Distributed Implementations of
Adaptive Collective Decision Making
Krzysztof R. Apt
CWI and University of Amsterdam
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Let us Introduce Ourselves
Project leaders:
Krzysztof Apt (CWI, UvA),
Farhad Arbab (CWI, Leiden U.),
Han La Poutré (CWI, TUE).
Postdocs:
Arantza Estévez-Fernandéz (PhD, Tilburg U.)
Helen Ma (PhD, Chinese University of Hong Kong),
Tomas Klos (Phd, U. Groningen)
Scientific programmer:
Han Noot (CWI)
Project started Oct 1, 2006, but in reality Jan 1, 2007.
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Motivation
Basic economic problem:
how to align the interests of rational agents so that their
joint decisions are beneficial for the society.
Most of the solutions provided by the economists adopt
a centralized perspective: (‘central planner’, ’authority’,
’decision maker’ etc).
Computer scientists developed a decentralized
perspective in the form of distributed processes.
Basic claim:
decentralized perspective is needed in the age of
internet.
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An Interview with Robert Aumann (2005)
Aumann:
[...] In computer science we have distributed
computing, in which there are many different processors.
The problem is to coordinate the work of these processors,
which may number in the hundreds of thousands, each
doing its own work.
Hart:
That is, how processors that work in a decentralized
way reach a coordinated goal.
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An Interview with Robert Aumann, ctd
Aumann:
Exactly. Another application is protecting
computers against hackers who are trying to break down
the computer. This is a very grim game, just like war is a
grim game, and the stakes are high; but it is a game.
That’s another kind of interaction between computers and
game theory.
Still another comes from computers that solve games, play
games, and design games —like auctions— particularly on
the Web. These are applications of computers to games.
[...]
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Underlying Assumptions
Agents (players) interact by jointly taking decisions that
affect all of them.
Each player seeks to maximize his payoff (profit)
(is rational).
To this end he can resort to cheating (strategic behaviour).
Each player believes all other players are rational and
can resort to strategic behaviour.
Players do not have complete knowledge of each other
payoff functions.
This leads to a study of non-cooperative games with
incomplete information (Bayesian games).
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Decision problems
Assume
players 1, . . ., n,
set of decisions D,
for each player a set of types Θi and a utility function
vi : D × Θ i → R
that he wants to maximize.
Decision rule: a function f : Θ → D, where
f : Θ1 × · · · × Θ n → D .
We call
(D, Θ1 , . . ., Θn , v1 , . . ., vn , f )
a decision problem.
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Classical View
The following sequence of events:
1. each player i is of type θi ,
2. each player i announces to the central planner a type θi0 ,
3. the central planner takes the decision d := f (θ10 , . . ., θn0 ),
and communicates it to each player,
4. the resulting utility for player i is then vi (d, θi ).
Problem to solve: Each player i wants to manipulate the
choice of d ∈ D so that vi (d, θi ) is maximized.
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Mechanism Design
How to induce the players to report their true types
(ensure truth telling).
Vickrey-Clarke Grove mechanism: by a clever use of
taxes truth telling becomes a dominant strategy.
Special case: Vickrey auction.
Sealed bid auction.
The winner pays the second highest bid.
Cheating does not help here.
Other applications:
public projects (single or multiple goods),
various forms of auctions (1-item, multi-unit,
combinatorial, . . .).
Interesting application:
landing slot allocation at the airports.
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Problems with Mechanism Design
Centralized perspective is assumed.
Sometimes taxes have to be paid even if the best
decision is not to decide anything.
Cooperative aspects are ignored.
Internet environment leads to new forms of cheating
(false or multiple identities).
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Distributed Mechanism Design
Different sequence of events:
1. each player i is of type θi ,
2. each player i announces to the other players a type θi0 ;
3. the players jointly take decision d := f (θ10 , . . ., θn0 ),
4. the resulting utility for player i is then vi (d, θi ).
Problems to solve:
distributed computation of taxes,
coordination of decisions,
avoidance of deadlock,
...
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Good News I
We have already a working prototype (Ma, Noot) based
on
client server architecture,
broadcasting.
The implementation handles correctly
Vickrey auctions,
financing of public projects
in a distributed setting.
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Current work
extension to combinatorial auctions,
modification to various forms of networks (trees, rings,
grid),
modification to other forms of communication,
provision for sophisticated forms of cheating.
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Sequential Mechanism Design
The following sequence of events:
1. each player i is of type θi ,
2. each player i in turn announces to the central player
and other players a type θi0 ;
3. the central planner takes the decision d := f (θ10 , . . ., θn0 ),
and communicates it to each player,
4. the resulting utility for player i is then vi (d, θi ).
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Good News II
Advantages of sequential mechanism design
(A. , Estévez-Fernandéz):
other dominant strategies then may exist than truth
telling.
such strategies can be used to minimize taxes,
cooperative aspects can be incorporated,
applicable to various forms of financing of public
projects.
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Future work
extension to combinatorial auctions,
study of repeated mechanism design,
elimination of the central planner,
incorporation into the current implementation,
...
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Summary
Walls between computer science and economics are
rapidly breaking.
We indend to be active players in this process.
Our aim is to combine computer science and
microeconomic techniques to provide realistic solutions
to collective decision making.
Means:
game theory,
distributed computing,
machine learning techniques.
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