## Electronic Journal of Probability

### Two-Player Knock 'em Down

#### 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

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
Secondary: 91A05: 2-person games

Rights

#### 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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