Pillage games with multiple stable sets

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • NICTA, University of New South Wales, Sydney


We prove that pillage games (Jordan in J Econ Theory 131.1:26–44, 2006, “Pillage and property”, JET) can have multiple stable sets, constructing pillage games with up to 2n−13 stable sets, when the number of agents, n, exceeds four. We do so by violating the anonymity axiom common to the existing literature to establish a power dichotomy: for all but a small exceptional set of endowments, powerful agents can overcome all the others; within the exceptional set, the lesser agents can defend their resources. Once the allocations giving powerful agents all resources are included in a candidate stable set, deriving the rest proceeds by considering dominance relations over the finite exceptional sets—reminiscent of stable sets’ derivation in classical cooperative game theory. We also construct a multi-good pillage game with only three agents that also has two stable sets.


Original languageEnglish
Pages (from-to)993-1013
JournalInternational Journal of Game Theory
Issue number4
Early online date15 Mar 2015
Publication statusPublished - Nov 2015


  • Pillage games, Cooperative game theory, Core, Stable sets, C63, C71, P14