Patent Publication Number: US-9413557-B2

Title: Pricing in social advertising

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is related to U.S. patent application Ser. No. 12/818,170, entitled “Reconstructing the Flow of Online Recommendations” and filed on Jun. 18, 2010, specifically incorporated by reference herein for all that it discloses or teaches. 
     BACKGROUND 
     Personal recommendations and word-of-mouth advertising can greatly influence an individual&#39;s purchase decision. Generally, a consumer is more likely to purchase a product or service based on referral from someone they know and/or trust than based on an independent advertisement. With the arrival of online communication services, such as email, blogs, microblogging services, social networking services, and electronic commerce sites, personal recommendations and word-of-mouth advertising proliferate in an online fashion. Providing incentives to recommending users and to those users who consume recommendations (e.g., shop and/or purchase on the basis of such recommendations) can amplify the effect of such advertising. However, fairly yet effectively incentivizing the participants in such advertising (e.g., recommending and recommended users) to encourage recommendations is a challenging problem. 
     SUMMARY 
     Implementations described and claimed herein address the foregoing problems by fairly allocating incentives to participants in a recommendation flow. In one example, a user may send an email to a friend recommending a product specified at a particular web site (e.g., identified by a Uniform Resource Identifier (URI) embedded in the email). Before sending the email containing the URI, the user submits the URI to a forwarding service, which associates the recommended URI with an identifier of the recommending user and returns a new URI that is mapped to the original URI and to the recommending user. The recommending user can then recommend the web site by forwarding the new URI to the friend. If the friend selects the new URI to review the web site, the forwarding service records the friend&#39;s decision to review the web site and directs the friend to the recommended web site. The forwarding service maintains a database of recommendations made by the recommending user, recommendations consumed (e.g., acted on) by the friend, whether the friend visited the recommended web site, etc. 
     In this manner, the forwarding service can provide such statistics to an ad service, which can provide incentives to the recommending user and the friend. Example incentives may include an accumulation of points by the recommending user, a discount to the friend if a purchase is made in response to the recommendation, etc. Further, a recommendation flow may include multiple recommendations resulting in or contributing to one or more purchases. To determine how much of an incentive each participant in the recommendation flow receives, a graph is created to model the recommendation flow and incentives are allocated using a cooperative game description based on this graph. The game description is processed to associate each participant with a power index that represents that participant&#39;s share of the incentive. 
     Other implementations are also described and recited herein. 
    
    
     
       BRIEF DESCRIPTIONS OF THE DRAWINGS 
         FIG. 1  illustrates an example recommendation flow employing a forwarding service for recommendations and an ad service for allocating incentives. 
         FIG. 2  illustrates an example forwarding service managing a recommendation. 
         FIG. 3  illustrates an example forwarding service managing multiple recommendations in a recommendation flow. 
         FIG. 4  illustrates example operations for a recommending phase of tracking online recommendations. 
         FIG. 5  illustrates example operations for a consuming phase of tracking online recommendations. 
         FIG. 6  illustrates a graph of an example recommendation flow. 
         FIG. 7  illustrates example operations for allocating incentives in an online recommendation flow. 
         FIG. 8  illustrates an example system that may be useful in implementing the described technology. 
     
    
    
