This instant specification relates to the auction of ranked goods.
Many popular search engines run an auction to determine the placement of advertisements next to search results. Current auctions performed by search engines, such as Google™ and Yahoo!®, permit advertisers to specify a single amount as their bid in the auction. This bid can be interpreted as the maximum amount the advertiser is willing to pay per click on its advertisement. In some current systems, the advertisers pay for each user who clicks on their advertisement, and the amount charged depends on the bids of other advertisers participating in the auction.
When search queries are received at the search engines, the bids may be used to rank advertisements related to the search queries for presentation with the search results. Advertisers may seek to have a high ranking, which can correspond to a more prominent display of their advertisements.
In general, this specification describes an auction of ranked goods.
In a first general aspect, a method is described. The method includes accessing bids for ranked goods and minimum rank indicators that each specifies a lowest rank for a good that is acceptable to a bidder, assigning a ranked good to a first bidder based on a first bid and a first minimum rank indicator each associated with the first bidder, and outputting a signal indicative of a cost of the assigned rank good based on a second bid associated with a next highest bidder having a second minimum rank indicator that specifies a rank that is inclusive of a rank of the ranked good assigned to the first bidder.
In a second general aspect, another method is described. The method includes accessing bids associated with bidders for advertisement placement, accessing for each bidder a minimum position indicator that specifies a lowest ranked position that is acceptable for the advertisement placement, assigning a ranked position for an advertisement associated with a first bidder based on a first bid from the first bidder and a first minimum position indicator from the first bidder, and outputting a signal indicative of a cost for the ranked position based on a second bid submitted by a next highest bidder having a second minimum position indicator that specifies a ranking that is inclusive of a rank of the ranked position assigned to the first bidder.
In another general aspect, a system is described. The system includes a data store for storing bids for ranked goods and minimum rank indicators that each specifies a lowest rank for the good that is acceptable for a bidder, an assigning module for assigning a ranked good to a first bidder based on a first bid and a first minimum rank indicator each associated with the first bidder, and means for outputting a signal indicative of a cost of the ranked good based on a second bid submitted by a next highest bidder having a second minimum rank indicator that is inclusive of a rank of the assigned ranked good.
In certain implementations, the systems and methods described here may provide none, one, or more of the following advantages. Simple allocation and pricing algorithms that include position restraints are provided, where the algorithms generalize desirable properties of current auctions that do not have position restraints. Auction attributes include an envy-free or symmetric Nash equilibrium (i.e., no actor has anything to gain by changing only his or her own strategy unilaterally) with the same outcome in allocation and pricing as the truthful Vickrey-Clarke-Groves (VCG) auction. Additionally, an auction can include an equilibrium that is the best equilibrium for advertisers in terms of a profit made by each advertiser.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features and advantages of the invention will be apparent from the description and drawings, and from the claims.
Like reference symbols in the various drawings indicate like elements.
In certain implementations, an auction system, such as a system 100 of
In certain implementations, the auction system can arrange, or order, bidders based on the submitted bids and assign a corresponding ranked good to each bidder. For example, the system can assign a first bidder with a highest bid to a first ranked good, a second bidder with the next highest bid to a second ranked good, etc. If the system assigns a bidder a ranked good that has a ranking below (or possibly equal to or below) the minimum rank specified by that bidder, the system can remove the bidder from the auction and reassign the ranked good to a bidder with the next highest bid.
In certain implementations, the auction system can assign a cost for a ranked good based on the bid of the next highest bidder if the next highest bidder specified a minimum rank that includes the ranked good to which the system is assigning a cost. For example, the system can order bidders based on their bids, and the system can assigned bidders to corresponding ranked goods based on their bids.
In determining the cost of a ranked good, the system can, for example, identify the next highest bidder for the ranked good. If the next highest bidder has specified a minimum rank that includes the ranked good, the system can use the next highest bidder's bid as the price for the ranked good.
However, if the minimum rank does not include the ranked good (e.g., the minimum rank is 7 and the ranked good has a rank of 8), the system selects the next bidder in line below the next highest bidder and determines if this next bidder has a minimum rank that includes the ranked good. In some implementations, the process can be repeated until a bidder is selected that has a minimum rank that includes the ranked good to which the system is assigning a cost. After locating an eligible bidder, the system can assign the bid associated with the eligible bidder as the cost of the ranked good.
