Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games

Manfred Kerber and Colin Rowat

Discussion Papers from Department of Economics, University of Birmingham

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: co-operative game theory; stable sets; algorithm; core (search for similar items in EconPapers)
JEL-codes: C63 C71 P14 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2012-11
New Economics Papers: this item is included in nep-gth and nep-mic
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Journal Article: Sufficient conditions for unique stable sets in three agent pillage games (2014)
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