Advertising Exchange System Valuation of Information Services
Disclosed is a system to price usage of a user-action Probability estimation system provided by an advertising exchange system. A bid from each bidder in an auction for an advertising opportunity is presented in a computer. The bidders comprise a first group of bidders that utilize the Probability estimation system and a second group of bidders that do not utilize the Probability estimation system. The bids are processed by determining a first equilibrium bid for a first bidder as a member of the first group. The bids are further processed by determining a second equilibrium bid for the first bidder as a member of the second group. The system then utilizes the first equilibrium bid and the second equilibrium bid to determine a value of utilizing the Probability estimation system.
1 . A method to price usage of a probability estimation system provided by an advertising exchange system for use in that advertising exchange system, the method comprising:
presenting, at a computer, a bid from each bidder in an auction for an advertising opportunity, where the bidders comprise a first group of bidders that utilize the probability estimation system and a second group of bidders that do not utilize the probability estimation system;
processing, in the computer, the bids by:
determining a first equilibrium bid for a first bidder as a member of the first group of bidders,
determining a second equilibrium bid for the first bidder as a member of the second group of bidders, and
utilizing the first equilibrium bid and the second equilibrium bid to determine a value of utilizing the Probability estimation system.
2 . The method of claim 1 , where the equilibrium bid for the first bidder as a member of the second group of bidders is a product of an expected value that utilizes probability estimation signals provided by bidders in the second group of bidders, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
3 . The method of claim 2 , where the equilibrium bid for the first bidder as a member of the second group of bidders is determined according to the equation
b
i
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
s
i
]
F
(
1
)
n
(
β
1
-
1
(
b
)
)
F
(
1
)
k
-
1
(
β
2
-
1
(
b
)
|
s
i
)
where,
*=denotes equilibrium,
i=a generic index identifying a bidder i,
b i *=effective CPM equilibrium bid for each second group k-bidder i, i=1, . . . , n+k,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|s i ]=a difference between an expected value of revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given s i ,
s i =a probability estimation signal provided by a bidder i in the second group of bidders,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 an equilibrium strategy function in a symmetric equilibrium for k-bidders not accessing a Probability estimation system, a probability distribution function of a first order statistic out of n draws
F (1) n (β 1 −1 (b))=of an inverse of an equilibrium bid function for a given b value, and
F (1) k−1 (β 2 −1 (b)|s i )=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value given s i .
4 . The method of claim 1 , where the equilibrium bid for the first bidder as a member of the first group of bidders is a product of an expected value that utilizes a probability estimation signal provided by a Probability estimation system of the advertising exchange system, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
5 . The method of claim 4 , where the equilibrium bid for the first bidder is determined according to the equation
b
j
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
π
]
F
(
1
)
n
-
1
(
β
1
-
1
(
b
)
)
F
(
1
)
k
(
β
2
-
1
(
b
)
)
where,
*=denotes equilibrium,
b j *=effective CPM equilibrium bid for each second group n-bidder j, j=1, . . . , n,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|π]=is a difference between an expected value of a revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given π,
π: π=p+ε, where π is an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
p=a true action probability of an advertising opportunity,
ε=is a noise term in a system's probability estimation,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 =an equilibrium strategy function in a symmetric equilibrium for k-bidders lacking access to a Probability estimation system,
F (1) n−1 (β 1 −1 (b))=a probability distribution function of a first order statistic out of n draws of an inverse of an equilibrium bid function for a given b value, and
F (1) k (β 2 −1 (b))=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value.
6 . The method of claim 1 , further comprising:
estimating, in the computer, a probability variance on a conversion probability estimator;
determining, in the computer, the value of utilizing the probability estimation by subtracting the first equilibrium bid from the second equilibrium bid;
obtaining, in the computer, an empirical distribution of the number of bidders in the first group of bidders and the number of bidders in the second group of bidders; and
calculating, in the computer, an expected added value for a bidder in the second group of bidders for usage of the Probability estimation system.
7 . The method of claim 6 , further comprising:
utilizing a probability variance estimator to estimate the probability variance on the conversion probability estimator.
8 . The method of claim 6 , further comprising:
applying the value of utilizing the probability estimation as an upper bound on the price charged to a bidder in the second group of bidders.
