Stable sets in three agent pillage games∗

We consider pillage games as in Jordan [2006, “Pillage and property”, JET] and show that, for anonymous, three agent pillage games: 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, a tight bound. Non-existence is easily determined by applying Zorn’s lemma to the locus of allocations for which the most powerful agent is as powerful as the other two combined. Examples are given both of our core results and cases not covered by them.