Dynamic MRR function optimization using calculus of variations.
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Dynamic Programming Principle for tug-of-war games with noise
Juan J. Manfredi, Mikko Parviainen, Julio D. Rossi (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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 reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...
Dynamic Programming Principle for tug-of-war games with noise
Juan J. Manfredi, Mikko Parviainen, Julio D. Rossi (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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 reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that the value functions of this game satisfy the Dynamic Programming Principle...
Dynamic Programming Principle for tug-of-war games with noise
Juan J. Manfredi, Mikko Parviainen, Julio D. Rossi (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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 reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...
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