Stable Sets in multi-good pillage games are small
It is known that, in one-good pillage games, stable sets are finite. For m goods, it has been conjectured that the stable sets have measure zero. We introduce a class of sets, termed pseudo-indifference sets, which includes level sets of utility functions, quasi-indifference classes associated with a preference relation not given by a utility function, production possibility frontiers, and Pareto efficient sets. We establish the truth of the conjecture by proving that pseudo-indifference sets in Rp have p-dimensional measure zero. This implies that stable sets in n-agent, m-good pillage games have m(n - 1)-dimensional measure zero. We then prove that each pseudo-indifference set in Rp has Hausdorff dimension at most p - 1, a much stronger result than measure zero. Finally, we establish a stronger version of the conjecture: stable sets in n-agent, m-good pillage games have dimension at most m(n-1)-1.
|Date of creation:||Feb 2010|
|Contact details of provider:|| Postal: Edgbaston, Birmingham, B15 2TT|
Web page: http://www.economics.bham.ac.uk
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:bir:birmec:10-05. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Colin Rowat)
If references are entirely missing, you can add them using this form.