One implementation is described in association with
In certain implementations, the auction system 104 receives minimum ranks 108a-c and bids 110a-c for ranked goods from each of the bidders 106a-c, respectively. The minimum ranks 108a-c can each indicate a lowest ranked good that the associated bidders 106a-c, respectively, are willing to accept. For example, the bidders 106a-c may be advertisers bidding for ad positions on a web page. The advertisers each have a minimum ad slot that the advertiser is willing to accept. For example, one advertiser can specify his minimum rank is the third ad slot from the top of the web page. The minimum rank indicates that the advertiser bidder will accept any ad slot in the range of the first slot through the third slot. In another example, the bidders 106a-c may be concertgoers bidding on ranked goods, such as seats in a theater. The concert bidders each have a minimum seat rank that the concert bidder is willing to accept. For example, one concert bidder can specify that a fourth row from a stage is his minimum seat rank. The minimum seat rank indicates that the concert bidder will accept a seat in the range of the first row through the fourth row, but not subsequent rows, such as the fifth row.
In another example, the bidders 106a-c may be passengers on a commercial airline service bidding on ranked goods, such as seats in an airplane. The passenger bidders each have a minimum seat rank that the passenger bidder is willing to accept, such as an exit seat, an aisle seat, a window seat, a first class seat, or a particular number of rows from the front of the airplane.
The auction system 104 stores the minimum ranks 108a-c and the bids 110a-c in a repository 112, according to some implementations. A bid ranking module 114, within the auction system 104, can rank the bidders' eligible bids from lowest to highest. An eligible bid may be, for example, a bid that meets a reserve bid price, or a minimum bid amount set and stored by the auction system 104.
In certain implementations, an assigning module 116 determines what ranked good, if any, will be assigned to each of the bidders 106a-c. The assigning module 116 assigns a ranked good to each of the bidders 106a-c based on an amount of the bidders' bids (e.g., the bidder with a highest eligible bid to a bidder with a lowest eligible bid). The assigning module 116 also can assign ranked goods using the minimum ranks 108a-c submitted by the bidders.
For example, the assigning module 116 can first assign the bidder 106a with the highest eligible bid 110a a highest ranked good (e.g., a first ad slot). If the minimum rank 108b of the next highest bidder 106b is less than or (less than or equal to) the next available ranked good (e.g., a second ad slot), then the assigning module 116 assigns that ranked good (the second ad slot) to the bidder 106b.
Otherwise, in some implementations, if the minimum rank 108b is higher than the next available ranked good, then the assigning module 116 does not assign a ranked good to the bidder 106b. For example, if the minimum rank 108b of the bidder 106b is one (e.g., the highest ranked good), then the bidder 106b is not assigned a ranked good if the bidder 106a has already been assigned the highest ranked good. Alternatively, if the minimum rank 108b of the bidder 106b is two or lower, then the bidder 106b is assigned the second highest ranked good. The assigning module 116 can continue the assignment process for all of the bidders 106a-c.
In certain implementations, a pricing module 117 determines the price or cost that each of the bidders 106a-c are charged for the ranked good assigned to the bidder. In particular, the pricing module 117 can assign a charge for each ranked good based on a bid of the next highest bidder whose minimum rank is less than the rank being priced.
For example, the bidder 106b may have the second highest bid 110b with a value of $5.00 and the minimum rank 108b of two. The bidder 106b is assigned the second ranked good as the rank of “two” is within the minimum rank 108b of the bidder 106b. The cost that the bidder 106b is charged is the bid of the next highest bidder whose minimum rank is less than the rank of “two,” which is the rank of the good assigned to the bidder 106b. The bidder 106c may have the third highest bid 110c of $4.00 and the minimum rank 108c of three. The minimum rank 108c of the next highest bidder 106c is less than the rank of two assigned to the bidder 106b. Therefore, in this example, the pricing module 117 determines that the cost to the bidder 106b of the second ranked good is $4.00. The pricing module 117 continues the pricing process for all of the bidders 106a-c.
