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Distributed Implementations of Adaptive Collective Decision Making Krzysztof R. Apt CWI and University of Amsterdam Distributed Implementations of Adaptive Collective Decision Making – p.1/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.2/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.3/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.4/17

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. [...] Distributed Implementations of Adaptive Collective Decision Making – p.5/17

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). Distributed Implementations of Adaptive Collective Decision Making – p.6/17

Decision problems Assume players 1 , . . ., n , set of decisions D , for each player a set of types Θ i and a utility function v i : D × Θ i → R that he wants to maximize. Decision rule: a function f : Θ → D , where f : Θ 1 × · · · × Θ n → D . We call ( D, Θ 1 , . . ., Θ n , v 1 , . . ., v n , f ) a decision problem. Distributed Implementations of Adaptive Collective Decision Making – p.7/17

Classical View The following sequence of events: 1. each player i is of type θ i , 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 v i ( d, θ i ) . Problem to solve: Each player i wants to manipulate the choice of d ∈ D so that v i ( d, θ i ) is maximized. Distributed Implementations of Adaptive Collective Decision Making – p.8/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.9/17

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). Distributed Implementations of Adaptive Collective Decision Making – p.10/17

Distributed Mechanism Design Different sequence of events: 1. each player i is of type θ i , 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 v i ( d, θ i ) . Problems to solve: distributed computation of taxes, coordination of decisions, avoidance of deadlock, . . . Distributed Implementations of Adaptive Collective Decision Making – p.11/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.12/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.13/17

Sequential Mechanism Design The following sequence of events: 1. each player i is of type θ i , 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 v i ( d, θ i ) . Distributed Implementations of Adaptive Collective Decision Making – p.14/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.15/17

Future work extension to combinatorial auctions, study of repeated mechanism design, elimination of the central planner, incorporation into the current implementation, . . . Distributed Implementations of Adaptive Collective Decision Making – p.16/17

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. Distributed Implementations of Adaptive Collective Decision Making – p.17/17