     DETAILED DESCRIPTIONS 
     As an initial matter, a URI is an example of a resource identifier and represents a string of characters used to identify a resource on a network. A universal resource locator (URL) is an example type of URI that identifies both a network resource and a means of accessing the network resource. For example, the best-known example of a URL is the “address” of a web page on the World Wide Web, such as “http://www.microsoft.com”, wherein the URI scheme “http” implies that a representation of the identified network resource may be obtained via HTTP from a network host named “www.microsoft.com”. A universal resource name (URN) is another example type of URI. 
       FIG. 1  illustrates an example recommendation flow  100  employing a forwarding service  102  for recommendations and an ad service  112  for allocating incentives. In the illustrated example, a user  104  visits a network resource (such as a product/service website  106 , a web service, a file transfer protocol (FTP) resource, a data storage system, etc.) and wishes to recommend it to a friend (e.g., a user  108 ). The recommending user  104 , therefore, transfers the URI of the network resource into a recommendation message  110  to send it to the consuming user  108 . Note: Users are designated in the figures by labeled blocks and are intended to represent the individual users and/or their computing systems. 
     Prior to triggering the transmission of the recommendation message  110  to the user  108 , the user  104  submits the URI to the forwarding service  102 , in a manner similar to using a URL shortening service. On the basis of this submission, the forwarding service  102  also receives a user identifier (UserID) of the user  104 . Given the UserID and the URI, the forwarding service  102  generates a trackable recommendation identifier (e.g., another URI), which it returns to the user  104 . The forwarding service  102  maintains a mapping between the originally received URI and the trackable recommendation identifier and another mapping between the UserID and the trackable recommendation identifier. These mappings may be unidirectional (e.g., from trackable recommendation identifier to original URI and/or UserID) or bidirectional (e.g., between trackable recommendation identifier to original URI and between trackable recommendation identifiers to UserID. Thereafter, upon receipt of the trackable recommendation identifier, the user  104  can trigger transmission of the recommendation message  110  containing the trackable recommendation identifier to the user  108 . 
     Upon receiving the recommendation message  110 , the user  108  can trigger the trackable recommendation identifier from the recommendation message  110  (e.g., selecting it, selecting a submission item from a context sensitive menu, sending the trackable recommendation identifier to a submission service, etc.), thereby submitting it to the forwarding service  102  for consumption (e.g., translation back into the original URI to the recommended network resource). In one implementation, a UserID of the user  108  may also be submitted to the forwarding service  102 , which can create a user mapping between the trackable recommendation identifier and the UserID of the user  108 . 
     In one implementation, the forwarding service  102  refers to recorded mappings of trackable recommendation identifiers and determines the original URI associated with the received trackable recommendation identifier, returning the original URI back to the user  108 . Upon receipt of the original URI, the user  108  can select the original URI to navigate to or otherwise access the network resource (e.g., the product/service website  106 ) identified by the original URI. In another implementation, the user  108  is redirected or given access directly to the network resource without returning the original URI to the user  108 . 
     In one implementation, the submission of the original URI to the forwarding service  102  credits the user  104  with an attempted recommendation, which may be rewarded by some measure maintained by the forwarding service  102 , the ad service  112 , or some other means. The ad service  112  is a component of the overall recommendation system that can query the forwarding service  102  for recommendation data relating to a user or a URI and take appropriate action. For example, the ad service  112  (or the forwarding service  102 ) can analyze such recommendation data and credit the user  104  with points toward a product or service rewards program, with a monetary credit, or with some other incentive. The forwarding service  102  and the ad service  112  are shown as residing in the same server  124 , but it should be understood that the forwarding service  102 , the ad service  112 , and/or their components may be distributed over multiple computing systems. 
     Additionally, or in an alternative implementation, the submission of the trackable recommendation identifier to the forwarding service by the user  108  may also result in the user  104  receiving credit for a consumed recommendation. For example, because the forwarding service  102  maintains a user mapping between the trackable recommendation identifier and the UserID of the user  104 , when the forwarding service  102  receives the submission from the user  108 , the forwarding service  102  can find this user mapping and credit the user  104  with some benefit (e.g., points, credit, etc.). 
     Additionally, or in an alternative implementation, the submission of the trackable recommendation identifier and the UserID of the user  108  to the forwarding service by the user  108  may result in the user  108  receiving some benefit. For example, because the forwarding service  102  can maintain a mapping between the trackable recommendation identifier and the UserID of the user  108 , when the forwarding service  102  receives the submission from the user  108 , it can find this mapping and credit the user  108  with some benefit (e.g., points, credits, discounts, etc.). The UserID of the user  108  may also be passed to the ad service  112 . 
     Both submission of the original URI by the user  104  and submission of the trackable recommendation identifier by the user  108  can also be recorded and analyzed by the forwarding service  102 , the ad service  112 , or some other means. For example, the ad service  112  may use such events in a statistical fashion to identify product/service trends, programming demographics, etc. As a specific example, the user  104  may be associated with a large number of recommendations of a television program popular among females between ages 13 and 16 (e.g., the user  104  frequently sends URLs of YouTube videos about the television programs to others). As such, an increase in recommendations by the user  104  and other similarly situated recommenders about a new television program may indicate a popular trending for the new program in the same demographic group. 