In certain implementations, this auction method may provide an envy-free or symmetric Nash equilibrium with the same outcome in allocation and pricing as the Vickrey-Clarke-Groves auction. That is, the auction may exhibit a Nash equilibrium because each individual bidder has nothing to gain by either changing its bid or minimum rank without another bidder also changing its bid or minimum rank. This is described in additional detail in “A method for conducting an auction for ranked positions among bidders that specify a bid and a maximum position,” by Gagan Aggarwal, Jon Feldman, S. Muthukrishnan, Rohit Rao, and Adam Wildaysky, Proceedings of the Fourth Workshop on Approximation and Online Algorithms (WAOA), 2006, the entirety of which is incorporated here.
In the implementation of
For example, each of the media 120a-d may include four ranked goods to be auctioned. The four ranked goods may be ranked according to their sequential order, such as a sequence of commercials in the television medium 120a, where the first appearing commercial at 7:15 p.m. is ranked first, the second appearing commercial is ranked second, etc. In another example, the commercials can be ranked based on an estimated amount of viewers for the time slot. More specifically, a commercial played at 8 p.m. before a popular sit-corn may be ranked first, while a commercial played at 1 a.m. after an infomercial may be ranked fourth. In some implementations, the ranking information for each good can be stored in the repository 112.
In another example, the telephone directory printed medium 120d can have four slots that are ranked according to size and position, such as s a large-sized ad on the upper left of a page may be ranked 1, a medium-sized ad on the lower right page may be ranked 2, and small-sized ads on the upper right may be ranked 3 and 4, respectively. In another example, the slots can be ranked based on whether they are in color. The newspaper printed medium 120b may have color ads on the upper half of pages (ads ranked 1 and 2) and black/white ads on the lower half of pages (ads ranked 3 and 4).
In other implementations, rankings for goods can be based on a display format of the good. For example, the web page medium 120c may rank online ads that include image higher than online ads that only include text.
In certain implementations, the auction system 104 charges the bidders 106a-c using the costs determined by the pricing module 117. For example, the auction system 104 may include account information for each of the bidders 106a-c, such as bank account and bank routing numbers or a credit number. The auction system 104 may use the account information and the costs to bill each of the bidders 106a-c. The billing may be further based on a number of times a bidder is assigned a ranked good in the media 120a-d. For example, in the case where the ranked goods are ad slots in the web page media 120c, a cost may be based on the number of times the ad is presented or the number of times a user of the web page media 120c selects the ad.
In another implementation a bidder may submit a value, such as a cost per impression that the bidder is willing to pay, and this value is combined with another value to generate the bid. For example, the auction system 104 may weight the value submitted by a bidder based on a click through rate (CTR) for the associated ad 206 to determine a weighted bid. The click through rate can be, for example, the number of times that past viewers have selected a hyperlink included in the ad 206 when the ad is presented with search results. For example, a CTR of 0.75 may indicate that, statistically, three quarters of the viewers of the ad 206 have selected the hyperlink included in the ad 206. The CTR can be multiplied by the submitted value to generate a weighted bid that favors ads that have high CTRs.
The auction system 104 receives a query 209, for example, as a result of a request for a search of web pages. In one example, the query 209 may include keywords to be searched for within the web pages. In certain implementations, the bid 110b of the bidder 106b is associated with one or more of the keywords in the query 209. That is, the bidder 106b bids to have the ad 206 presented in association with the search results 204 from the query 209 including the keywords.
For example, the query 209 may include the keywords “file” and “taxes.” The advertiser 106b may provide a tax preparation service and makes a bid to have the ad 206 for its services presented in association with web searches based on the keyword “taxes.” The auction system 104 determines in which ad slot, if any, to present the ad 206 and a cost to charge the bidder 106b.
In the implementation shown in
In certain implementations, the pricing module 117 prices the ad slots assigned to the advertisers. For example, the pricing module 117 assigns a cost to an assigned ranked good, where the cost is based on the bid of the next highest bidder whose minimum rank is less than (or less than or equal to) the assigned ranked good. In some implementations, the pricing module 117 determines the bid of the next highest bidder by the click-through-rate associated with that bidder to generate a weighted bid that is used to determine the ordering of the bidders.
