Selling Information Through Consulting Yiling Chen Harvard University

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Selling Information Through Consulting Yiling Chen Harvard University Haifeng Xu University of Virginia Shuran

Selling Information Through Consulting Yiling Chen Harvard University Haifeng Xu University of Virginia Shuran Zheng Harvard University

We know a lot about selling items. . .

We know a lot about selling items. . .

How do we sell a piece of information?

How do we sell a piece of information?

Market of Information Consumer Information Credit Reports Recommendation

Market of Information Consumer Information Credit Reports Recommendation

How is information different from items? • Can be partially revealed seller • e.

How is information different from items? • Can be partially revealed seller • e. g. Flight. Aware buyer … … …

Outline Selling information to budget-constrained buyers 1. Motivation • Why budget-constrained buyers? 2. Our

Outline Selling information to budget-constrained buyers 1. Motivation • Why budget-constrained buyers? 2. Our Results • Model • Main theorem • Proof ideas

Motivation • Babaioff et al. [2012]: buyers with unlimited budget • Budget-constrained buyers

Motivation • Babaioff et al. [2012]: buyers with unlimited budget • Budget-constrained buyers

Motivation loss wait 0 take a train 100

Motivation loss wait 0 take a train 100

Motivation • Suppose Flight. Aware knows the exact delay and wants to sell it.

Motivation • Suppose Flight. Aware knows the exact delay and wants to sell it. • 2 buyers: buyer 1 buyer 2 loss 400 600 prior belief [0, 7. 9984] [0, 8. 0016]

Our Results Consider budget-constrained buyers • Simple optimal mechanism • Compute via a polynomial-size

Our Results Consider budget-constrained buyers • Simple optimal mechanism • Compute via a polynomial-size LP • Improves the previous exponential-size LP by Babaioff et al. [2012] that solves one-round optimal mechanism when there is no budget constraint Adding budget constraint makes the problem easier

Model: information buyer •

Model: information buyer •

Model: information seller •

Model: information seller •

Model: information as signals • good bad 2/3 1/3 2/3 s good bad

Model: information as signals • good bad 2/3 1/3 2/3 s good bad

Model: mechanisms • Multiple-round mechanisms • Recommend actions to the buyer and then charge

Model: mechanisms • Multiple-round mechanisms • Recommend actions to the buyer and then charge some prices Assuming the buyer maximizes his own utility

Our Contribution •

Our Contribution •

Our Contribution • good bad 2/3 1/3 2/3

Our Contribution • good bad 2/3 1/3 2/3

Our Contribution • good bad 2/3 1/3 2/3 wait, refund 0

Our Contribution • good bad 2/3 1/3 2/3 wait, refund 0

Our Contribution Theorem: There always exists an IC and IR Consulting Mechanism that achieves

Our Contribution Theorem: There always exists an IC and IR Consulting Mechanism that achieves no less revenue than any (possibly multiple-round) mechanisms.

Proof ideas Generic Protocol do not know how to compute One-round Mechanism LP with

Proof ideas Generic Protocol do not know how to compute One-round Mechanism LP with exponentially many variables and exp. constraints

One-round Mechanism • • LP with exponentially many variables and exponentially many constraints

One-round Mechanism • • LP with exponentially many variables and exponentially many constraints

Proof ideas Generic Protocol do not know how to compute One-round Mechanism LP with

Proof ideas Generic Protocol do not know how to compute One-round Mechanism LP with exponentially many variables and exp. constraints Consulting Mechanism simple structure; LP with polynomial size

Proof ideas Duality Variable transformation Duality

Proof ideas Duality Variable transformation Duality

Proof ideas • Two possible payments • Can be reduced to a consulting mechanism

Proof ideas • Two possible payments • Can be reduced to a consulting mechanism

Polynomial-size LP •

Polynomial-size LP •

Summary Selling information to budget-constrained buyers • Simple one-round optimal mechanism: consulting mechanisms •

Summary Selling information to budget-constrained buyers • Simple one-round optimal mechanism: consulting mechanisms • Compute the optimal mechanism via a polynomial-size LP

Thanks & Questions?

Thanks & Questions?

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