9 . The method of claim 6 , where the expected added value for a bidder in the second group of bidders is a difference between an expected profit for a bidder utilizing a Probability estimation system provided by the advertising exchange system and an expected profit for a bidder not utilizing a Probability estimation system provided by the advertising exchange system.
10 . The method of claim 9 , where calculating the expected added value for a bidder in the second group of bidders includes utilizing the equation
Δ( n,k )= E v,p,π [( pv−b j n+1,k−1 (π))|π]− E v,p,s [( pv−b j n,k ( s ))| s i ]
where,
n=a number of bidders who are part of the first group of bidders that utilize a Probability estimation system,
k=a number of bidders who are part of a second group of bidders that do not utilize a Probability estimation system,
Δ(n,k)=a value of a Probability estimation system service to the i th bidder in the second group of bidders,
p=a true action probability of an advertising opportunity,
π=an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
b i =effective CPM bid price for each bidder i, i=1, . . . , n+k,
v=an expected revenue for a given bidder from an auctioned impression provided that a consumer takes actions using an ad,
s=an estimate for a probability of action by a bidder in the second group of bidders,
E v,p,π [(pv−b j n+1,k−1 (π))|π]=an expected profit for a bidder in the second group of bidders when that bidder purchases information from the advertising exchange system and becomes a bidder in the first group of bidders, and
E v,p,s [(pv−b j n,k (s i ))|s i ]=an expected profit for a bidder in the second group of bidders when that bidder does not purchase information from the advertising exchange system to remain as a bidder in the second group of bidders.
11 . A computer readable medium containing executable instructions stored thereon, which, when executed in a computer, cause the computer to price usage of a Probability estimation system provided by an advertising exchange system for use in that advertising exchange system, the instructions for:
presenting, at a computer, a bid from each bidder in an auction for an advertising opportunity, where the bidders comprise a first group of bidders that utilize the Probability estimation system and a second group of bidders that do not utilize the Probability estimation system;
processing, in the computer, the bids by:
determining a first equilibrium bid for a first bidder as a member of the first group of bidders,
determining a second equilibrium bid for the first bidder as a member of the second group of bidders, and
utilizing the first equilibrium bid and the second equilibrium bid to determine a value of utilizing the Probability estimation system.
12 . The computer readable medium of claim 11 , where the equilibrium bid for the first bidder as a member of the second group of bidders is a product of an expected value that utilizes probability estimation signals provided by bidders in the second group of bidders, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
13 . The computer readable medium of claim 12 , where the equilibrium bid for the first bidder as a member of the second group of bidders is determined according to the equation
b
i
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
s
i
]
F
(
1
)
n
(
β
1
-
1
(
b
)
)
F
(
1
)
k
-
1
(
β
2
-
1
(
b
)
|
s
i
)
where,
*=denotes equilibrium,
i=a generic index identifying a bidder i,
b i *=effective CPM equilibrium bid for each second group k-bidder i, i=1, . . . , n+k,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|s i ]=a difference between an expected value of revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given s i ,
s i =a probability estimation signal provided by a bidder i in the second group of bidders,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 an equilibrium strategy function in a symmetric equilibrium for k-bidders not accessing a Probability estimation system,
F (1) n (β 1 −1 (b))=a probability distribution function of a first order statistic out of n draws of an inverse of an equilibrium bid function for a given b value, and
F (1) k−1 =(β 2 −1 (b)|s 1 )=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value given s i .
14 . The computer readable medium of claim 11 , where the equilibrium bid for the first bidder as a member of the first group of bidders is a product of an expected value that utilizes a probability estimation signal provided by a Probability estimation system of the advertising exchange system, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
15 . The computer readable medium of claim 14 , where the equilibrium bid for the first bidder is determined according to the equation
b
j
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
π
]
F
(
1
)
n
-
1
(
β
1
-
1
(
b
)
)
F
(
1
)
k
(
β
2
-
1
(
b
)
)
where,
*=denotes equilibrium,
b j *=effective CPM equilibrium bid for each second group n-bidder j, j=1, . . . , n,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|π]=is a difference between an expected value of a revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given π,
π: π=p+ε, where π is an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
p=a true action probability of an advertising opportunity,
ε=is a noise term in a system's probability estimation,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 =an equilibrium strategy function in a symmetric equilibrium for k-bidders lacking access to a Probability estimation system,
F (1) n−1 (β 1 −1 (b))=a probability distribution function of a first order statistic out of n draws of an inverse of an equilibrium bid function for a given b value, and
F (1) k β 1 −1 (b))=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value.
