Anonymizing Web Services Through a Club Mechanism With Economic Incentives

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Anonymizing Web Services Through a Club Mechanism
With Economic Incentives

• Mamata Jenamani
• Leszek Lilien
• Bharat Bhargava
• Department of Computer Sciences and
• Center for Education and Research in Information
  Assurance and Security (CERIAS)
• Purdue University, West Lafayette, Indiana

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Motivation

• Preserving privacy during Web transactions - a
  major concern
• Failure of most commercial services in providing
  such services
• Besides technical, many economic and social
  factors contribute to the failures
• Anonymizing Web services a solution for
  preserving privacy on the Web
• Game theory for economic analysis

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Proposed Club Mechanism

• Anonymity through group co-operation An
  anonymity club
• A trustworthy central authority
• Randomly matching any two club members
• Can resolve conflict among club members
• Each member tries to maximize her profit
• Cheating most rational alternative in each
  single transaction
• Cooperating most rational alternative in
  repeated sequential transactions

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Rules for the Sequential Strategy

• Becoming a club member by paying a one time
  initiation fee F to the central authority
• Two members partner for an anonymizing Web
  transaction during the time period t
• Two members receive a benefit Pt each by
  maintaining anonymity and using each others
  service
• Two strategies cooperate or defect
• If Alice feels that Bob cheats her, she reports
  it to the central authority
• - Pclaim the loss suffered by the complainant
• The central authority investigates the fraud
• If fraud is confirmed, Bob pays a fine f and
  Pclaim, Alice gets compensation Pclaim and the
  central authority gets fine f.
• Otherwise, Alice is charged with a false
  complaint and pays fine g to the central
  authority.
• The culprit who does not pay a fine or a
  compensation is expelled from the club.

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Prisoners Dilemma Played at Each Stage

• Assumptions
• Both partners have symmetric privacy needs
• They have equal number of requests for
  anonymizing
• Benefit from privacy protection is higher than
  the benefits received by sacrificing the
  partners privacy (i.e. Pt gt lt)
• At each stage each agent has two choices either
  to defect (D) or to cooperate (C).
• The only Nash equilibrium for both players in
  this game is to defect

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PD Played at Each Stage cont.
Payoff structure of the Prisoners Dilemma game

• Pt be the benefit from privacy protection
  received by an agent within time period t
• -Pt as the cost of privacy violation if it is
  suffered by an agent during that period
• Pts are independently identically distributed
  random variables with a common distribution P
• Pmax a value beyond which distribution P has no
  positive probability density,
• E(P) is the expectation of P
• lt be the benefit from disclosing the privacy of
  another agent
• a similar assumption for the random variable lt
• lmax as an estimate of the maximum possible
  benefit received by a defecting agent

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An Agents Time-Weighted Average Payoff

• Discount factor ,
• For interest rate i,
• Time weighted average payoff
• Payoff stream for time period t
• Total (Lifetime) Payoff
• using the relationship
• and the formula for geometric series
• we get
• Maximizing time weighted average payoff is
  equivalent to maximizing total payoff
• Incentive for cooperation in a time period even
  though defection is a dominant strategy at each
  stage

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Analysis of the Economic Incentives

• Conditions such as paying initiation fee and fine
  occur at time period t0
• The total payoff starting from period t0 is
• The total payoff starting from period t1 is
• Exploring conditions under which the proposed
  sequential strategy motivates the agents to
  cooperate

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Proposition 1
An agent will join the proposed anonymizing club,
if the initiation fee (given at time period t0)
is less than the difference between his total
future payoff from this service (starting from
time period t1) and the maximum future payoff
from adopting any other privacy preserving
technology, i.e. if the following inequality is
satisfied
where is the maximum of all expected payoffs
from any other privacy-preserving technology
available at that time period. Proof
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Proposition 2
An agent will cooperate at every stage in the
sequential repeated game, if the maximum value of
the benefit from the cheating behavior is less
than the total future payoff (from t0) minus the
maximum payoff achievable in the current
transaction, i.e. if the following condition is
satisfied
Proof
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Proposition 3
A defector who is proven guilty is willing to pay
the fine, if it is lower than the difference
between his total future payoff (starting from
t1) and the compensation claimed by his partner,
i.e. if the following condition is satisfied
Proof
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Proposition 4
If a players complaint is proven false, he is
willing to pay the fine imposed on him, if it is
lower than his total future payoff (starting from
t1), i.e. if the following condition is
satisfied
Proof
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Theorem
The proposed sequential strategy is an
equilibrium strategy if the fine is imposed
following conditions in Propositions 3 and 4,
i.e., if
and
The average payoff for an agent in this strategy
is
Proof
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Future Work

• Consideration of agents belief in the fairness
  of the central authority
• Consideration of the fixed costs associated with
  starting the service
• Defining the minimum number of participants
  starting a club
• Considering the cost involved in running the
  matching algorithm - another variable cost, such
  as annual club membership
• The probabilistic modeling of cheating behavior
  of individual agents
• Consideration of unequal privacy concerns of
  individual agents
• Consideration of unequal number of anonymizing
  transactions

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Proof of Proposition 1
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Proof of Proposition 2
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Proof of Proposition 3
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Proof of Proposition 4
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Proof of the Theorem
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