Pillage games with multiple stable sets

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Pillage games with multiple stable sets. / Mackenzie, Simon; Kerber, Manfred; Rowat, Colin.

In: International Journal of Game Theory, Vol. 44, No. 4, 11.2015, p. 993-1013.

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@article{f24dae08c6d04eb0987eea1ab27749ef,
title = "Pillage games with multiple stable sets",
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{\textquoteright} derivation in classical cooperative game theory. We also 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, C63, C71, P14",
author = "Simon Mackenzie and Manfred Kerber and Colin Rowat",
year = "2015",
month = nov,
doi = "10.1007/s00182-015-0462-1",
language = "English",
volume = "44",
pages = "993--1013",
journal = "International Journal of Game Theory",
issn = "0020-7276",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Pillage games with multiple stable sets

AU - Mackenzie, Simon

AU - Kerber, Manfred

AU - Rowat, Colin

PY - 2015/11

Y1 - 2015/11

N2 - 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.

AB - 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.

KW - Pillage games

KW - Cooperative game theory

KW - Core

KW - Stable sets

KW - C63

KW - C71

KW - P14

U2 - 10.1007/s00182-015-0462-1

DO - 10.1007/s00182-015-0462-1

M3 - Article

VL - 44

SP - 993

EP - 1013

JO - International Journal of Game Theory

JF - International Journal of Game Theory

SN - 0020-7276

IS - 4

ER -