In other implementations, the cost may be based on the weighted bid of the next highest bidder and the click-through-rate of the advertiser that was assigned the ranked good. For example, the pricing module 117 may determine that the next highest weighted bid after the weighted bid of the advertiser 106b is $0.80. The pricing module 117 divides the determined weighted bid by the click-through-rate of the advertiser 106b to determine a cost of $1.07 to the advertiser 106b for the ad slot 202.
The auction system 104 outputs the rank information 118c via the interface 208 to a web server 210, in some implementations. The web server 210 can present the ad 206 in the second ad slot 202, along with the search results 204. The auction system 104 bills the advertiser 106b for the assignment of the ad slot 202. The auction system 104 may directly debit an account, such as a credit card or bank account. Alternatively, the auction system 104 may send an invoice to the advertiser 106b including the cost of the ad slot 202. In certain implementations, the auction system 104 bills the advertiser 106b after an action occurs as a result of presenting the ad 206, such as a click on a hyperlink or a purchase of a product.
Referring to
In step 304, minimum ranks associated with the bids are received. For example, the auction system 104 receives the minimum rank 108b of five from the advertiser 106c, indicating that the advertiser 106c will accept ad slots ranked five and above.
In certain implementations, the auction system 104 can generate a minimum rank for the bidder if one is not provided. For example, the minimum rank can be equal to the lowest rank of the ranked goods (e.g., the minimum rank would equal “5,” if only five ad slots were available). In other implementations, the auction system 104 can generate the minimum rank based on an average or medium of current minimum ranks submitted by the other bidders. In yet other implementations, the auction system 104 can generate the minimum rank based on previous minimum ranks submitted by the bidder in similar auctions (e.g., auctions for the same or similar keywords) or that were submitted by the bidder in all previous auctions.
In step 306, a query including one or more keywords from a user is received. For example, the auction system 104 receives the query 209 including the keywords “file” and “taxes.”
In step 308, an ad auction associated with the keywords in the query is performed. For example, the bid ranking module 114 can order the bids 110a-c received from the bidders 106a-c based on the bid amounts. In certain implementations, the bid ranking module 114 multiplies the bids 110a-c by a weighting factor before ordering, such as a click-through-rate of each bidder in the case of ad slots for web pages.
A rank is determined for each of the bidders in step 310. For example, the assigning module 116 can determine the ranks assigned to the advertisers 106a-c. Each rank corresponds to a particular ad slot. The assigning module 116 assigns the ranks to the advertisers 106a-c based on the order determined by the bid ranking module 114. In certain implementations, the assigning module 116 does not assign a rank to an advertiser where the minimum rank of the advertiser is greater than the rank to be assigned. This will be discussed in more detail in association with
A cost for each of the ranks assigned to the bidders is determined in step 312. For example, the pricing module 117 can determine costs for the ranked goods assigned to the advertisers 106a-c. The cost of a ranked good assigned to a bidder is based on the bid of the next highest bidder that specified a minimum rank that includes the rank of the good being assigned a cost. This will be discussed in more detail in association with
In step 314, ads are displayed to the user. For example, the auction system 104 outputs the ads, including the ad 206, to the web server 210. The web server 210 presents the search results 204 and the ad slots with ads to the user that submitted the search query.
In step 316, the advertisers are charged for the display or selection of the ads. For example, the auction system 104 may directly debit a credit card or bank account for the costs when the ads are presented to the user or when the user performs an action, such as clicking on a hyperlink in an ad.
Referring to
If there is another bidder with a lower bid, as indicated by step 404, then a minimum rank associated with the next highest ranked bidder can be received, as indicated by step 406. For example, the pricing module 117 receives the minimum rank 108c from the advertiser 106c, which is the next highest bidder relative to the advertiser 106b.
If the minimum rank of the next highest bidder is not higher than the rank assigned to the bidder as indicated in step 408, then a cost for the ranked good is set to the bid of the next highest bidder. For example, the pricing module 117 sets the cost of the ad slot 202 assigned to the advertiser 106b as $0.80 because the next highest bidder, advertiser 106c, has a minimum rank of “2,” which is inclusive (and in fact, equal to) the second ranked ad slot assigned to the advertiser 106b.
Otherwise, if the minimum rank of the next highest bidder is higher than the rank of the good assigned to the bidder, then it is determined if there is another bidder with a lower bid than the previously selected next highest bidder, as indicated by the step 404.
