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Logic Journal of IGPL Advance Access published online on May 20, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp008
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Algorithms for Finding Coalitions Exploiting a New Reciprocity Condition

Guido Boella

Università di Torino, Italy.
E-mail: guido{at}di.unito.it

Luigi Sauro

Università di Napoli, Italy.
E-mail: sauro{at}na.infn.it

Leendert van der Torre

University of Luxembourg, Luxembourg.
E-mail: leon.vandertorre{at}uni.lu


  Abstract

We introduce a reciprocity criterion for coalition formation among goal-directed agents, which we call the indecomposable do-ut-des property. It refines an older reciprocity property, called the do-ut-des or give-to-get property by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of algorithms and their complexity. We provide an algorithm to decide whether a coalition has the desired property, and we show that the problem to verify whether a single coalition satisfies the property is tractable. Moreover, we provide an algorithm to search all the sub-coalitions of a given coalition satisfying the new property. Even if this problem is not computationally tractable, we show that in several cases, also the complexity of this problem may decrease considerably.

Received for publication 17 October 2008.
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