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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