an economic solution to spam thede loder, marshall van alstyne, rick wash

An Economic Solution to Spam

Thede Loder, Marshall Van Alstyne, Rick Wash

Spam Examples

Want these guys in your mailbox?

Spam King: Alan Ralsky spewed tens of thousands of e-mail sales pitches per hour, bringing on the wrath of Verizon. Tech. Review Aug ‘03

Richard Colbert, spammer. NYT 09-28-03

The Spam Problem

• Estimated yearly loss to businesses $10 billion (Ferris Research)

• ISPs estimate the cost of spam at $2-$3 per user per month (IDG)

• 6+ spam laws are pending in congress (NYTimes)• 8 states have already made spam laws including

recent CA law (NYTimes)• 50% of all email is now spam (Brightmail)

Existing or Proposed Solutions

• Two Categories: legislative, technological• Technological Candidates:

– Filtering: Rule based (static or dynamic), Bayesian Filters, collective/community classification

– Challenge Response: quasi-Turing tests, return address testing, computational challenge (solve hard problem)

• Legislative Candidates:– Banning, labeling

– Taxation, stamps

Problems with Pure Technology Solutions

• Filtering: – False positives, false negatives

– Costly arms-race

– Consensus definition

– Shuts down exchange

• Challenge response: – Requires human interaction

– Costly arms race

– Blocks automated emails

Problems with Legislative Solutions

• Banning and labeling:– Enforceability (jurisdiction?)– Costly to police and adjudicate– Labeling lacks incentive compatibility

• Taxation and Stamps:– Blocks wanted along with unwanted email– Kills cost-effectiveness of email as medium

…and Spam is Getting Worse

What’s going on?

Modeling Email

Value to Sender (s)

Value to Recipient (r)

0Vr Vr

• Each email has a party-dependent expected value:– value to the sender s – value to the recipient r

• s and r bounded by Vs and Vr (upper and lower)

- +

0 Vs

__Vs__

____

- +

• r and s are expected values• Sender knows s before sending• Sender does not know r• Sender knows or learns their marginal cost, and

will not send when s < cost• Base cost to send cs is the same for all

distributions• Recipient knows r upon receipt but only after

losing an unavoidable receiving/processing cost cr

Basic Assumptions

Email Value - Single Distribution

cr

cs

(value to sender)

r (value to recipient)

Cost for recipient to receive (sender must send)

Cost for sender to send

s

= region of positive probability in the distribution for email with values (r, s)

cr =

cs =

Vr

Vs

__

Vs__

Vr

__

__

Derivation of Payoffs 1

• We assume f is uniform in each dimension and independent of s and r.

),( rsf 1),( =∫∫A

rsf

• General form: distribution of point probabilities

such that

),( rsf = distribution specific constant (k)

Derivation of Payoffs 2

• Baseline Recipient Surplus is

dsdrrsfcrRSA

r∫∫−= ),()(0

dsdrcrkA

r∫∫−= )(

Whererrss VVVV

k+

•+

=11

Derivation of Payoffs 3

• Similarly, we can determine the Sender Surplus (SS) and the Social Welfare (SW)

dsdrcskSSA

s∫∫−= )(0

000 SSRSSW +=

Social Welfare Contribution

Sent email with (r, s) northeast of the diagonal line makes a positive contribution to social welfare if received

cr

r

SW+

s

= positive contribution to SW

= negative contribution to SW

cs

Social Welfare (SW) = RS + SS

For a single email:

Interpreting Existing Solutions

cs

cs+ tax

r

Flat Tax, Computational Challenge

lossUnwantedUnwanted

cr

SW+

s

cs

cs/n

r

FilteredWaste

Unsent

Filtering (all types)

Unsent

loss

loss

loss

Existing Solutions 2Challenge Response - quasi-Turing Test

cs+ test cost

r

lossUnwantedUnwanted

Unsent

loss

Criminalizing Spam

cs+ risk of penalty

r

loss

Unsent

loss

cs

UnwantedUnwanted

cs

Perfect Filter

cr

r

SW+

s

cs cs/

FilteredFiltered

ReceivedReceived

Definition: A technological filter which:

1) Operates without cost2) Makes no mistakes (no false

positives or false negatives)3) Intuits and internalizes all reader

preferences4) Works for an arbitrarily large

number of different distributions5) Eliminates, prior to receipt, any

email where r < cr

Unsent

“In terms of individual and aggregate social welfare, a system that facilitates valuable exchange will generally dominate a system that grants unilateral veto power to either party”

Not all filtered email is waste

cr

r

SW+

s

= positive contribution to welfare

= negative contribution to welfare

= not sent (s < cs)

UnwantedUnwantedSome spam has positive

contribution

cs

= unwanted by recipient (r < cr)

Unsent

If it’s not waste, don’t destroy it

cr

r

SW+

s

UnwantedUnwanted

cs

Unsent

• filter everything• set bond > Vs • (stop using email entirely)

• filter everything• set bond to transfer sender surplus!