16 . The computer readable medium of claim 11 , further comprising:
estimating, in the computer, a probability variance on a conversion probability estimator;
determining, in the computer, the value of utilizing the probability estimation by subtracting the first equilibrium bid from the second equilibrium bid;
obtaining, in the computer, an empirical distribution of the number of bidders in the first group of bidders and the number of bidders in the second group of bidders; and
calculating, in the computer, an expected added value for a bidder in the second group of bidders for usage of the Probability estimation system.
17 . The computer readable medium of claim 16 , further comprising:
utilizing a probability variance estimator to estimate the probability variance on the conversion probability estimator.
18 . The computer readable medium of claim 16 , further comprising:
applying the value of utilizing the probability estimation as an upper bound on the price charged to a bidder in the second group of bidders.
19 . The computer readable medium of claim 16 , where the expected added value for a bidder in the second group of bidders is a difference between an expected profit for a bidder utilizing a Probability estimation system provided by the advertising exchange system and an expected profit for a bidder not utilizing a Probability estimation system provided by the advertising exchange system.
20 . The computer readable medium of claim 19 , where calculating the expected added value for a bidder in the second group of bidders includes utilizing the equation
Δ( n,k )= E v,p,π[( pv−b j n+1,k−1 (π))|π]− E v,p,s [( pv−b j n,k ( s ))| s i ]
where,
n=a number of bidders who are part of the first group of bidders that utilize a Probability estimation system,
k=a number of bidders who are part of a second group of bidders that do not utilize a Probability estimation system,
Δ(n,k)=a value of a Probability estimation system service to the i th bidder in the second group of bidders,
p=a true action probability of an advertising opportunity,
π=an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
b i =effective CPM bid price for each bidder i, i=1, . . . , n+k,
v=an expected revenue for a given bidder from an auctioned impression provided that a consumer takes actions using an ad,
s=an estimate for a probability of action by a bidder in the second group of bidders,
E v,p,π[(pv−b j n+1,k−1 (π))|π]=an expected profit for a bidder in the second group of bidders when that bidder purchases information from the advertising exchange system and becomes a bidder in the first group of bidders, and
E v,p,s [(pv−b j n,k (s i ))|s i ]=an expected profit for a bidder in the second group of bidders when that bidder does not purchase information from the advertising exchange system to remain as a bidder in the second group of bidders.
23 . A system to price usage of a Probability estimation system provided by the system for use in that system, the system comprising:
at least one server, comprising at least one processor and memory, to present a bid from each bidder in an auction for an advertising opportunity, where the bidders comprise a first group of bidders that utilize the Probability estimation system and a second group of bidders that do not utilize the Probability estimation system; and
a processing platform, comprising at least one processor and memory, coupled to the server to process the bids by determining a first equilibrium bid for a first bidder as a member of the first group of bidders, determining a second equilibrium bid for the first bidder as a member of the second group of bidders, and utilizing the first equilibrium bid and the second equilibrium bid to determine a value of utilizing the Probability estimation system.
24 . The system of claim 23 , where the equilibrium bid for the first bidder as a member of the second group of bidders is a product of an expected value that utilizes probability estimation signals provided by bidders in the second group of bidders, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
25 . The system of claim 24 , where the equilibrium bid for the first bidder as a member of the second group of bidders is determined according to the equation
b
i
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
s
i
]
F
(
1
)
n
(
β
1
-
1
(
b
)
)
F
(
1
)
k
-
1
(
β
2
-
1
(
b
)
|
s
i
)
where,
*=denotes equilibrium,
i=a generic index identifying a bidder i,
b i *=effective CPM equilibrium bid for each second group k-bidder i, i=1, . . . , n+k,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|s i ]=a difference between an expected value of revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given s i ,
s i =a probability estimation signal provided by a bidder i in the second group of bidders,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 an equilibrium strategy function in a symmetric equilibrium for k-bidders not accessing a Probability estimation system, a probability distribution function of a first order statistic out of n draws
F (1) n (β 1 −1 (b))=of an inverse of an equilibrium bid function for a given b value, and
F (1) k−1 (β 2 −1 (b)|s 1 )=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value given s i .