     Further, the user  108  can submit the trackable recommendation identifier or the original URI to the forwarding service  102  to send a recommendation message  114  containing a trackable recommendation identifier to another user  116 . If the user  108  submits the trackable recommendation URI to the forwarding service  102 , then the trackable recommendation identifier can provide a single level of recommendation (e.g., identifying only the user  108 ) or a flow of recommendations (e.g., identifying both the user  104  and the user  108 ). The forwarding service  102  can track the submission of user  108  as well as selection of the resulting trackable recommendation identifier by the user  116 . In yet another recommendation stage, the user  116  can forward a recommendation message  118  containing a trackable recommendation identifier to another user  120 . Records of all such recommendations can be maintained and/or analyzed by the forwarding service  102 , the ad service  112  or other means. 
     It should be understood that the forwarding service  102  and/or the ad service  112  maintain recommendation data that can be used to credit the recommending and consuming users with something of value. For example, the forwarding service  102  may maintain a count of the number of consumed recommendations a recommending user has made and credit the recommending user with points towards a discounted purchase. Recommendation data may also be classified in particular product/service categories, based on timestamps, based on geographical or demographical parameters, etc. to develop a model of the marketplace relating to the recommended resources. The ad service  112  may also or alternatively maintain the recommendation data or query the forwarding service for the recommendation data, from which it can make crediting and/or incentive decisions (e.g., crediting the consuming user with a discount versus points). 
     In another alternative implementation, the original URI returned to the consuming user from the forwarding service  102  may also be modified to include one or more parameters to cause the network resource (e.g., the recommended website) to treat the consuming user differently than the general population. For example, the company publishing the recommended website may pay the forwarding service company a fee to map a discount parameter to the original URI. In this manner, the returned URI can include this parameter, and the web server accessed through the returned URI can redirect the consuming user to a web page that offers a discount to recommended consumers. 
       FIG. 1  has been described as processing a URI through a client interface (similar to an interface used to short URLs). In an alternative implementation, the recommending user can simply route the recommendation message through a forwarding service that automatically personalizes all (or a specifically marked subset) of the URIs found within the recommendation message before forwarding it on to a consuming user identified by the recommending user. In this manner, the recommending user can integrate the steps used to provide a recommendation (e.g., personalizing the URI and sending the recommendation). Furthermore, the forwarding service can also be more integrated in the recommendation procedure (e.g., it can detect when a recommendation was actually sent to a user and which user received it). Other implementations may also be employed. 
     The forwarding service  102  and/or the ad service  112  may reside in the cloud or be executed from a server within a local area network. For example, a forwarding service may be implemented within an email or unified communications server of an enterprise. Alternatively, an Internet or Web-based service (similar to a URL shortening service) may implement the forwarding service and/or the ad service. 
     In one implementation, based on the tracking of online recommendation flows, the ad service  112  allocates incentives to the participants in the online recommendation flows. As shown in  FIG. 1 , the ad service  112  receives recommendation flow information from the forwarding service  102  and allocates credit (represented by the “$” symbol and dashed arrows  122 ) based on a variety of potential factors. Note: Although the “$” symbol is used to represent a credited incentive, it should be understood that incentives need not be monetary in nature and may include any incentive of value, including recognition, messages of appreciation, etc. 
     A variety of incentive allocation mechanisms may be employed. For example, one implementation may apply an equal allocation among every participant in the recommendation flow. In another implementation, a varying allocation may be based on the “distance” (e.g., the number of recommendations) in the flow between the original recommending user and the consuming user, in which the incentive diminishes with a larger distance. However, more complex allocation systems may also be employed, particularly if the recommendation flow is not strictly sequential but includes multiple recommendation flow branches. 
     In one such allocation system, the contribution of individual recommending users in an online recommendation flow may be modeled to determine a relative level of contribution of each user to a shared outcome (e.g., a consuming user actually purchasing based on the recommendation flow). Multi-agent (or multi-user) domains, where cooperation among agents contributes to achieving a common goal, can be modeled as “coalitional games” or “cooperative games.” Cooperation influences many types of interactions among self-interested agents. In many domains, individual agents (e.g., recommending users, consuming users) rely on each other to achieve the common goal. The users involved in a recommendation flow that results in a purchase, for example, may form a winning “coalition” that is eligible for some incentive. 
     Nevertheless, different users may be unequal in their power to affect the shared outcome. For example, a user may be considered more important in a winning coalition if the user&#39;s removal from the coalition would cause the coalition to “lose”. Such a user is referred to as a “critical” user and may be attributed with a representation of more power in the coalition, therefore be deserving of a larger share of the incentive as compared to other noncritical users in the coalition. Accordingly, a cooperative game may be employed to fairly allocate the “power” and therefore the appropriate level of incentives throughout the winning coalition. 
