Introducing revenue-generating features

1. A computing device for determining a number of periods for introducing revenue-generating inconvenience to a service by a service provider, the computing device comprising:

a processor to:

identify a probability function describing a probability that a user will continue to utilize the service based on a level of inconvenience introduced to the service,

determine whether the probability function is logarithmically convex,

determine, when the probability function is logarithmically convex, that the level of inconvenience should be introduced in a single increase to generate revenue, and

determine, when the probability function is not logarithmically convex, a number of periods for introducing the level of inconvenience that generates revenue over time.

2. The computing device of claim 1 , wherein the processor identifies the probability function as a plurality of data points, each data point representing a probability that the user will continue utilizing the service when a corresponding level of inconvenience is introduced to the service.

3. The computing device of claim 1 , wherein, when the probability function is logarithmically convex, the processor determines that the level of inconvenience should be introduced in a single increase to maximize total revenue earned by the service provider.

4. The computing device of claim 3 , wherein, when the probability function is logarithmically convex, the processor further:

determines the level of inconvenience as a value that maximizes the probability function for a particular level of inconvenience multiplied by a revenue earned by the service provider for the particular level of inconvenience.

5. The computing device of claim 1 , wherein, when the probability function is not logarithmically convex, the processor further:

determines the number of periods and the level of inconvenience by solving an optimization problem to maximize a total revenue earned over future periods, wherein:

the total revenue is a sum of a revenue calculated for each future period, and

the revenue for each future period is a revenue value for a current level of inconvenience during the period multiplied by a fraction of users remaining during the period as predicted using the probability function.

6. The computing device of claim 5 , wherein, in determining the fraction of users remaining during each period, the processor considers a cumulative effect of multiple introductions of inconvenience on the probability that the user will continue to utilize the service.

7. The computing device of claim 1 , wherein the service is a website and the inconvenience is at least one of a number of advertisements and a subscription fee.

8. A machine-readable storage medium encoded with instructions executable by a processor of a computing device for determining a number of periods over which a level of revenue-generating inconvenience should be introduced to a service by a service provider, the machine-readable storage medium comprising:

instructions for identifying a probability function describing a probability that a user will continue to utilize the service as a function of a level of inconvenience introduced to the service;

instructions for determining whether the probability function is logarithmically convex; and

instructions for determining the number of periods over which the level of inconvenience should be introduced to the service to generate revenue for the service provider based on whether the probability function is logarithmically convex or not logarithmically convex.

9. The machine-readable storage medium of claim 8 , wherein the instructions for identifying the probability function identify a plurality of data points, each data point representing the probability that the user will continue to utilize the service when a corresponding level of inconvenience is introduced.

10. The machine-readable storage medium of claim 9 , wherein the instructions for identifying the probability function determine the plurality of data points based on at least one of:

a testing procedure by which a control sample of users to which no inconvenience is introduced is compared to a test sample of users to which varying levels of inconvenience are introduced, and

a survey procedure by which a test sample of users are queried to determine whether the users would continue to utilize the service when varying levels of inconvenience are introduced.

11. The machine-readable storage medium of claim 9 , wherein the instructions for determining whether the probability function, p(x), is logarithmically convex comprise:

instructions for calculating a value, θ, for each set of consecutive data points, x i−1 , x i , and x i+1 , wherein:

θ

=

x

i

+

1

-

x

i

x

i

+

1

-

x

i

-

1

;

instructions for determining, for each set of consecutive data points, whether an inequality is satisfied, wherein the inequality is:

log( p ( x i ))≦θ log( p ( x i−1 ))+(1−θ)log( p ( x i+1 )); and

instructions for determining that the probability function is logarithmically convex when the inequality is satisfied for all sets of consecutive data points and otherwise determining that the probability function is not logarithmically convex.

12. The machine-readable storage medium of claim 8 , wherein, when the probability function is logarithmically convex, the instructions for determining the number of periods over which the level of inconvenience should be introduced determine the number of periods to be 1, such that the level of inconvenience is introduced in a single increase.

13. The machine-readable storage medium of claim 12 , wherein the instructions for determining the number of periods further comprise:

instructions for calculating the level of inconvenience as a value that maximizes a revenue function, wherein the revenue function is defined as the probability function for a particular level of inconvenience multiplied by a revenue earned by the service provider for the particular level of inconvenience.

14. The machine-readable storage medium of claim 8 , wherein, when the probability function is not logarithmically convex, the instructions for determining the number of periods over which the level of inconvenience should be introduced comprise:

instructions for solving an optimization problem to find the number of periods and the level of inconvenience that maximize a revenue function representing a total revenue earned over future periods, wherein the revenue for each future period is equal to a value representing a fraction of remaining users predicted using the probability function multiplied by a potential revenue for the future period.

15. The machine-readable storage medium of claim 14 , wherein, in determining the value representing the fraction of remaining users, the instructions for solving the optimization problem consider a cumulative effect of multiple introductions of inconvenience on the probability that the user will continue to utilize the service.

16. A method for adding revenue-generating features to a website in a manner that generates revenue, the method comprising:

identifying, by a computing device, a probability function representing a probability that a user will continue using the website as a function of a number of increases in revenue-generating features in the website;

determining whether the probability function is logarithmically convex;

determining a number of periods over which the revenue-generating features should be added to the website based on whether the probability function is logarithmically convex or not logarithmically convex; and

adding the revenue-generating features to the website over the determined number of periods.

17. The method of claim 16 , wherein identifying the probability function comprises:

determining a plurality of data points, each data point representing the probability that the user will continue using the website when a corresponding level of revenue-generating features is added to the website.

18. The method of claim 16 , wherein identifying the probability function comprises:

adding a number of revenue-generating features for a subset of users of the website; and

determining the probability function based on a fraction of users in the subset of users that continue using the website after adding the number of revenue-generating features.

19. The method of claim 16 , wherein, when the probability function is logarithmically convex, determining the number of periods comprises:

determining that the revenue-generating features should be added to the website in a single increase equal to a total number of revenue-generating features; and

calculating the total number of revenue-generating features as a value that maximizes the probability function for a particular number of revenue-generating features multiplied by a revenue earned for the particular number of revenue-generating features.

20. The method of claim 16 , wherein, when the probability function is not logarithmically convex, determining the number of periods comprises:

solving an optimization problem to determine the number of periods and a number of revenue-generating features to be added during each period that maximizes a revenue function representing a total revenue earned by the revenue-generating features over future periods.