Electronic Journal of Probability

Two-Player Knock 'em Down

James Fill and David Wilson

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Knock 'em Down game theory Nash equilibrium

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


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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