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Algorithms, Incentives, and Multidimensional Preferences Nima - - PowerPoint PPT Presentation

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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 User User Input Output Algorithm Algorithm 2 / 4

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SLIDE 1

Algorithms, Incentives, and Multidimensional Preferences

Nima Haghpanah (MIT) January 15, 2016

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SLIDE 2

Algorithms and Incentives

Past: Algorithms as black box Now: Algorithm as Platform Input Output Algorithm Algorithm

User User User

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SLIDE 3

Algorithms and Incentives

Past: Algorithms as black box Now: Algorithm as Platform Input Output Algorithm Algorithm

User User User

Examples:

◮ Routing Protocols ◮ Crowdsourcing ◮ Electronic Commerce, Sharing Economy

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SLIDE 4

Algorithms and Incentives

Past: Algorithms as black box Now: Algorithm as Platform Input Output Algorithm Algorithm

User User User

Examples:

◮ Routing Protocols ◮ Crowdsourcing ◮ Electronic Commerce, Sharing Economy

Design requirement: Consider user incentives

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SLIDE 5

Revenue Maximizing Mechanisms

ISP service:

◮ High quality vs. low quality

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SLIDE 6

Revenue Maximizing Mechanisms

ISP service:

◮ High quality vs. low quality

How should the services, and lotteries over them, be priced?

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SLIDE 7

Revenue Maximizing Mechanisms

ISP service:

◮ High quality vs. low quality

How should the services, and lotteries over them, be priced?

◮ Distribution f : (vH, vL) ∼ f ◮ Goal: maximize expected revenue

vL vH

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SLIDE 8

Revenue Maximizing Mechanisms

ISP service:

◮ High quality vs. low quality

How should the services, and lotteries over them, be priced?

◮ Distribution f : (vH, vL) ∼ f ◮ Goal: maximize expected revenue

Chen et. al, 2015: computationally hard vL vH

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SLIDE 9

Revenue Maximizing Mechanisms

ISP service:

◮ High quality vs. low quality

How should the services, and lotteries over them, be priced?

◮ Distribution f : (vH, vL) ∼ f ◮ 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

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SLIDE 10

Technique

Reduce the average-case problem to a point-wise problem

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SLIDE 11

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. (1, 0) (0, 0)

allocation virtual value φ

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SLIDE 12

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

◮ Revenue of any mechanism = Ev[x(v) · φγ(v)]

(1, 0) (0, 0)

allocation covering γ (paths) virtual value φγ

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SLIDE 13

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

◮ Revenue of any mechanism = Ev[x(v) · φγ(v)]

Challenge:

◮ Find γ such that φγ satisfies second property

(1, 0) (0, 0)

allocation covering γ (paths) virtual value φγ

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