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Title
A Study of Two Models of Competitive Interaction
Description
We study two models of a competitive game in which players continuously receive points and wager them in one-on-one battles. In each model the loser of a battle has their points reset, while the points the winner receives is what sets the two models apart. In the knockout model the winner receives no new points, while in the winner-takes-all model the points that the loser had are added to the winner's total. Recurrence properties are assessed for both models: the knockout model is recurrent except for the all-zero state, and the winner-takes-all model is transient, but retains some aspect of recurrence. In addition, we study the population-level allocation of points; for the winner-takes-all model we show explicitly that the proportion of individuals having any number j of points, j=0,1,... approaches a stationary distribution that can be computed recursively. Graphs of numerical simulations are included to exemplify the results proved.
Date Created
2016-12
Contributors
- VanKirk, Maxwell Joshua (Author)
- Lanchier, Nicolas (Thesis director)
- Foxall, Eric (Committee member)
- Barrett, The Honors College (Contributor)
- School of Mathematical and Statistical Sciences (Contributor)
Topical Subject
Resource Type
Extent
17 pages
Language
eng
Copyright Statement
In Copyright
Primary Member of
Series
Academic Year 2016-2017
Handle
https://hdl.handle.net/2286/R.I.40564
Level of coding
minimal
Cataloging Standards
System Created
- 2017-10-30 02:50:58
System Modified
- 2021-08-11 04:09:57
- 3 years 3 months ago
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