If there is not another bidder, the cost of the ranked good is set to a default cost, as indicated by step 412. For example, the pricing module 117 may determine an average cost for the particular ranked good from past auctions and assign the average cost to the bidder where no next highest bidder has a minimum rank greater than the rank assigned to the bidder.
The process 312 can end after steps 412 or 410. In some implementations, the process 312 can be executed repeatedly to assign a cost to each ranked good.
Referring to
In step 504, a first rank is assigned to a highest bidder. For example, the assigning module 116 assigns the first rank to the advertiser 106a, which submitted the highest bid of all the bidders.
In step 506, it is determined If there is another bidder. If so, a next highest bidder is selected, as indicated in step 508. For example, the assigning module 116 selects the advertiser 106b, which submitted the next highest bid.
In step 510, it is determined if the next rank to be assigned to the next highest bidder is less than a rank specified by a minimum rank of the next highest bidder. If the ranked to be assigned to the next highest bidder is within the minimum rank of the next highest bidder, then the rank is assigned to the next highest bidder, as indicated by step 512. For example, the next highest bidder may have a minimum rank of 5 and is currently ranked as the fourth highest bidder (which corresponds to the fourth ranked good). In this case, the bidder would be assigned the fourth ranked good because it does not violate the minimum rank of “5” specified by the bidder.
If the next rank to be assigned is less than the minimum rank of the next highest bidder (e.g., the minimum rank is “3” and the assigned rank is “4”), then it may be determined if there is another bidder with a lower bid, as indicated by step 506. If no other bidders remain, then the process 310 can end.
In certain implementations, the assigning module 116 assigns ranks 608 to the bidders 602. Bidder A has the highest bid, $5.00, and is therefore assigned the first rank (which can correspond to a first ranked good, such as a first ranked advertising slot). Bidder B has the second highest bid $4.00, a minimum rank of 5, and is, consequently, assigned the second rank. Bidder C has the third highest bid $3.00 and a minimum rank of 5, and therefore bidder C is assigned the third rank. Bidder D has the fourth highest bid, $2.00, but bidder D has a minimum rank of 2, therefore bidder D is not assigned a rank because the rank that would be assigned to bidder D is below the specified minimum rank of 2. Bidder E has the fifth highest bid, $1.00, and a minimum rank of 5, therefore bidder E is assigned the fourth rank.
The pricing module 117 assigns costs 610 to the ranks 608 assigned to the bidders 602. In some implementations, the pricing module 117 determines the costs 610 before removing bidders that do not have an assigned rank. The pricing module 117 determines the costs 610 as the bid of the next highest bidder that was assigned a rank and whose minimum rank encompasses the rank to be priced. The pricing module 117 determines the cost to bidder A of the first rank as $4.00, which is the bid of bidder B. The pricing module 117 determines the cost to bidder B of the second rank as $3.00, which is the bid of bidder C. The pricing module 117 determines the cost to bidder C of the third rank as $1.00, which is the bid of bidder E.
The cost to bidder C is not the bid $2.00 of the bidder D because bidder D's minimum rank of 2 excludes the rank of assigned rank of C, which is the third rank. In another example, if the minimum rank of D was 3, the rank assigned to C would be assigned a cost of $2.00 even though the bidder D would not receive a rank because bidder D's minimum rank of 3 would still exclude it from being assigned the fourth rank.
The bidder E does not have a next highest bidder, therefore, in some implementations, the pricing module 117 assigns a default cost, such as $0.05, to the bidder E.
The memory 720 stores information within the system 700. In one implementation, the memory 720 is a computer-readable medium. In one implementation, the memory 720 is a volatile memory unit. In another implementation, the memory 720 is a non-volatile memory unit.
The storage device 730 is capable of providing mass storage for the system 700. In one implementation, the storage device 730 is a computer-readable medium. In various different implementations, the storage device 730 may be a floppy disk device, a hard disk device, an optical disk device, or a tape device.
The input/output device 740 provides input/output operations for the system 700. In one implementation, the input/output device 740 includes a keyboard and/or pointing device. In another implementation, the input/output device 740 includes a display unit for displaying graphical user interfaces.