     Further, the described technology may consider the various recommendations in a recommendation flow (e.g., along with their quality or assessed influence on an eventual result) by estimating the contribution of each such recommendation on the final result (e.g., the purchasing decision by the consuming user). Some of these recommendations were not communicated direction to the actual consuming user but to other recommending users within the recommendation flow that leads to the consuming user. Nevertheless, such recommending users still receive some credit for the result, as described herein. 
     In some implementations, the UserID of a recommending user may be considered when evaluating the effectiveness of the user&#39;s recommendations (e.g., the probability that the user&#39;s recommendation will result in a purchase or a subsequent forwarding by the recipient). For example, it is possible to augment a representation of the recommendation flow (e.g., a datastore such as a graph or table) with weights on the associations between users (e.g., on edges of a graph). Alternatively, certain conditions may be placed on recommendations before they are recognized as a successful association between two users. 
       FIG. 2  illustrates an example forwarding service  200  managing a recommendation. A user  204  (e.g., a “recommending user”) may access a website  206  and decide to recommend it to another user  208  (e.g., a “consuming user”). In this context, the term “recommending user” identifies a user in a role of recommending a resource to another user, and the term “consuming user” identifies another user in a role of responding to a trackable recommendation by submitting a trackable recommendation identifier to the forwarding service  200 . Note: The user  204  need not actually access the website  206  in order to obtain an accurate URI to the website  206 , but accessing a website is a common method of obtaining an accurate URI (e.g., copying the URI from a web address field in a browser). 
     To recommend the website  206  to the user  208 , the user  204  submits a user identifier (UserID 1 ) of the user  204  and the URI (gURI—generic URI) to the forwarding service  200 . The gURI represents a recommended resource identifier. The forwarding service  200  creates a trackable recommendation identifier (pURI—personalized URI), a resource identifier mapping between the gURI and the pURI, and a user mapping between the UserID 1  and the pURI. The mappings are stored in a datastore  212  accessible by the forwarding service  212 . The forwarding service  200  then sends the pURI back to the user  204 , who sends a recommendation message  210  containing the pURI to the user  208 . 
     Upon receipt of the recommendation message  210 , the user  208  can “consume” the recommendation by triggering submission of the pURI in the recommendation message  210  (e.g., the pURI in the body of a recommendation email) and the user identifier (UserID 2 ) of the user  208  to the forwarding service  200 . The forwarding service  200  records in the datastore  212  the consumption of the recommendation by the user  208  of the pURI, creates a mapping between the pURI and the UserID 2 , finds the mapping associated with the pURI in the datastore  212 , and returns the corresponding gURI to the user  208  (or redirects the user  208 &#39;s browser to the resource identified by the gURI). In this manner, the user  208  can access the recommended web site  206 . 
     By maintaining both the initial recommendation by the user  204  and the consumption of the recommendation by the user  208 , the forwarding service  200 , an ad service  214 , or other means can track personal recommendations made online and their effectiveness. Furthermore, using the user mappings, consumed recommendations can be tracked back to the recommending user, who can be credited with a consumed recommendation and therefore rewarded with an incentive, award, or some other valuable benefit. For example, the recommending user associated with the pURI submitted by the consuming user may be awarded points that can be traded for other products or services. Records of such consumed recommendations can also be stored in and/or distributed to other datastores, such as datastore  216 . 
     In an alternative implementation, the forwarding service  200  may also receive from the user  204  a recommendation qualifier, such as “like,” “dislike,” “refer,” etc. For example, if the user wishes to recommend that the friend  208  avoid buying a product reviewed at a particular URI, the user  204  can attribute a “dislike” recommendation qualifier to the submission of the UserID and gURI to the forwarding service  200 . The user  204  may also annotate the returned pURI with text (“This product is AWFUL!”) in the recommendation message  210  before sending it to the user  208 . Recommendation qualifiers may also be recorded by the forwarding service  200 , stored in the datastore  212 , and used by the forwarding service  200 , the ad service  212 , or other means to evaluate marketing trends, etc. 
     In yet another alternative implementation, the forwarding service  200  may also receive from the user  208  a consumption qualifier, such as “like,” “dislike,” “refer,” “ignore,” etc. For example, if the user  208  already knows about the recommended product or website or does not trust the recommendations of the user  204 , the user  208  can attribute an “ignore” consumption qualifier to the submission of the UserID and pURI to the forwarding service  200 . Consumption qualifiers may also be recorded by the forwarding service  200 , stored in the datastore  212 , and used by the forwarding service  200 , the ad service  212 , or other means to evaluate marketing trends, etc. Consumption qualifiers may also alter the way the forwarding service  200  responds to a consuming user&#39;s submission. For example, the forwarding service  200  may not return the gURI or redirect the user  208  to a recommended web site based on the receipt of an “ignore” consumption qualifier. 
     Other information may also be recorded by the forwarding service  200 , including a recommending time stamp of the submission by the user  204 , a consuming time stamp of the submission by the user  208 , global positioning system (GPS) coordinates and other information, device type, whether the recommending user has actually purchased the recommended product/service, etc. For example, less credit may be attributed to a recommending user or a consuming user if a long period of time exists between a recommendation timestamp and a consuming timestamp. In another example, different levels of credit may be attributed to a recommending user or a consuming user depending on the geographic location of either user. 
