International Journal of Game Theory

, Volume 40, Issue 3, pp 461–466 | Cite as

A Ramsey bound on stable sets in Jordan pillage games



Jordan (J Econ Theory 131(1):26–44, 2006) defined ‘pillage games’, a class of cooperative games whose dominance operator is represented by a ‘power function’ satisfying coalitional and resource monotonicity axioms. In this environment, he proved that stable sets must be finite. We provide a graph theoretical interpretation of the problem which tightens the finite bound to a Ramsey number. We also prove that the Jordan pillage axioms are independent.


Pillage Cooperative game theory Stable sets 

JEL Classification

C71 P14 


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  1. Brandt F, Fischer F, Harrenstein P (2007) The computational complexity of choice sets. In: Samet D (ed) Proceedings of the eleventh conference on the theoretical aspects of rationality and knowledge. Presses Universitaires de Louvain, pp 82–91Google Scholar
  2. Diestel R (2005) Graph theory number 173 in graduate texts in mathematics, 3rd edn. Springer, New YorkGoogle Scholar
  3. Jordan JS (2006) Pillage and property. J Econ Theory 131(1): 26–44CrossRefGoogle Scholar
  4. Kerber M, Rowat C (2009) Stable sets in three agent pillage games. Working Paper 09-07, University of Birmingham, Department of Economics, June 2009Google Scholar
  5. König D (1936) Theorie der endlichen und unendlichen Graphen: Kombinatorische Topologie der Streckenkomplexe. Akad. Verlag, LeipzigGoogle Scholar
  6. Korte B, Vygen J (2006) Combinatorial optimization: theory and algorithms. Number 21 in Algorithms and combinatorics, 3rd edn. Springer, BerlinGoogle Scholar
  7. Kremer M (1993) The O-ring theory of economic development. Q J Econ 108(3): 551–575CrossRefGoogle Scholar
  8. Radziszowski SP (2006) Small Ramsey numbers, revision #11. Electronic J Comb, 1 August 2006. Dynamic Surveys DS1Google Scholar
  9. Richardson M (1953) Solutions of irreflexive relations. Ann Math 58(3): 573–590CrossRefGoogle Scholar
  10. Saxton D (2010) Strictly monotonic multidimensional sequences and stable sets in pillage games. Mimeo, April 6 2010Google Scholar
  11. Shapley LS (1959) A solution containing an arbitrary closed component. In: Tucker AW, Luce RD (eds) Contribution to the theory of games, vol IV of Annals of Mathematical Studies. Princeton University Press, Princeton, pp 87–93Google Scholar
  12. Xiaodong X (2002) Classical Ramsey theory and its application. Master’s thesis, National University of Defense Technology, Changsha, China (in Chinese)Google Scholar
  13. Xiaodong X, Zheng X, Exoo G, Radziszowski SP (2004) Constructive lower bounds on classical multicolor Ramsey numbers. Electronic J Comb 11(1)Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of BirminghamBirminghamUK
  2. 2.Department of EconomicsUniversity of BirminghamBirminghamUK

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