A Ramsey bound on stable sets in Jordan pillage games
- 140 Downloads
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.
KeywordsPillage Cooperative game theory Stable sets
JEL ClassificationC71 P14
Unable to display preview. Download preview PDF.
- 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
- Diestel R (2005) Graph theory number 173 in graduate texts in mathematics, 3rd edn. Springer, New YorkGoogle Scholar
- 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
- König D (1936) Theorie der endlichen und unendlichen Graphen: Kombinatorische Topologie der Streckenkomplexe. Akad. Verlag, LeipzigGoogle Scholar
- Korte B, Vygen J (2006) Combinatorial optimization: theory and algorithms. Number 21 in Algorithms and combinatorics, 3rd edn. Springer, BerlinGoogle Scholar
- Radziszowski SP (2006) Small Ramsey numbers, revision #11. Electronic J Comb, 1 August 2006. Dynamic Surveys DS1Google Scholar
- Saxton D (2010) Strictly monotonic multidimensional sequences and stable sets in pillage games. Mimeo, April 6 2010Google Scholar
- 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
- Xiaodong X (2002) Classical Ramsey theory and its application. Master’s thesis, National University of Defense Technology, Changsha, China (in Chinese)Google Scholar
- Xiaodong X, Zheng X, Exoo G, Radziszowski SP (2004) Constructive lower bounds on classical multicolor Ramsey numbers. Electronic J Comb 11(1)Google Scholar