GAMBLING IN CONTESTS WITH RANDOM INITIAL LAW
成果类型：
Article
署名作者：
Feng, Han; Hobson, David
署名单位：
University of Warwick
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/14-AAP1088
发表日期：
2016
页码：
186-215
关键词：
摘要：
This paper studies a variant of the contest model introduced in Seel and Strack [J. Econom. Theory 148 (2013) 2033-2048]. 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 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 has 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, nonnegative 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, infinity) nu has a decreasing density; and the density of nu only decreases at points where the convex order constraint is binding.