Mechanism Design with
Strategic Mediators
Moran Feldman
EPFL
Joint work with:
Moshe Babaioff, Microsoft Research
Moshe Tennenholtz, Technion
Mechanism Design
Mechanism
Decision
Should make
a global
decision
Players
Incentive
compatible
Requirements
(Approximately)
optimizes a
global objective
2
Introducing Strategic Mediators
Optimization Goal
Mechanism
Mediators
Players
Global
welfare
of
In a federal country, Welfare
the
his players
elected representative
of a state represents the
global interests of the
state’s population.
Personal
welfare
3
Facility Location on a Line
•
•
•
•
•
•
n clients are located along a line metric.
A facility should be placed on the line.
The cost of client is its distance from the facility.
The social cost is the total costs of all clients.
The optimal facility location is the median.
The median mechanism makes being truthful a
dominant strategy. [Moulin 1980]
Summary:
1-competitive

strong incentive
compatibility concept


4
Adding Strategic Mediators
Direct Revelation Mechanism
Each mediator reports the
locations of all its clients.
Locations of
B, D and E
Next Objective
Choosing an incentive
compatibility concept
?
Location
of E
A
B
C
D
E
5
First Attempt – Dominant Strategy Truthful
• The mechanism:
– Must locate the facility at the location of the
client to get any finite ratio.
– Must accept the location reported by the
mediator, in case everyone is truthful.
• If the client lies:
– The mediator must still report the right client
location, i.e., he must alter the report of the
client.
• Follows from the sequential nature of the
problem – all entities share their objective.
6
Two-Sided IC
Definitions
• Agent-Side IC mechanism: It is a
dominant strategy for an agent
to be truthful assuming its
mediator is truthful.
• Mediator-Side IC Stronger
mechanism:
It
than requiring
is a dominant strategy
for a to be an extruthfulness
mediator to be truthful
post Nash equilibrium.
assuming its clients are
truthful.
• A mechanism is Two-Sided IC if
it is Agent-Side IC and
Mediator-Side IC.
7
Weighted Median of Medians
• Calculate the median of the
agents of every mediator.
Pretend they all are located at
this median.
• Locate the facility at the
median of the resulting set.
Theorem
The above algorithm is Two-Sided IC
and 3-competitive, which is the best
possible deterministicly.
2
3
8
Analysis
• Previous works implies: [Procaccia and Tennenholtz 2013 and
Dekel et al. 2010]
– 3-competitive, which is optimal deterministicly
– Mediator-Side IC
The median
median
• The
What
can anisagent achieve by lying?
can only move
unchanged.
– At
most, it has the power to push the median
away.
Either
has no
away.
No effect.
• What can that do?
effect or moves
the facility away.
Median of
mediator
Agent
9
Random Algorithm
Real
agentafter
locations:
Locations
every agent is “moved” to the median of its
mediator:
2
3
u1, u2
u3, u4, u5
Randomly select a location for the facility from the middle
half of the agents:
u1
…
un/4+1
…
u3n/4
…
un
10
Result
The above algorithm is Two-Sided IC and 2-competitive, which is
the best possible.
Analysis Idea
(A) For a central segment, in any solution about half of the
agents use it.
(B) For an extreme segment, the virtual move of the agents
can make the segment only slightly more central. Hence,
the facility remains on its right side.
(C) For other segments:
• (A) applies partially, i.e., a mistake is not that bad.
• (B) applies when the random facility location is chosen
near the other end.
11
Extensions
• Generalizing the line
metric into a tree metric.
– All the above results
generalize to tree metrics.
The random algorithm is
more involved.
• Multiple levels of
mediators.
– The competitive ratio is
exponential in the number
of levels.
12
Open Problems
• Extending the model:
– Multiple facilities.
– More general metrics.
– Both have been studies without mediators
[Procaccia and Tennenholtz 2013, Lu et al. 2010].
• Studying the impact of introducing strategic
mediators in other settings.
13
14