• filter nothing• set bond = 0

• Follows from mechanism design - an economic, rather than pure technological or legislative design

• Simple screening mechanism• Challenge demands an escrowed monetary bond of the

amount (a ‘fee’)• Recipient has sole discretion to keep or return • Effect: a recipient-controlled variable ‘tax’ on senders, by

type. • ‘Tax’ proceeds go to recipient• Used for non-whitelisted senders

The Attention Bond Mechanism

Architecture for ABM

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

Here, p = 0

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Recipient Payoff

cr

r

SW+

s

cs

For any particular distribution, the recipient can remove the sender incentive to send emails for which s < cs+p, while at the same time gaining p.

Positive payoff to recipient

Negative payoff to recipient

Unsent

UnwantedUnwanted

WantedWanted

cs+p

cr -p

Extended Model and Comparison

• How do RS, SS, and SW compare?

• Multiple Distributions

• Perfect Filter – average cost per receipt goes to cs/

• ABM - Cost to sender increases by pd . Cost now cs+ pd

The no intervention baseline

drdscrkRSr

r

s

s

v

v

v

c r )(0 ∫∫ −=Reader Surplus defined:

( )( ) ⎟

⎠

⎞⎜⎝

⎛ −+

−−

= rrr

ss

ss cvv

vv

cvRS

20Baseline surplus

The Reader’s choice of screendrdspcrRS

r

r

s

s

v

v

v

pc rB )(∫∫++−=

φφReader Surplus defined:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ −+

−−=+r

rrss c

vvcv

p 22

1φOptimal Screen:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛ −+

−−=+r

rrss c

vvcvp

22

1

φOptimal Seize Rate Policy:

Reader Surplus:

( ) ( )2

24

1⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛−

++−

−= r

rrss

ssB c

vvcv

vvRS

0RSRSB ≥Always:

The Perfect FilterdrdscrRS

r

r

s

s

v

c

v

c rPF )(/∫∫ −=

Reader Surplus defined:

Reader Surplus:( )

( )( )ssrr

ssrr

PF vvvv

cvcv

RS−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

=2

2

η

PFB RSRS ≥Bonding wins if: ( ) ⎟⎠

⎞⎜⎝

⎛ −+

−≥ rrr

ss cvv

cvp2

8)2( 2φ

Social Planner’s choice of screen

drdscscrRSSSWr

r

s

s

v

v

v

pc srSPSPSP )(∫∫+−+−=+=

φWelfare defined:

⎟⎠

⎞⎜⎝

⎛ −+

= rrr c

vv

p 2

1*φOptimal Screen:

SPB WW4

3=Always:

• V distribution expected to be mostly ‘Valuable’ • W distribution expected to be mostly ‘Waste’ • Sender does not know r• Sender knows to which distribution (V or W) their

email belongs

Comparison of ABM to PF2-Distribution Case

VV

Distribution V

cr

r

SW+

s

cs

“Valuable”

WW

Distribution W

cr

r

SW+

s

cs

“Waste”

VV

V Sent With Attention Bond

cr

r

SW+

s

cs cs + pv

For each distribution, the recipient can choose a policy with a seize probability px

UnsentUnsentVV

W Sent with Attention Bond

WW

cr

r

SW+

s

cs cs + pw

Unsent WUnsent W

For a mostly unwanted email distribution, the recipient is best off if they seize with a high probability (greater p product)

Recipient Surplus - ABM

cr

r

SW+

s

cs

cs + pw

V V

cs + pv

WW

WW

Recipient Surplus – Perfect Filter

cr

r

SW+

s

cs

cs /v

cs /w

VV

WW

Welfare Basis - ABM

WW

cr

r

SW+

s

cs

cs + pw

VV

cs + pv

Welfare Basis - Perfect Filter

cr

r

SW+

s

cs

VV

WW

cs /v

cs /w

FilteredFilteredWasteWaste

Filtered WasteFiltered Waste

Policy Independence

• Choose any one p or choose (subject to boundary conditions)

• No social inefficiency for adding as many distributions as you want (true for readers and senders). Each distribution can be separately optimized

• Policy can be adjusted to individual senders, not just “spammers” and “good-guys”

• Contrast to filter, which suffer from dramatically increased type 1 and type 2 errors with more distributions

• There is no incentive to misappropriate the bond ex-post

Caveats and Adoption Issues

• “bottom chop”– Email with high value to the recipient but a low value to

the sender will not be sent (sender not willing to risk bond)

• Infrastructure and Transaction costs– requires escrow service(s), server infrastructure changes,

low cost transaction system for small transactions, inter-escrow payment network (later)

• Network effects– Mulitiple escrow companies, if not connected, slow

adoption

Additional Social Benefits

• Reduced friction; recipients have incentive to publish their contact information, not obscure it

• No costly arms race• Direct Marketing still possible• Permits communication otherwise eliminated (e.g. political

speech)• Costs remain cheaper than post office-style direct

marketing• Tailors to an individuals unique preferences• Signaling information about a recipient via claim history

Conclusion

• Enabling transactions helps readers more than unilateral veto

• Screening mechanism forces senders to reveal their type

• Many desirable secondary effects

Future Work

• Signaling• Non-uniform distributions• Allow cs and cr to vary with distribution?• What happens when sender knows r? (with some

certainty or exactly)• Infrastructure issues• Show determination of minimal for multiple

distributions