Sufficient Conditions for the Unique Stable Sets in Three Agent Pillage Games
AbstractPillage 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.
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Bibliographic InfoPaper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 12-11.
Length: 32 pages
Date of creation: Nov 2012
Date of revision:
co-operative game theory; stable sets; algorithm; core;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- P14 - Economic Systems - - Capitalist Systems - - - Property Rights
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-19 (All new papers)
- NEP-GTH-2013-01-19 (Game Theory)
- NEP-MIC-2013-01-19 (Microeconomics)
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