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Two-Player Knock 'em Down


 
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1. Title Title of document Two-Player Knock 'em Down
 
2. Creator Author's name, affiliation, country James Allen Fill; The Johns Hopkins University
 
2. Creator Author's name, affiliation, country David B Wilson; Microsoft
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Knock 'em Down; game theory; Nash equilibrium
 
3. Subject Subject classification Primary: 91A60; Secondary: 91A05
 
4. Description Abstract We analyze the two-player game of Knock 'em Down, asymptotically as the number of tokens to be knocked down becomes large. Optimal play requires mixed strategies with deviations of order $\sqrt{n}$ from the naïve law-of-large numbers allocation. Upon rescaling by $\sqrt{n}$ and sending $n\to\infty$, we show that optimal play's random deviations always have bounded support and have marginal distributions that are absolutely continuous with respect to Lebesgue measure.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) National Science Foundation
 
7. Date (YYYY-MM-DD) 2008-02-14
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/485
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-485
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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