Pillage Games with Multiple Stable Sets

26 Pages Posted: 16 Apr 2013

See all articles by Simon MacKenzie

Simon MacKenzie

Independent

Manfred Kerber

University of Birmingham - School of Computer Science

Colin Rowat

University of Birmingham - Department of Economics

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

MacKenzie, Simon and Kerber, Manfred and Rowat, Colin, Pillage Games with Multiple Stable Sets (February 27, 2013). Available at SSRN: https://ssrn.com/abstract=2251274 or http://dx.doi.org/10.2139/ssrn.2251274

Simon MacKenzie

Independent ( email )

Manfred Kerber

University of Birmingham - School of Computer Science ( email )

Edgbaston
Edgbaston, Birmingham B15 2TT B17 0JH
United Kingdom

Colin Rowat (Contact Author)

University of Birmingham - Department of Economics ( email )

Economics Department
Birmingham, B15 2TT
United Kingdom
+44 121 414 3754 (Phone)
+44 121 414 7377 (Fax)

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