Algorithms, Incentives, and Multidimensional Preferences
Nima Haghpanah (MIT)
January 15, 2016
1/4
Algorithms and Incentives
Past: Algorithms as black box
Now: Algorithm as Platform
User
Input
Algorithm
User
Output
Algorithm
2/4
Algorithms and Incentives
Past: Algorithms as black box
Now: Algorithm as Platform
User
Input
Algorithm
User
Output
Algorithm
Examples:
I
Routing Protocols
I
Crowdsourcing
I
Electronic Commerce, Sharing Economy
2/4
Algorithms and Incentives
Past: Algorithms as black box
Now: Algorithm as Platform
User
Input
Algorithm
User
Output
Algorithm
Examples:
I
Routing Protocols
I
Crowdsourcing
I
Electronic Commerce, Sharing Economy
Design requirement:
Consider user incentives
2/4
Revenue Maximizing Mechanisms
ISP service:
I High quality vs. low quality
3/4
Revenue Maximizing Mechanisms
ISP service:
I High quality vs. low quality
How should the services, and lotteries over them, be priced?
3/4
Revenue Maximizing Mechanisms
ISP service:
I High quality vs. low quality
How should the services, and lotteries over them, be priced?
I Distribution f : (vH , vL ) ∼ f
I Goal: maximize expected revenue
vL
vH
3/4
Revenue Maximizing Mechanisms
ISP service:
I High quality vs. low quality
How should the services, and lotteries over them, be priced?
I Distribution f : (vH , vL ) ∼ f
I Goal: maximize expected revenue
Chen et. al, 2015: computationally hard
vL
vH
3/4
Revenue Maximizing Mechanisms
ISP service:
I High quality vs. low quality
How should the services, and lotteries over them, be priced?
I Distribution f : (vH , vL ) ∼ f
I Goal: maximize expected revenue
Chen et. al, 2015: computationally hard
Theorem (Haghpanah, Hartline, 2015)
If types with high vH are less sensitive ⇒ Only offering high quality optimal
vL
vH
3/4
Technique
Reduce the average-case problem to a point-wise problem
4/4
Technique
Reduce the average-case problem to a point-wise problem
Lemma (Haghpanah, Hartline, 2015)
There exists a virtual value function φ such that
1
Revenue of any mechanism = Ev [x(v) · φ(v)]
2
Selling only high quality maximizes x(v) · φ(v) pointwise.
allocation
virtual value φ
(1, 0)
(0, 0)
4/4
Technique
Reduce the average-case problem to a point-wise problem
Lemma (Haghpanah, Hartline, 2015)
There exists a virtual value function φ such that
1
Revenue of any mechanism = Ev [x(v) · φ(v)]
2
Selling only high quality maximizes x(v) · φ(v) pointwise.
Idea: for any covering of space γ, there exists φγ such that
I Revenue of any mechanism = Ev [x(v) · φγ (v)]
allocation
virtual value φγ
covering γ (paths)
(1, 0)
(0, 0)
4/4
Technique
Reduce the average-case problem to a point-wise problem
Lemma (Haghpanah, Hartline, 2015)
There exists a virtual value function φ such that
1
Revenue of any mechanism = Ev [x(v) · φ(v)]
2
Selling only high quality maximizes x(v) · φ(v) pointwise.
Idea: for any covering of space γ, there exists φγ such that
I Revenue of any mechanism = Ev [x(v) · φγ (v)]
Challenge:
I Find γ such that φγ satisfies second property
allocation
virtual value φγ
covering γ (paths)
(1, 0)
(0, 0)
4/4