A Ramsey Bound on Stable Sets in Jordan Pillage Games
Jordan  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 use graph theory to reinterpret this result, tightening the bound, highlighting the role played by resource monotonicity, and suggesting a strategy for yet tighter bounds.
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- Jordan, J.S., 2006. "Pillage and property," Journal of Economic Theory, Elsevier, vol. 131(1), pages 26-44, November.
- Manfred Kerber & Colin Rowat, 2009. "Stable Sets in Three Agent Pillage Games," Discussion Papers 09-07, Department of Economics, University of Birmingham.