Pillage Games with Multiple Stable Sets
26 Pages Posted: 16 Apr 2013
Date Written: February 27, 2013
Abstract
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, instead endowing some agents to overpower all but a small number of opposing configurations of agents. Thus, when the core is non-empty, it dominates all but finitely many allocations. As the core must belong to any stable set, derivation of stable sets then requires considering dominance relations among these finite sets of allocations – reminiscent of stable sets’ derivation in classical cooperative game theory. While our constructions are most easily illustrated for non-empty core, we also present a pillage game with multiple stable sets but an empty core. Finally, we construct a multi-good pillage game with only three agents that also has two stable sets.
Keywords: pillage games, cooperative game theory, core, stable sets
JEL Classification: C63, C71, P14
Suggested Citation: Suggested Citation