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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 × Θi → R

that he wants to maximize. Decision rule: a function f : Θ → D, where

f : Θ1 × · · · × Θn → 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 θ′

i,

• 3. the central planner takes the decision d := f(θ′

1, . . ., θ′ n),

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 θ′

i;

• 3. the players jointly take decision d := f(θ′

1, . . ., θ′ n),

• 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

• n

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 θ′

i;

• 3. the central planner takes the decision d := f(θ′

1, . . ., θ′ n),

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):

• ther 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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