     It should be understood that the trackable recommendation identifier may be sent to multiple recipients (e.g., via an email distribution list, a “tweet”, a blog posting, etc.). In this circumstance, the UserID of the recommending user is mapped to the trackable recommendation identifier so that the recommending user can receive credit from individual consumptions by any number of consuming users who trigger the trackable recommendation identifier. Moreover, although each consuming user triggered the same trackable recommendation identifier, unique mappings between the UserID of each consuming user and the trackable recommendation identifier may be recorded, so that each consuming user is credited with the consumed recommendation. 
       FIG. 3  illustrates an example forwarding service  300  managing multiple recommendations in a recommendation flow. A recommending user  304  may access a website  306  and decide to recommend it to a consuming user  308 . 
     To recommend the website  306  to the user  308 , the user  304  submits a user identifier (UserID 1 ) and the URI (gURI—generic URI) to the forwarding service  300 . The forwarding service  300  creates a trackable recommendation identifier (pURI 1 ), a mapping between the gURI and the pURI 1 , and a mapping between the UserID 1  and the pURI 1 . The mappings are stored in a datastore  312  accessible by the forwarding service  312 . The forwarding service  300  then sends the pURI 1  back to the user  304 , who sends a recommendation message  310  containing the pURI 1  to the user  308 . 
     Upon receipt of the recommendation message  310 , the user  308  can trigger submission of the pURI in the recommendation message  310  (e.g., the pURI 1  in the body of a recommendation email) and the user identifier (UserID 2 ) of the user  308  to the forwarding service  300 . The forwarding service  300  records in the datastore  312  the consumption of the recommendation by the user  308  of the pURI 1 , creates a mapping between the pURI 1  and the UserID 2 , finds the mapping associated with the pURI 1  in the datastore  312 , and returns the corresponding gURI to the user  308  (or redirects the user  308 &#39;s browser to the resource identified by the gURI). In this manner, the user  308  can access the web site  306 . By maintaining both the initial recommendation by the user  304  and the consumption of the recommendation by the user  308 , the forwarding service  300  can track personal recommendations made online and their effectiveness. 
     In the example of  FIG. 3 , the user  308  also decides to recommend the website  306  to another user  320 . In this context, the user  308  now takes the role of a recommending user in relation to the user  320 &#39;s role as a consuming user. In one implementation, not shown in  FIG. 3 , the user identifier of the user  320  (UserID 2 ) and the gURI of the website  306  are submitted to the forwarding service  300 , which maps and records as described previously, and returns a new trackable recommendation identifier (pURI 2 ) to the user  308 . The user  308  can then send a recommendation message  318  containing pURI 2  to the user  320 . Upon receipt of the recommendation message  318 , the user  320  can submit pURI 2  to the forwarding service  300 . The forwarding service  300  records and maps as described previously, and returns the corresponding gURI to the user  320  (or redirects the user  320 &#39;s browser to the resource identified by the gURI). In this manner, the user  320  can access the recommended web site  306 . In this implementation, the forwarding service  300  maintains relevant recommendation information, but only one level of recommendation. 
     In an alternative implementation, as shown in  FIG. 3 , the user  308  can submit UserID 2  and pURI 1  to the forwarding service  300 , which creates a new trackable recommendation identifier (pURI 2 ), a mapping between the gURI and the pURI 2 , a mapping between the UserID and the pURI 2 , and a new mapping showing the multiple levels of recommendation from user  304  to user  308  to user  320 . In this manner, the forwarding service  300  can track propagation of recommendations through multiple users. The forwarding service  300  then sends the pURI 2  back to the user  308 , who sends a recommendation message  318  containing the pURI 2  to the user  320 . The number of recommendation levels maintained by the forwarding service  300  are unlimited by the described technology. 
     Upon receipt of the recommendation message  318 , the user  320  can trigger submission of the pURI 2  in the recommendation message  318  and the user identifier (UserID 3 ) of the user  320  to the forwarding service  300 . The forwarding service  300  records and maps as described previously, and returns the corresponding gURI to the user  320  (or redirects the user  320 &#39;s browser to the resource identified by the gURI). In this manner, the user  320  can access the recommended web site  306 . 
     Additional information may also be received by the forwarding service  300 , including timestamps, GPS coordinates and other information, recommendation qualifiers, consumption qualifiers, etc. By maintaining the recommendation by the users  304  and  308  and the consumptions by the users  308  and  320 , the forwarding service  300 , an ad service  314 , or other means can track personal recommendations made online and their effectiveness. Records of such recommendations can also be stored in and/or distributed to other datastores, such as datastore  316 . 
     Some benefits to the described technology include measuring the effectiveness of recommendations, determining who can influence the purchasing actions of whom, how strong is this influence, etc. Furthermore, political campaigns can use trackable online recommendations to analyze the impact of various news items, the popularity of candidates and issues, etc. 
     By reconstructing the flow of recommendations, a forwarding service and/or ad service can reward individuals based on the actual causal influence associated with their online recommendations. A recommending user and/or a consuming user may be credited with any valuable reward, including mere recognition, tradable/marketable points, free or reduced priced goods/services, etc. 
       FIG. 4  illustrates example operations  400  for a recommending phase of tracking online recommendations. A receiving operation  402  receives a UserID and a gURI or pURI from a recommending user. For example, if the recommending user is recommending a previously untracked resource identifier, then the associated gURI is received via the receiving operation  402  to record the recommendation and generate a new trackable recommendation identifier (e.g., a new pURI) in a generating operation  404 . In contrast, if the recommending user is recommending a previously generated trackable recommendation identifier, then the associated pURI is received via the receiving operation  402  to record the new recommendation and to generate a new trackable recommendation identifier (e.g., a new pURI) in the generating operation  404 . 
