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

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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