Automated Mechanism Design
Tuomas Sandholm
Presented by Dimitri Mostinski
November 17, 2004
Mechanism Design
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Art of designing the rules of the game (aka.
mechanism) so that a desirable outcome
(according to a given objective) is reached
despite the fact that each agent acts in his own
selfinterest
Some examples of applications
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Auctions
Voting protocols
Divorce settlement procedures
Collaborative rating systems
Manual Mechanism Design
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Traditional approach to mechanism design
Good design is hypothesized based on designers
experience and intuition and then desirable
properties are proven formally
Over last 40 years a small number of canonical
mechanisms were created, each designed for a
class of settings and a specific objective
Problems with Manual MD
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The most famous and most broadly applicable general mechanisms,
VCG and dAGVA, only maximize social welfare
The general mechanisms that do focus on a self-interested designer
are only applicable in very restricted settings
The designer may also be interested in the outcome per se
It is often assumed that side payments can be used to tailor the
agents' incentives, but this is not always practical
The most common mechanisms assume that the agents have
quasilinear preferences ui(o; p1, .. ,p N) = vi(o)− pi
Impossibility Results
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Traditional research has yielded a number of
impossibility results of the form “no mechanism
works across a class of settings” for different
definitions of “works” and different classes of
settings.
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E.g. Gibbard-Satterthwaite theorem states that for
the class of general preferences, no mechanism
exists where
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an outcome outcome can be any one of at least three
candidates
the mechanism is nondictatorial
truth telling is a dominant strategy for all agents
Automatic Mechanism Design
(AMD)
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A novel approach to mechanism design
proposed by Conitzer and Sandholm in
2002
Mechanism is computationally created for
the specic problem instance at hand
Advantages of AMD
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It can be used in settings beyond the classes of
problems that have been successfully studied in manual
mechanism design to date
It can allow one to circumvent the impossibility results
by considering an instance of the class not the class
itself
It can yield mechanisms that produce better results and
are harder to manipulate by using the information that
the mechanism designer has about the agents‘
preferences
It shifts the burden of mechanism design from humans
to a machine.
AMD formalism
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Am automatic mechanism design setting is
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A finite set of outcomes O
A finite set of N agents
For each agent I
A finite set of types Qi
 A probability distribution gi over Qi
 A utility function ui : Qi x O  R
 An objective function whose expectation the
designer wishes to maximize g(o; p1, .. ,p N)
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More AMD formalism
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A mechanism consists of
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An outcome selection function
o : Q1x .. x QN  O if it is deterministic
A distribution selection function
p : Q1x .. x QN  P(O) if it is randomized
For each agent i a payment selection function
pi : Q1x .. x QN  R if it involves payments
Individual Rationality
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An agent must never be worse off by participating in the
mechanism
Types of Individual Rationality
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Ex ante the agent would participate if it knew nothing at all (not
even its own type)
Ex interim the agent would always participate if it knew only its
own type
Ex post the agent would always participate even if it knew
everybody's type
In an AMD setting with an IR constraint there exists a
fallback outcome o0 such that for every agent i ui(qi,o0) =
0
Incentive Compatibility
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The agents should never have an incentive to
misreport their type
Two most common solution concepts are
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implementation in dominant strategies
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Truth telling is the optimal strategy even if all other agents’
types are known
implementation in Bayesian Nash equilibrium
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Truth telling is the optimal strategy if other agents’ types are
not yet known, but they are assumed to be truthful
Formally the AMD problem
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Given
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Automated mechanism design setting
An IR notion (ex interim, ex post, or none)
A solution concept (dominant strategies or Bayesian Nash
equilibrium)
Possibility of payments and randomization
A target value G
Determine
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If there exists a mechanism of the specified type that satisfies
both the IR notion and the solution concept, and gives an
expected value of at least G for the objective.
Complexity results
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Consider a case of only one agent
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Proving hardness for this case would imply lower bound on the
general problem
AMD is NP-hard (by reduction to MINSAT) if
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The two discussed IR options coincide here
The two solution concepts coincide as well
Payments are not allowed
Payments are allowed but the designer is looking for something other
than social welfare maximization
AMD can be solved in (expected) polynomial time using randomized
algorithm for LP problems
If the input is structured in a way that it can be concisely
communicated it can also be faster processed
An example
2
Low
High
Low
Joint
Husband
High
Wife
Burned
1
Low
High
3
Low
High
Low
Husband
Husband
Low
Husband
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Husband
Husband
.57
Husband
.43 Wife
High
Wife
.45 Burned
.55
Husband
Some results of AMD
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It reinvented the Myerson auction which
maximizes the seller's expected revenue in a 1object auction
It created expected revenue maximizing
combinatorial auctions
It created optimal mechanisms for a public good
problem (deciding whether or not to build a
bridge)
It created optimal mechanisms for public goods
problems with multiple goods
Conclusion
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Automated mechanism design is a brand
new area of research
The problems that were long studied for
manual mechanism design can all be
applied to AMD