Feng, Han and Hobson, David (2015) Gambling in contests with random initial law. Annals of Applied Probability, 26 (1). pp. 186-215.

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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:	5 January 2015
Dates:	Date Event 5 January 2015 Available
Date of first compliant deposit:	19 January 2016
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:	ArXiv

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