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We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position...
We consider a two-player zero-sum-game in a bounded open domain Ω
described as follows: at a point Ω, Players I and II
play an -step tug-of-war game with probability , and
with probability ( + = 1), a
random point in the ball of radius centered at is
chosen. Once the game position reaches the boundary, Player II pays Player I the amount
given by a fixed payoff function . We give a detailed proof of the fact
that the value...
When and the -harmonic measure on the boundary of the half plane is not additive on null sets. In fact, there are finitely many sets , ,..., in , of -harmonic measure zero, such that .
We consider a two-player zero-sum-game in a bounded open domain Ω
described as follows: at a point Ω, Players I and II
play an -step tug-of-war game with probability , and
with probability ( + = 1), a
random point in the ball of radius centered at is
chosen. Once the game position reaches the boundary, Player II pays Player I the amount
given by a fixed payoff function . We give a detailed proof of the fact
that the value...
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