The features described can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The apparatus can be implemented in a computer program product tangibly embodied in an information carrier, e.g., in a machine-readable storage device or in a propagated signal, for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions of the described implementations by operating on input data and generating output. The described features can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
Suitable processors for the execution of a program of instructions include, by way of example, both general and special purpose microprocessors, and the sole processor or one of multiple processors of any kind of computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer will also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, ASICs (application-specific integrated circuits).
To provide for interaction with a user, the features can be implemented on a computer having a display device such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user and a keyboard and a pointing device such as a mouse or a trackball by which the user can provide input to the computer.
The features can be implemented in a computer system that includes a back-end component, such as a data server, or that includes a middleware component, such as an application server or an Internet server, or that includes a front-end component, such as a client computer having a graphical user interface or an Internet browser, or any combination of them. The components of the system can be connected by any form or medium of digital data communication such as a communication network. Examples of communication networks include, e.g., a LAN, a WAN, and the computers and networks forming the Internet.
The computer system can include clients and servers. A client and server are generally remote from each other and typically interact through a network, such as the described one. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
Although a few implementations have been described in detail above, other modifications are possible. For example, in certain implementations, the ranked goods can include other items, such as substantially identical items having different physical conditions. For example, the ranked goods could include baseball cards for Hank Aaron in various physical states of condition from mint condition to very poor condition.
In other implementations, the ranked goods can also include items, such as substantially identical items having different physical locations. For example, the ranked good may be a particular condominium model that is located at an increasing distance from a desired location, such as a ski slope, lake, ocean, etc. In another example, the ranked good can be hotel rooms (where the rooms have similar attributes, such as space, cable TV, etc.) that are located at an increase distance from a particular location or geographical zone, such as distance from the “Strip” in Las Vegas.
Additionally, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the following claims. Accordingly, other implementations are within the scope of the following claims.
Number | Name | Date | Kind |
---|---|---|---|
5835896 | Fisher et al. | Nov 1998 | A |
5905975 | Ausubel | May 1999 | A |
5974398 | Hanson et al. | Oct 1999 | A |
6078866 | Buck et al. | Jun 2000 | A |
6243691 | Fisher et al. | Jun 2001 | B1 |
6269361 | Davis et al. | Jul 2001 | B1 |
6973436 | Shkedi | Dec 2005 | B1 |
6985885 | Goldberg et al. | Jan 2006 | B1 |
7062466 | Wagner et al. | Jun 2006 | B2 |
7072853 | Shkedi | Jul 2006 | B2 |
7177832 | Semret et al. | Feb 2007 | B1 |
7191147 | Heene et al. | Mar 2007 | B2 |
7225151 | Konia | May 2007 | B1 |
20030236739 | Borgeson et al. | Dec 2003 | A1 |
20040148222 | Sabella et al. | Jul 2004 | A1 |
20060026060 | Collins | Feb 2006 | A1 |
20060253425 | Borgs et al. | Nov 2006 | A1 |
20070016473 | Anderson et al. | Jan 2007 | A1 |
20080004962 | Muthukrishnan et al. | Jan 2008 | A1 |
20080249855 | Collins et al. | Oct 2008 | A1 |
Entry |
---|
Chen, D. Y. (2009). Essays on mobile advertising and commerce. (Order No. 3365219, Harvard University). ProQuest Dissertations and Theses, 106-n/a. Retrieved from http://search.proquest.com/docview/304891044?accountid=14753. (304891044). |
Shihada, B. (2001). Active network approach to the design of secure online auction systems. (Order No. MQ66614, Dalhousie University (Canada)). ProQuest Dissertations and Theses, 91-91 p. Retrieved from http://search.proquest.com/docview/304733223?accountid=14753. (304733223). |
Leonard, Herman B. “Elicitation of Honest Preferences for the Assignment of Individuals to Positions” The Journal of Political Economy, vol. 91, Issue 3 (Jun. 1983) pp. 461-479. |
Alvin E. Roth and Axel Ockenfels, “Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet,” American Economic Review, vol. 92, No. 4, Sep. 2002, 1093-1103. |
Borgs et al., “Bid optimization in online advertisement auctions”, presented Jun. 11, 2006 at the Second Workshop on Sponsored Search Auctions, 14 pages. |
Eso et al., “An Iterative Online Auction for Airline Seats”, IBM Research Report RC 21987, 2001, 14 pages. |