Discontinuity and non-existence of equilibrium in the probabilistic spatial voting model
This paper shows that in the simplest one-dimensional, two-candidate probabilistic spatial voting model (PSVM), a pure strategy Nash equilibrium may fail to exist. The existence problem studied here is the result of a discontinuity in the function mapping the candidates' platforms into their probabilities of winning. Proposition 1 of the paper shows that, whenever this probability of winning function satisfies a certain monotonicity property, it must be discontinuous on the diagonal. As an immediate consequence of the discontinuity in the probability of winning function, the candidates' objective functions are discontinuous as well. It is therefore impossible to invoke standard theorems guaranteeing the existence of a pure strategy equilibrium, and an example is developed in which in fact there is no pure strategy equilibrium. Finally, however, it is demonstrated that, for a large class of probability of winning functions, the PSVM satisfies all the conditions of a theorem of Dasgupta and Maskin (1986a) which guarantees that it will always have an equilibrium in mixed strategies.
If 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.
Volume (Year): 16 (1999)
Issue (Month): 4 ()
|Note:||Received: 31 December 1996/Accepted: 12 May 1998|
|Contact details of provider:|| Web page: http://www.springer.com|
|Order Information:||Web: http://www.springer.com/economics/economic+theory/journal/355|
When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:16:y:1999:i:4:p:533-555. 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: (Sonal Shukla)or (Rebekah McClure)
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.