     A mapping operation  406  maps the UserID to the new pURI and maps the received gURI or pURI to the new pURI. In this manner, the mapping allows the recommending user to be identified using the new pURI and allows the new pURI to be translated back into the gURI when the new pURI is submitted by a consuming user (i.e., the user that receives and acts on the recommendation). A sending operation  408  returns the new pURI to the recommending user. 
       FIG. 5  illustrates example operations  500  for a consuming phase of tracking online recommendations. A receiving operation  502  receives a UserID and pURI from a consuming user. A credit operation  504  maps the received pURI to one or more recommending users based on one or more user mappings and credits such recommending users with a consumed recommendation. A mapping operation  506  maps the UserID of the consuming user to the pURI. In this manner, the mapping allows the consuming user to be identified using the pURI. In an alternative implementation, receipt and mapping of the consuming user&#39;s user identifier may be omitted. 
     A translation operation  508  looks up a gURI based on the pURI. In some circumstances, the translation operation  508  requires only one lookup stage (e.g., if the pURI is associated with a single level recommendation). In other circumstances, the translation operation  508  may required multiple lookup stages (e.g., if the pURI is associated with a single level recommendation). The translation operation  508  yields a gURI associated with the original recommendation, and a returning operation  510  returns the gURI to the consuming user (or redirects the consuming user&#39;s browser to the network resource identified by the gURI). 
       FIG. 6  illustrates a graph  600  of an example recommendation flow, although another datastore, such as a table may be employed. An original recommending user  602  sends trackable recommendations to three users,  604 ,  606 , and  608 . A user  604  forwards the recommendation to another user  610 ; the user  606  forwards the recommendation to users  612  and  614 ; the user  608  also forwards the recommendation to the user  614 . The user  614  forwards the recommendation to the user  612 , who forwards the recommendation to a user  616 . The user  616  forwards the recommendation to a consuming user  618 , who visits the website to evaluate the product/service, purchases the recommended product/service, etc, which triggers an incentive. 
     In this example, the recommendations have traversed through one or more paths to the consuming user  618 , who acts in a way that triggers an incentive. Such triggering actions typically represent an action that the product or service vendor is intending to generate through recommendations and is therefore willing to provide rewards for recommendations that result in the actions. Example triggering actions may include an actual purchase but may also include an evaluation of the product or service, completion of a survey, provision of contact information for a follow up sales call, etc. Based on detection of a triggering action, the ad service can identify those users in the recommendation flow that are deemed deserving of an incentive and can therefore allocate a portion of that incentive one or more of these recommending users. 
     As shown in  FIG. 6 , one of the recommendations made by the original recommending user  602  (i.e., the recommendation forwarded to the user  604 ) is not shown as having resulted in the triggering action performed by the consuming user  618 . However, one or both of the recommendations forwarded to the user  606  and the user  608  may have contributed to the triggering action of consuming user  618 , as shown by the directed arcs flowing via various branches from the user  602  to the user  618 . Based on this recommendation flow, the users  602 ,  606 ,  608 ,  612 ,  614 ,  616 , and  618  are classified as being in a coalition  620  associated with the triggering action of the consuming user  618 . The coalition  620  is referred to as a “winning” coalition because it resulted in a trigger action. It should be understood that other coalitions also exists in the recommendation flow described by the graph  600 , such as a coalition including users  602  and  606 , another coalition including users  608 ,  614 , and  612 , another (winning) coalition including users  612 ,  616 , and  618 , etc., for a multitude of different coalitions (“cooperating combinations”) of users. These descriptions of these coalitions are input to the cooperative gaming engine and influence the “power” of each user in the recommendation flow. 
     Based on the identified coalition  620 , a description of the portion of the graph  600  within the coalition  620  is submitted to a cooperative gaming engine to determine the “power” of each user in the coalition  620  with reference to the triggering action. That is, the cooperative gaming engine determines how an incentive associated with the triggering action is to be allocated among the users in the coalition. 
     Generally, a cooperative game is composed of a set of n users, I, and a functional mapping of any coalition of the users to a real value ν: 2 I → . In one implementation, ν is constrained to values of 0 or 1 (e.g., ν: 2 I →{0,1}), such that a coalition C⊂I wins if ν(C)=1 and loses if wins if ν(C)=0. A user i is said to be critical in a winning coalition C if the user&#39;s removal from that coalition would make it a losing coalition. For example, the user  616  would be said to be critical in the winning coalition  620  of  FIG. 6 . A critical user has a strong influence on the result of the game, so this property is related to various measures of power. It should be understood that multiple users may be critical in the same coalition (see e.g., the user  612 , who is also critical). 
     An example approach to measuring the power of individual users in a recommendation flow is the Shapley-Shubik power index, which reflects the assumption that any ordering of the users entering the coalition has an equal probability of occurring. The Shapely-Shubik index is given by sh i (ν)=(sh i (ν), . . . , sh n (ν)), where 
                   sh   i     ⁡     (   v   )       =       1     n   !       ⁢       ∑     π   ⁢           ⁢   ε   ⁢           ⁢   Π       ⁢           ⁢     [       v   ⁡     (         S   π     ⁡     (   i   )       ⋃     {   i   }       )       -     v   ⁡     (       S   π     ⁡     (   i   )       )         ]           ,         
π denotes a permutation (reordering) of the users, so that π: {1, . . . , n}→{1, . . . } and π is reversible, Π denotes the set of all possible permutations, and S π (i) denotes the predecessors of i in π, so that S π (i)={j|π(j)&lt;π(i)}.
 
