Feng, Han (2014) Variants of gambling in contests. PhD thesis, University of Warwick.
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Abstract
In the Seel-Strack contest (Seel and Strack [2013]), n agents each privately observe an independent copy of a drifting Brownian motion which starts above zero. Each agent chooses when to stop the process she observes, and the winner of the contest is the agent who stops her Brownian motion at the highest value amongst the set of agents. The objective of each agent is to maximise her probability of winning the contest. We will give a new derivation of the results of Seel and Strack [2013] based on a Lagrangian approach. This approach facilitates our analysis of the variants of the Seel-Strack problem.
We will consider a generalisation of the Seel-Strack contest in which the observed processes are independent copies of some time-homogeneous diffusion. We will use a change of scale to reduce this contest to a contest in which the observed processes are diffusions in natural scale. It turns out that, unlike in the Seel-Strack problem, the way of breaking ties becomes important.
Moreover, we will discuss an extension of the Seel-Strack contest to one in which an agent is penalised when her strategy is suboptimal, in the sense that her chosen strategy does not win the contest, but there existed an alternative strategy which would have resulted in victory. We will see that different types of penalty have different effects.
Seel and Strack [2013] studied the asymmetric 2-player contest in which the observed processes start from different constants. We will redrive their results using the Lagrangian method and then study a general asymmetric n-player contest. We will find that some results in the 2-player contest do not hold for the general n-player contest.
In a symmetric 2-player contest, the Seel-Strack model assumes that the observed processes start from the same positive constant. We will extend the results to the case where the starting values of the processes are independent non-negative random variables that have the same distribution.
| Item Type: | Thesis [via Doctoral College] (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Game theory, Brownian motion processes |
| Official Date: | June 2014 |
| Dates: | Date Event June 2014 Submitted |
| Institution: | University of Warwick |
| Theses Department: | Department of Statistics |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Hobson, David (David G.) |
| Sponsors: | University of Warwick. Department of Statistics |
| Extent: | vii, 111 leaves : charts |
| Language: | eng |
| URI: | https://wrap.warwick.ac.uk/62967/ |
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