Genericity with Infinitely Many Parameters
AbstractGenericity analysis is widely used to show that desirable properties that fail in certain "knife-edge" economic situations nonetheless obtain in "typical" situations. For finite-dimensional spaces of parameters, the usual notion of genericity is full Lebesgue measure. For infinite dimensional spaces of parameters (for instance, the space of preferences on a finite-dimensional commodity space, no analogue of Lebesgue measure is available; the lack of such an analogue has prompted the use of less compelling topological notions of genericity. Christensen (1974) and Hunt, Sauer and Yorke (1992) have proposed a measure-theoretic notion of genericity, which Hunt, Sauer and Yorke call prevalence, which coincides with full Lebesgue measure in Euclidean space and which extends to infinite-dimensional vector spaces. This notion is not directly applicable in most economic settings because the relevant parameter sets are small subsets of vector spaces -- especially cones or order intervals -- not vector spaces themselves. We adapt the notion to economically relevant environments by defining two notions of prevalence relative to a convex set in a topological vector space. The first notion is very easy to understand and apply, and has all of the properties one would desire except that it is not closed under countable unions; the second notion contains the first and has all the good properties of the first notion except simplicity; it is closed under countable unions. We provide four economic applications: 1) generic existence of equilibrium in financial models, 2) generic finiteness of the number of pure strategy Nash equilibria and Pareto inefficiency of "non-vertex" Nash equilibria for games with a continuum of actions and smooth payoffs, 3) generic regularity of exchange economies when some agents are constrained to have 0 endowment of some goods, 4) generic single-valuedness of the core of transferable utility games.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.
Volume (Year): 1 (2001)
Issue (Month): 1 (February)
Contact details of provider:
Web page: http://www.degruyter.com
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Peter Golla).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.