     The naïve implementation of calculating the Shapley-Shubik power index is computationally complex and may be impractical for applying to pricing in social advertising in some contexts. For example, for n users, there are n! permutations to consider. Using Stirling&#39;s approximation, there are about O(2 n log n ) permutations to evaluate, which presents potentially intractable computation obstacles without severe limitations. 
     Accordingly, an implementation of the described technology seeks to approximate Shapely-Shubik power indices by randomly sampling permutations of the users. Each sample is evaluated to determine whether a user i is critical in that sample. A user i is deemed critical in the returned permutation π (denoted as Critical(i, π) if:
 
ν( S   π ( i )∪{ i })−ν( S   π ( i ))=1
 
     After several sampled permutations of users are evaluated, the Shapley-Shubik power index sh i (ν) of the user i is estimated by the proportion of the sampled permutations where a user i is critical. Accordingly, the probability P that a user i is critical in a random permutation π is represented by its Shapley-Shubik power index:
 
 P   πεΠ (Critical( i ,π))= sh   i (ν)
 
     Given the probability P the random variable X j  can be defined by letting π j  be a random permutation, with X j  being 1 if the user i is critical in π j  and being 0 if the user i is not critical in π j , the maximum likelihood estimator for sh i (ν), where k represents the number of sample permutations, is determined by 
     
       
         
           
             
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     A confidence interval for the estimator sĥ i (ν) may be computed to provide a bound on the probability that this value is approximately correct. Given the sample of X 1 , . . . , X k  of k samples, a confidence interval of [sĥ i (ν)−ε,sĥ i (ν)+ε] includes values that are within a distance of ε from the correct power index value, sh i (ν) (e.g., values that are within an acceptable level of accuracy). A probability δ also is defined, representing the low probability that the correct power index sh i (ν) is not within the confidence interval. Accordingly, the confidence interval is defined as centered at sĥ i (ν), having a width of 2·ε&gt;0, and containing the correct power index value, sh i (ν), with a probability of at least 1−δ. 
     Using Hoeffding&#39;s inequality, relationships among the number of samples k, the confidence level δ, and the “accuracy” level ε (i.e., the width parameter of the confidence interval), yielding: 
     
       
         