26 . The system of claim 23 , where the equilibrium bid for the first bidder as a member of the first group of bidders is a product of an expected value that utilizes a probability estimation signal provided by a Probability estimation system of the advertising exchange system, a probability distribution function out of a first number of draws, and a probability distribution function out of a second number of draws.
27 . The system of claim 26 , where the equilibrium bid for the first bidder is determined according to the equation
b
j
*
=
arg
max
b
E
[
(
p
·
v
i
-
b
)
|
π
]
F
(
1
)
n
-
1
(
β
1
-
1
(
b
)
)
F
(
1
)
k
(
β
2
-
1
(
b
)
)
where,
*=denotes equilibrium,
b j *=effective CPM equilibrium bid for each second group n-bidder j, j=1, . . . , n,
arg max=stands for an argument of a maximum, that is to say, a set of points of a given argument for which a value of a given expression attains its maximum value,
E[(p·v i −b)|π]=is a difference between an expected value of a revenue a bidder can make from an impression auctioned (p·v i ) and a bid (b) given π,
π: π=p+ε, where π is an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
p=a true action probability of an advertising opportunity,
ε=is a noise term in a system's probability estimation,
β 1 =an equilibrium strategy function in a symmetric equilibrium for n-bidders accessing a Probability estimation system,
β 2 =an equilibrium strategy function in a symmetric equilibrium for k-bidders lacking access to a Probability estimation system,
F (1) n−1 (β 1 −1 (b))=a probability distribution function of a first order statistic out of n draws of an inverse of an equilibrium bid function for a given b value, and
F (1) k (β 2 −1 (b))=a probability distribution function of a first order statistic out of k−1 draws of an inverse of an equilibrium bid function for a given b value.
28 . The system of claim 23 , the processing platform further for
estimating, in the computer, a probability variance on a conversion probability estimator;
determining, in the computer, the value of utilizing the probability estimation by subtracting the first equilibrium bid from the second equilibrium bid;
obtaining, in the computer, an empirical distribution of the number of bidders in the first group of bidders and the number of bidders in the second group of bidders; and
calculating, in the computer, an expected added value for a bidder in the second group of bidders for usage of the Probability estimation system.
29 . The system of claim 28 , the processing platform further for
utilizing a probability variance estimator to estimate the probability variance on the conversion probability estimator.
30 . The system of claim 28 , the processing platform further for
applying the value of utilizing the probability estimation as an upper bound on the price charged to a bidder in the second group of bidders.
31 . The system of claim 28 , where the expected added value for a bidder in the second group of bidders is a difference between an expected profit for a bidder utilizing a Probability estimation system provided by the advertising exchange system and an expected profit for a bidder not utilizing a Probability estimation system provided by the advertising exchange system.
32 . The system of claim 31 , where calculating the expected added value for a bidder in the second group of bidders includes utilizing the equation
Δ( n,k )= E v,p,π [( pv−b j n+1,k−1 (π))|π]− E v,p,s [( pv−b j n,k ( s ))| s i ]
where,
n=a number of bidders who are part of the first group of bidders that utilize a Probability estimation system,
k=a number of bidders who are part of a second group of bidders that do not utilize a Probability estimation system,
Δ(n,k)=a value of a Probability estimation system service to the i th bidder in the second group of bidders,
p=a true action probability of an advertising opportunity,
π=an optimal estimation of p provided by a Probability estimation system of the advertising exchange system,
b i =effective CPM bid price for each bidder i, i=1, . . . , n+k,
v=an expected revenue for a given bidder from an auctioned impression provided that a consumer takes actions using an ad,
s=an estimate for a probability of action by a bidder in the second group of bidders,
E v,p,π[(pv−b j n+1,k−1 (π))|π]=an expected profit for a bidder in the second group of bidders when that bidder purchases information from the advertising exchange system and becomes a bidder in the first group of bidders, and
E v,p,s [(pv−b j n,k (s i ))|s i ]=an expected profit for a bidder in the second group of bidders when that bidder does not purchase information from the advertising exchange system to remain as a bidder in the second group of bidders.