Two-player Knock 'em Down
James Allen Fill, The Johns Hopkins University
David B Wilson, Microsoft
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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