| Two-player Knock 'em Down (2008) | |||||||||||||
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 √n from the naïve law-of-large numbers allocation. Upon rescaling by √n and sending n→∞, 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. | |||||||||||||
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