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Abstract
We prove that pillage games (Jordan in J Econ Theory 131.1:26–44, 2006, “Pillage and property”, JET) can have multiple stable sets, constructing pillage games with up to 2n−13 stable sets, when the number of agents, n, exceeds four. We do so by violating the anonymity axiom common to the existing literature to establish a power dichotomy: for all but a small exceptional set of endowments, powerful agents can overcome all the others; within the exceptional set, the lesser agents can defend their resources. Once the allocations giving powerful agents all resources are included in a candidate stable set, deriving the rest proceeds by considering dominance relations over the finite exceptional sets—reminiscent of stable sets’ derivation in classical cooperative game theory. We also construct a multi-good pillage game with only three agents that also has two stable sets.
Original language | English |
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Pages (from-to) | 993-1013 |
Journal | International Journal of Game Theory |
Volume | 44 |
Issue number | 4 |
Early online date | 15 Mar 2015 |
DOIs | |
Publication status | Published - Nov 2015 |
Keywords
- Pillage games
- Cooperative game theory
- Core
- Stable sets
- C63
- C71
- P14
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Dive into the research topics of 'Pillage games with multiple stable sets'. Together they form a unique fingerprint.Projects
- 1 Finished
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Formal Representation and Proof for Cooperative Games: A Foundation for Complex Social Behaviour
Kerber, M. & Rowat, C.
Engineering & Physical Science Research Council
1/05/12 → 30/04/15
Project: Research Councils