# Tractable and Expressive Class of Marginal Contribution Nets and Its Applications

Elkind, Edith, Goldberg, Leslie Ann, Goldberg, Paul W. and Wooldridge, Michael (2008) Tractable and Expressive Class of Marginal Contribution Nets and Its Applications. In, AAMAS-08

## Description/Abstract

Coalitional games raise a number of important questions from the point of view of computer science, key among them being how to represent such games compactly, and how to efficiently compute solution concepts assuming such representations. \emph{Marginal contribution nets} (MC-nets), introduced by Ieong and Shoham, are one of the simplest and most influential representation schemes for coalitional games. MC-nets are a rule-based formalism, in which rules take the form \emph{pattern} $\longrightarrow$ \emph{value}, where \emph{pattern}'' is a Boolean condition over agents, and \emph{value}'' is a numeric value. Ieong and Shoham showed that, for a class of what we will call basic'' MC-nets, where patterns are constrained to be a conjunction of literals, marginal contribution nets permit the easy computation of solution concepts such as the Shapley value. However, there are very natural classes of coalitional game that require an exponential number of such basic MC-net rules. We present \emph{read-once MC-nets}, a new class of MC-nets that is provably more compact than basic MC-nets, while retaining the attractive computational properties of basic MC-nets. We show how the techniques we develop for read-once MC-nets can be applied to other domains, in particular, computing solution concepts in network flow games on series-parallel networks.

Item Type: Conference or Workshop Item (Paper) Faculty of Physical Sciences and Engineering > Electronics and Computer Science 265285 05 Mar 2008 18:56 27 Mar 2014 20:10 Google Scholar http://eprints.soton.ac.uk/id/eprint/265285