the ‘truth’. This is also the dominant strategy. The true value of the object also includes secondary considerations of the value, such as the possible loss of profit in case a bidder competitor wins the object.

The first point lead to second – if all bidders (players) follow the equilibrium (dominant) strategy, it will lead to the maximal possible economic efficiency for all of the players. There is no possible loss of value for those who did not win the auction, because there is no chance that a bidder will wrongly estimate the completion and overpay, unlike in case of First Price (English) sealed offer auction.

Proof that Vickrey auction dominant strategy is to offer real value of the auction’s

As mentioned, the truth revealing property of Vickrey action is what makes it really interesting. Let’s prove this statement:

When dealing in Vickrey auction, it is a dominant strategy to offer the real value of the object.

Proof. John wants to buy a car in an auction. The value of the car to John 100$. John is considering to offer more than the car’s value, let’s say 105$. The other’s highest bid is to John practically a random number. The auction can end in three ways for John – a) Someone else offers more, b) John offers the most, someone else offered more than is the perceived car value (eg. 102$), c) John offers the highest bid, the second highest bid is less that the car’s value to John (eg. 98$).

In first case a), John is not getting the car. In case b), John gets the car, but he is overpaying the perceived value of the car – even though he is only paying the second highest bid. That would not happen if he only offered the car’s perceived value (Case c)). Thus, it is more reasonable to offer only the perceived value, as offering more can only lead to overpaying. Offering less than the perceived value is a similar case. This also show the main benefit of Vickrey auction – the bidder is never overpaying if playing the dominant strategy. This makes it useful in cases where the auctioneer profit is not the most important aspect of the auction, as other aspect has to be acknowledged, such as stability of a network of happiness of players.

Uses of Vickrey auction

Even though Vickrey auction is not as know or popular as other, more straightforward types of auctions, it still sees numerous uses in real-life, aside from the already mentioned use to sell advertising on internet.

Word of Warcraft auctions

Word of Warcraft is a well-known online Massively multiplayer online role-playing game (MMORPG) published in 2004 but still somehow popular. Players are often part of guilds and need specific items to achieve their in-game goals. As items are distributed somewhat randomly among players, players need to exchange them for different items, or, more commonly, for in game currency. Such exchange can be done though auction set in a player’s guild. Different types of auctions can be used, but Vickrey Auction is especially popular. In such in-guild auction, an item is offered to the other guild members. After that, a standard Vickrey auction takes place: All interested players offer a price, after which the second-best price is paid to the highest bidder. Compared to the other commonly used system – fixed prices – this allows better effectivity of the guild and higher joy from the game.

Network routing

A modified version of Vickrey auction, Vickrey-Clark-Groove auction, is used in one of the methods to fulfil networking request in the field of Network Routing. A scheme to assign a route through nodes in the network is necessary, as the nodes are not always able to fulfil all request given their technical limitations. Such nodes are known as “Selfish” nodes and are programmed to fulfil something that could be described as their utilities. The are pairs in the network which need a path with a given bandwidth to be assigned to them, and nodes are able to offer this bandwidth. The pair need to offer a payment to the nodes for the needed bandwidth. Given the fact that such transactions are done with automatically set prices, the Vickrey auction is a suitable option, because it prevents the pairs from overpaying and allows the most efficient paths in the network to be found.

Closed groups auctions

Vickrey auctions is sometimes used in groups where the seller prefers the group welfare and happiness to his own profit. As this requires an amount of solidarity, this is not so common. Of of such groups are philatelist groups (stamp collectors), where Vickrey auction is the preferred type of auction since the year 1893 when it was first used.