Sufficient Conditions for Unique Stable Sets in Three Agent Pillage Games

32 Pages Posted: 4 Jul 2013

See all articles by Manfred Kerber

Manfred Kerber

University of Birmingham - School of Computer Science

Colin Rowat

University of Birmingham - Department of Economics

Date Written: November 16, 2012

Abstract

Pillage games (Jordan, 2006, “Pillage and property”, JET) have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions’ power as well as to their utility. Extending von Neumann and Morgenstern’s analysis of three agent games in characteristic function form to anonymous pillage games, we find: when the core is non-empty, it must take one of five forms; all such 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 axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory’s flexibility.

Keywords: cooperative game theory, stable sets, algorithm, core

JEL Classification: C63, C71, P14

Suggested Citation

Kerber, Manfred and Rowat, Colin, Sufficient Conditions for Unique Stable Sets in Three Agent Pillage Games (November 16, 2012). Available at SSRN: https://ssrn.com/abstract=2289230 or http://dx.doi.org/10.2139/ssrn.2289230

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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