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

• Published in: Mathematical logic quarterly Vol. 55; no. 4; pp. 362 - 376
• Main Authors: Elkind, Edith, Goldberg, Leslie Ann, Goldberg, Paul W., Wooldridge, Michael
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01-08-2009; WILEY‐VCH Verlag
• Subjects: Coalitional games; marginal contribution networks; read-once formulas; Shapley value
• DOI: 10.1002/malq.200810021
• EISSN: 1521-3870
• ISSN: 0942-5616

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. 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 rulebased formalism, in which rules take the form pattern → value, where “pattern ” is a Boolean condition over agents, and “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 games that require an exponential number of such basic MC‐net rules. We present 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 (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)