           
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     Using the estimator sĥ i (ν) and the confidence interval, the power of the individual users can be ranked (e.g., to allocate portions of the incentive to different users based on the power rankings). In order to rank the users according to their power indices, the users are sorted according to the intervals&#39; centers. If no two intervals c intersect and if each interval c i  contains the actual power index of the user i so that sh i (ν)εc i , the sort results in the correct rankings. 
     In the context of allocating an incentive to users in a recommendation flow, the power indices of all users in a winning coalition sum to one. As such, the incentive can be allocated in accordance with relative power indices. For example, if a $100 incentive is to be shared among three users of a winning coalition, wherein the three users have power indices of 0.1, 0.3, and 0.6 respectively, then the incentive would be allocated as $10 to one user, $30 to another user, and $60 to the last user. 
     Although a particular approximation approach is described for determining Shapley-Shubik power indices, other methods may also be employed. For example, generating functions may be used to compute power indices efficiently in some contexts. Methods for computing a Banzhaf value using multilinear extensions may be employed, and the Banzhaf value may be employed in a manner similar to the Shapley value to develop a power indices. A Shapley value may also be approximated using a Monte-Carlo approach in one implementation, and a Shapely-Shubik power index of weighted voting game may be calculated using a randomized method in another implementation. Accordingly, various detailed approaches may be employed to develop the power indices described herein. 
       FIG. 7  illustrates example operations  700  for allocating incentives in an online recommendation flow. A tracking operation  702  tracks one or more recommendations in a recommendation flow. In one implementation, a trackable recommendation identifier may be handled and stored by a forwarding service, although other tracking techniques may be employed, such as maintaining all recommendations, tracking, and purchase handling within a single web service. A storage operation  704  stores the recommendation flow information in a datastore. 
     A graphing operation  706  generates a graph of the recommendation flow based on the recommendation flow information in the data store. In one implementation, each user in the recommendation flow is represented as a vertex in the graph, and each recommendation is represented as a arc or edge in the graph. 
     A game description operation  708  determines a winning coalition within the graph, generates an induced graph containing only the users (vertices) of the winning coalition and the recommendations (edges) that connect them, and identifies the various users as recommending users or consuming users. 
     Note: A cooperative game provides a mapping from coalitions to values. The value of a coalition is defined through the game description (e.g., a graph, table, etc.). In one implementation, a coalition has a value of 1 if it connects the source of the recommendation to the consuming user. In an alternative implementation, a value of a coalition is the number of recommending users connected with the consuming user in the game description. In yet another implementation, the value of the coalition is 1 if it connects the source of the recommendation to the consuming users through graph paths in which all of the edges in the path have a weight of at least 0.5. These implementations are merely examples and many other implementations may be employed. 
     A power index operation  710  determines the power index of each flow participant represented in the induced graph. The power index approximation described with regard to  FIG. 6  provides one implementation for determining the power indices, although other brute force and approximation methods may be employed. An allocation operation  712  allocates portions of an incentive to the flow participants based on the computed power indices. 
       FIG. 8  illustrates an example system that may be useful in implementing the described technology. The example hardware and operating environment of  FIG. 8  for implementing the described technology includes a computing device, such as general purpose computing device in the form of a gaming console or computer  20 , a mobile telephone, a personal data assistant (PDA), a set top box, or other type of computing device. In the implementation of  FIG. 8 , for example, the computer  20  includes a processing unit  21 , a system memory  22 , and a system bus  23  that operatively couples various system components including the system memory to the processing unit  21 . There may be only one or there may be more than one processing unit  21 , such that the processor of computer  20  comprises a single central-processing unit (CPU), or a plurality of processing units, commonly referred to as a parallel processing environment. The computer  20  may be a conventional computer, a distributed computer, or any other type of computer; the invention is not so limited. 
     The system bus  23  may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, a switched fabric, point-to-point connections, and a local bus using any of a variety of bus architectures. The system memory may also be referred to as simply the memory, and includes read only memory (ROM)  24  and random access memory (RAM)  25 . A basic input/output system (BIOS)  26 , containing the basic routines that help to transfer information between elements within the computer  20 , such as during start-up, is stored in ROM  24 . The computer  20  further includes a hard disk drive  27  for reading from and writing to a hard disk, not shown, a magnetic disk drive  28  for reading from or writing to a removable magnetic disk  29 , and an optical disk drive  30  for reading from or writing to a removable optical disk  31  such as a CD ROM or other optical media. 
     The hard disk drive  27 , magnetic disk drive  28 , and optical disk drive  30  are connected to the system bus  23  by a hard disk drive interface  32 , a magnetic disk drive interface  33 , and an optical disk drive interface  34 , respectively. The drives and their associated computer-readable media provide nonvolatile storage of computer-readable instructions, data structures, program modules and other data for the computer  20 . It should be appreciated by those skilled in the art that any type of computer-readable media which can store data that is accessible by a computer, such as magnetic cassettes, flash memory cards, digital video disks, random access memories (RAMs), read only memories (ROMs), and the like, may be used in the example operating environment. 
     A number of program modules may be stored on the hard disk, magnetic disk  29 , optical disk  31 , ROM  24 , or RAM  25 , including an operating system  35 , one or more application programs  36 , other program modules  37 , and program data  38 . A user may enter commands and information into the personal computer  20  through input devices such as a keyboard  40  and pointing device  42 . Other input devices (not shown) may include a microphone, joystick, game pad, satellite dish, scanner, or the like. These and other input devices are often connected to the processing unit  21  through a serial port interface  46  that is coupled to the system bus, but may be connected by other interfaces, such as a parallel port, game port, or a universal serial bus (USB). A monitor  47  or other type of display device is also connected to the system bus  23  via an interface, such as a video adapter  48 . In addition to the monitor, computers typically include other peripheral output devices (not shown), such as speakers and printers. 
     The computer  20  may operate in a networked environment using logical connections to one or more remote computers, such as remote computer  49 . These logical connections are achieved by a communication device coupled to or a part of the computer  20 ; the invention is not limited to a particular type of communications device. The remote computer  49  may be another computer, a server, a router, a network PC, a client, a peer device or other common network node, and typically includes many or all of the elements described above relative to the computer  20 , although only a memory storage device  50  has been illustrated in  FIG. 8 . The logical connections depicted in  FIG. 8  include a local-area network (LAN)  51  and a wide-area network (WAN)  52 . Such networking environments are commonplace in office networks, enterprise-wide computer networks, intranets and the Internet, which are all types of networks. 
     When used in a LAN-networking environment, the computer  20  is connected to the local network  51  through a network interface or adapter  53 , which is one type of communications device. When used in a WAN-networking environment, the computer  20  typically includes a modem  54 , a network adapter, a type of communications device, or any other type of communications device for establishing communications over the wide area network  52 . The modem  54 , which may be internal or external, is connected to the system bus  23  via the serial port interface  46 . In a networked environment, program modules depicted relative to the personal computer  20 , or portions thereof, may be stored in the remote memory storage device. It is appreciated that the network connections shown are example and other means of and communications devices for establishing a communications link between the computers may be used. 
     In an example implementation, a forwarding service, an ad service, and other modules and services may be embodied by instructions stored in memory  22  and/or storage devices  29  or  31  and processed by the processing unit  21 . A UserIDs, mappings, recommendation qualifiers, power indices, timestamps, and other data may be stored in memory  22  and/or storage devices  29  or  31  as persistent datastores. Further, a forwarding service and an ad service represent hardware and/or software configured to provide service functionality for network-connected systems. Such services may be implemented using a general purpose computer and specialized software (such as a server executing service software), a special purpose computing system and specialized software (such as a mobile device or network appliance executing service software), or other computing configurations. 
     The embodiments of the invention described herein are implemented as logical steps in one or more computer systems. The logical operations of the present invention are implemented (1) as a sequence of processor-implemented steps executing in one or more computer systems and (2) as interconnected machine or circuit modules within one or more computer systems. The implementation is a matter of choice, dependent on the performance requirements of the computer system implementing the invention. Accordingly, the logical operations making up the embodiments of the invention described herein are referred to variously as operations, steps, objects, or modules. Furthermore, it should be understood that logical operations may be performed in any order, unless explicitly claimed otherwise or a specific order is inherently necessitated by the claim language. 
     The above specification, examples, and data provide a complete description of the structure and use of exemplary embodiments of the invention. Since many embodiments of the invention can be made without departing from the spirit and scope of the invention, the invention resides in the claims hereinafter appended. Furthermore, structural features of the different embodiments may be combined in yet another embodiment without departing from the recited claims.