Gambling in Contests with Random Initial Law
AbstractThis paper studies a variant of the contest model introduced by Seel and Strack. In the Seel-Strack contest, each agent or contestant privately observes a Brownian motion, absorbed at zero, and chooses when to stop it. The winner of the contest is the contestant who stops at the highest value. The model assumes that all the processes start from a common value $x_0>0$ and the symmetric Nash equilibrium is for each agent to utilise a stopping rule which yields a randomised value for the stopped process. In the two-player contest this randomised value should have a uniform distribution on $[0,2x_0]$. In this paper we consider a variant of the problem whereby the starting values of the Brownian motions are independent, non-negative, random variables that have a common law $\mu$. We consider a two-player contest and prove the existence and uniqueness of a symmetric Nash equilibrium for the problem. The solution is that each agent should aim for the target law $\nu$, where $\nu$ is greater than or equal to $\mu$ in convex order; $\nu$ has an atom at zero of the same size as any atom of $\mu$ at zero, and otherwise is atom free; on $(0,\infty)$ $\nu$ has a decreasing density; and the density of $\nu$ only decreases at points where the convex order constraint is binding.
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.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1405.7801.
Date of creation: May 2014
Date of revision:
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-06-07 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Seel, Christian & Strack, Philipp, 2013. "Gambling in contests," Journal of Economic Theory, Elsevier, Elsevier, vol. 148(5), pages 2033-2048.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.