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An Interdisciplinary Approach to Coalition Formation

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Author Info

  • Rudolf Berghammer

    (Computer-Aided Program Development - Institute of Computer Science - Christian-Albrechts-Universität zu Kiel)

  • Agnieszka Rusinowska

    ()
    (GATE - Groupe d'analyse et de théorie économique - CNRS : UMR5824 - Université Lumière - Lyon II - Ecole Normale Supérieure Lettres et Sciences Humaines)

  • Harrie De Swart

    (Faculteit Wijsbegeerte-Logica en taalanalyse - Universiteit van Tilburg)

Abstract

A stable government is by definition not dominated by any other government. However, it may happen that all governments are dominated. In graph-theoretic terms this means that the dominance graph does not possess a source. In this paper we are able to deal with this case by a clever combination of notions from different fields, such as relational algebra, graph theory and social choice theory, and by using the computer support system RelView for computing solutions and visualizing the results. Using relational algorithms, in such a case we break all cycles in each initial strongly connected component by removing the vertices in an appropriate minimum feedback vertex set. In this way we can choose a government that is as close as possible to being un-dominated. To achieve unique solutions, we additionally apply the majority ranking recently introduced by Balinski and Laraki. The main parts of our procedure can be executed using the RelView tool. Its sophisticated implementation of relations allows to deal with graph sizes that are sufficient for practical applications of coalition formation.

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File URL: http://halshs.archives-ouvertes.fr/docs/00/40/64/60/PDF/GRAPH-EJOR4.pdf
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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00406460.

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Date of creation: 2009
Date of revision:
Publication status: Published, European Journal of Operational Research, 2009, 195, pp. 487-496
Handle: RePEc:hal:journl:halshs-00406460

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00406460/en/
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Related research

Keywords: Graph theory; RelView; relational algebra; dominance; stable government;

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References

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  1. Rudolf Berghammer & Harrie De Swart & Agnieszka Rusinowska, 2007. "Applying relational algebra and RelView to coalition formation," Post-Print halshs-00159845, HAL.
  2. Michel Balinski & Rida Laraki, 2006. "A Theory of Measuring, Electing and Ranking," Working Papers hal-00243040, HAL.
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Citations

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Cited by:
  1. Nessah, Rabia & Tazdaı¨t, Tarik, 2013. "Absolute optimal solution for a compact and convex game," European Journal of Operational Research, Elsevier, vol. 224(2), pages 353-361.
  2. Berghammer, Rudolf & Bolus, Stefan & Rusinowska, Agnieszka & de Swart, Harrie, 2011. "A relation-algebraic approach to simple games," European Journal of Operational Research, Elsevier, vol. 210(1), pages 68-80, April.
  3. Agnieszka Rusinowska & Rudolf Berghammer & Harrie De Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
  4. Berghammer, Rudolf & Bolus, Stefan, 2012. "On the use of binary decision diagrams for solving problems on simple games," European Journal of Operational Research, Elsevier, vol. 222(3), pages 529-541.
  5. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2011. "Computing Tournament Solutions using Relation Algebra and REL VIEW," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639942, HAL.

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