It is known that, in one – good pillage games, stable sets are finite. For m goods, it has been conjectured that the stable sets have measure zero. We introduce a class of sets, termed pseudo-indiff erence sets, which includes level sets of utility functions, quasi-indiff erence classes...

We prove that pillage games (Jordan, 2006, “Pillage and property”, JET) can have multiple stable sets, constructing pillage games with up to 2^{(n-1)/3} stable sets, when the number of agents, n, exceeds four. We do so by violating the anonymity axiom common to the existing literature,...