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Stable Sets in Three Agent Pillage Games

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  • Manfred Kerber
  • Colin Rowat

Abstract

Jordan [2006, “Pillage and property”, JET] characterises stable sets for three special cases of ‘pillage games’. For anonymous, three agent pillage games we show that: when the core is non-empty, it must take one of five forms; all such pillage games with an empty core represent the same dominance relation; when a stable set exists, and the game also satisfies a continuity and a responsiveness assumption, it is unique and contains no more than 15 elements. This result uses a three step procedure: first, if a single agent can defend all of the resources against the other two, these allocations belong to the stable set; dominance is then transitive on the loci of allocations on which the most powerful agent can, with any ally, dominate the third, adding the maximal elements of this set to the stable set; finally, if any allocations remain undominated or not included, the game over the remaining allocations is equivalent to the ‘majority pillage game’, which has a unique stable set [Jordan and Obadia, 2004, “Stable sets in majority pillage games”, mimeo]. Non-existence always reflects conditions on the loci of allocations along which the most powerful agent needs an ally. The analysis unifies the results in Jordan [2006] when n = 3.

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Bibliographic Info

Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 09-07.

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Length: 29 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:bir:birmec:09-07

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Postal: Edgbaston, Birmingham, B15 2TT
Web page: http://www.economics.bham.ac.uk
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Related research

Keywords: pillage; cooperative game theory; core; stable sets; algorithm;

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Cited by:
  1. Manfred Kerber & Colin Rowat, 2012. "Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games," Discussion Papers 12-11, Department of Economics, University of Birmingham.
  2. Simon MacKenzie & Manfred Kerber & Colin Rowat, 2013. "Pillage Games with Multiple Stable Sets," Discussion Papers 13-07, Department of Economics, University of Birmingham.
  3. Manfred Kerber & Colin Rowat, 2009. "A Ramsey Bound on Stable Sets in Jordan Pillage Games," Discussion Papers 09-01r, Department of Economics, University of Birmingham.

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