The Library
Gambling in contests with random initial law
Tools
Tools
Tools
Feng, Han and Hobson, David (2016) Gambling in contests with random initial law. Annals of Applied Probability, 26 (1). pp. 186-215.
|
PDF
WRAP_AAP1088 Jan 16.pdf - Published Version - Requires a PDF viewer. Download (548Kb) | Preview |
|
![[img]](http://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP_RandomStartAAPr141119.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (1259Kb) |
Official URL: http://dx.doi.org/10.1214/14-AAP1088
Abstract
This paper studies a variant of the contest model introduced in Seel and Strack (2013). 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 agent who stops at the highest value. The model assumes that all the processes start from a common value x0 > 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 has a uniform distribution on [0, 2x0].
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 µ. We consider a twoplayer 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 ν, where ν is greater than or equal to µ in convex order; ν has an atom at zero of the same size as any atom of µ at zero, and otherwise is atom free; on (0, ∞) ν has a decreasing density; and the density of ν only decreases at points where the convex order constraint is binding.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Games of chance (Mathematics) | ||||||
| Journal or Publication Title: | Annals of Applied Probability | ||||||
| Publisher: | Institute of Mathematical Statistics | ||||||
| ISSN: | 1050-5164 | ||||||
| Official Date: | 1 February 2016 | ||||||
| Dates: |
|
||||||
| Volume: | 26 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 186-215 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
