Electronic Journal of Probability

Two-Player Knock 'em Down

James Fill and David Wilson

Full-text: Open access

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.

Article information

Source
Electron. J. Probab. Volume 13 (2008), paper no. 9, 198-212.

Dates
Accepted: 14 February 2008
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819082

Digital Object Identifier
doi:10.1214/EJP.v13-485

Mathematical Reviews number (MathSciNet)
MR2386732

Zentralblatt MATH identifier
1186.91055

Subjects
Primary: 91A60: Probabilistic games; gambling [See also 60G40]
Secondary: 91A05: 2-person games

Keywords
Knock 'em Down game theory Nash equilibrium

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Fill, James; Wilson, David. Two-Player Knock 'em Down. Electron. J. Probab. 13 (2008), paper no. 9, 198--212. doi:10.1214/EJP.v13-485. https://projecteuclid.org/euclid.ejp/1464819082


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References

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