Implementation and computation of a value for generalized characteristic function games

Tomasz P. Michalak, Piotr L. Szczepański, Talal Rahwan, Agata Chrobak, Simina Brânzei, Michael Wooldridge, Nicholas R. Jennings

Research output: Contribution to journalArticle

Abstract

Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik [1994] value and the Sánchez-Bergantiños [1997] value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article makes two key contributions. First, building upon the mechanism by Dasgupta and Chiu [1998], we present a non-cooperative mechanism that implements both the Nowak-Radzik value and the Sánchez-Bergantiños value in Subgame-Perfect Nash Equilibria in expectations. Second, in order to facilitate an efficient computation supporting the implementation mechanism, we propose the Generalized Marginal-Contribution Nets representation for this type of game. This representation extends the results of Ieong and Shoham [2006] and Elkind et al. [2009] for characteristic function games and retains their attractive computational properties.

Original languageEnglish (US)
Article number16
JournalACM Transactions on Economics and Computation
Volume2
Issue number4
DOIs
StatePublished - Oct 1 2014

Fingerprint

Characteristic Function
Generalized Functions
Game
Coalitions
Subgame Perfect Equilibrium
Shapley Value
Characteristic function
Nash Equilibrium
Social Networks
Economics
Modeling

Keywords

  • Algorithms
  • Economics
  • Generalized characteristic function games
  • Implementation
  • J.4 [social and behavioral sciences]
  • Representation
  • Shapley value
  • Theory

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Economics and Econometrics
  • Marketing
  • Computational Mathematics

Cite this

Michalak, T. P., Szczepański, P. L., Rahwan, T., Chrobak, A., Brânzei, S., Wooldridge, M., & Jennings, N. R. (2014). Implementation and computation of a value for generalized characteristic function games. ACM Transactions on Economics and Computation, 2(4), [16]. https://doi.org/10.1145/2665007

Implementation and computation of a value for generalized characteristic function games. / Michalak, Tomasz P.; Szczepański, Piotr L.; Rahwan, Talal; Chrobak, Agata; Brânzei, Simina; Wooldridge, Michael; Jennings, Nicholas R.

In: ACM Transactions on Economics and Computation, Vol. 2, No. 4, 16, 01.10.2014.

Research output: Contribution to journalArticle

Michalak, TP, Szczepański, PL, Rahwan, T, Chrobak, A, Brânzei, S, Wooldridge, M & Jennings, NR 2014, 'Implementation and computation of a value for generalized characteristic function games', ACM Transactions on Economics and Computation, vol. 2, no. 4, 16. https://doi.org/10.1145/2665007
Michalak, Tomasz P. ; Szczepański, Piotr L. ; Rahwan, Talal ; Chrobak, Agata ; Brânzei, Simina ; Wooldridge, Michael ; Jennings, Nicholas R. / Implementation and computation of a value for generalized characteristic function games. In: ACM Transactions on Economics and Computation. 2014 ; Vol. 2, No. 4.
@article{79c7ec275c0a4bb587120e80138ae315,
title = "Implementation and computation of a value for generalized characteristic function games",
abstract = "Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik [1994] value and the S{\'a}nchez-Berganti{\~n}os [1997] value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article makes two key contributions. First, building upon the mechanism by Dasgupta and Chiu [1998], we present a non-cooperative mechanism that implements both the Nowak-Radzik value and the S{\'a}nchez-Berganti{\~n}os value in Subgame-Perfect Nash Equilibria in expectations. Second, in order to facilitate an efficient computation supporting the implementation mechanism, we propose the Generalized Marginal-Contribution Nets representation for this type of game. This representation extends the results of Ieong and Shoham [2006] and Elkind et al. [2009] for characteristic function games and retains their attractive computational properties.",
keywords = "Algorithms, Economics, Generalized characteristic function games, Implementation, J.4 [social and behavioral sciences], Representation, Shapley value, Theory",
author = "Michalak, {Tomasz P.} and Szczepański, {Piotr L.} and Talal Rahwan and Agata Chrobak and Simina Br{\^a}nzei and Michael Wooldridge and Jennings, {Nicholas R.}",
year = "2014",
month = "10",
day = "1",
doi = "10.1145/2665007",
language = "English (US)",
volume = "2",
journal = "ACM Transactions on Economics and Computation",
issn = "2167-8375",
publisher = "Association for Computing Machinery (ACM)",
number = "4",

}

TY - JOUR

T1 - Implementation and computation of a value for generalized characteristic function games

AU - Michalak, Tomasz P.

AU - Szczepański, Piotr L.

AU - Rahwan, Talal

AU - Chrobak, Agata

AU - Brânzei, Simina

AU - Wooldridge, Michael

AU - Jennings, Nicholas R.

PY - 2014/10/1

Y1 - 2014/10/1

N2 - Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik [1994] value and the Sánchez-Bergantiños [1997] value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article makes two key contributions. First, building upon the mechanism by Dasgupta and Chiu [1998], we present a non-cooperative mechanism that implements both the Nowak-Radzik value and the Sánchez-Bergantiños value in Subgame-Perfect Nash Equilibria in expectations. Second, in order to facilitate an efficient computation supporting the implementation mechanism, we propose the Generalized Marginal-Contribution Nets representation for this type of game. This representation extends the results of Ieong and Shoham [2006] and Elkind et al. [2009] for characteristic function games and retains their attractive computational properties.

AB - Generalized characteristic function games are a variation of characteristic function games, in which the value of a coalition depends not only on the identities of its members, but also on the order in which the coalition is formed. This class of games is a useful abstraction for a number of realistic settings and economic situations, such as modeling relationships in social networks. To date, two main extensions of the Shapley value have been proposed for generalized characteristic function games: the Nowak-Radzik [1994] value and the Sánchez-Bergantiños [1997] value. In this context, the present article studies generalized characteristic function games from the point of view of implementation and computation. Specifically, the article makes two key contributions. First, building upon the mechanism by Dasgupta and Chiu [1998], we present a non-cooperative mechanism that implements both the Nowak-Radzik value and the Sánchez-Bergantiños value in Subgame-Perfect Nash Equilibria in expectations. Second, in order to facilitate an efficient computation supporting the implementation mechanism, we propose the Generalized Marginal-Contribution Nets representation for this type of game. This representation extends the results of Ieong and Shoham [2006] and Elkind et al. [2009] for characteristic function games and retains their attractive computational properties.

KW - Algorithms

KW - Economics

KW - Generalized characteristic function games

KW - Implementation

KW - J.4 [social and behavioral sciences]

KW - Representation

KW - Shapley value

KW - Theory

UR - http://www.scopus.com/inward/record.url?scp=85032865026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032865026&partnerID=8YFLogxK

U2 - 10.1145/2665007

DO - 10.1145/2665007

M3 - Article

VL - 2

JO - ACM Transactions on Economics and Computation

JF - ACM Transactions on Economics and Computation

SN - 2167-8375

IS - 4

M1 - 16

ER -