Dynamic Programming Principle for tug-of-war games with noise
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 reach...
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paper:paper_12928119_v18_n1_p81_Manfredi2023-06-08T16:10:14Z Dynamic Programming Principle for tug-of-war games with noise Rossi, Julio Daniel Dirichlet boundary conditions Dynamic Programming Principle P-Laplacian Stochastic games Two-player zero-sum games Dirichlet boundary condition Dynamic Programming Principle P-Laplacian Stochastic game Zero-sum game Boundary conditions Dynamic programming 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\\begin{equation*} u(x) = α{2} in ol Bε(x) u (y) + y in ol Bε(x) u (y) + β kint Bε(x) u(y) ud y, end equation* for x Ω with u(y) = F(y) when y Ω. This principle implies the existence of quasioptimal Markovian strategies. © 2010 EDP Sciences, SMAI. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v18_n1_p81_Manfredi http://hdl.handle.net/20.500.12110/paper_12928119_v18_n1_p81_Manfredi |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Dirichlet boundary conditions Dynamic Programming Principle P-Laplacian Stochastic games Two-player zero-sum games Dirichlet boundary condition Dynamic Programming Principle P-Laplacian Stochastic game Zero-sum game Boundary conditions Dynamic programming |
| spellingShingle |
Dirichlet boundary conditions Dynamic Programming Principle P-Laplacian Stochastic games Two-player zero-sum games Dirichlet boundary condition Dynamic Programming Principle P-Laplacian Stochastic game Zero-sum game Boundary conditions Dynamic programming Rossi, Julio Daniel Dynamic Programming Principle for tug-of-war games with noise |
| topic_facet |
Dirichlet boundary conditions Dynamic Programming Principle P-Laplacian Stochastic games Two-player zero-sum games Dirichlet boundary condition Dynamic Programming Principle P-Laplacian Stochastic game Zero-sum game Boundary conditions Dynamic programming |
| description |
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\\begin{equation*} u(x) = α{2} in ol Bε(x) u (y) + y in ol Bε(x) u (y) + β kint Bε(x) u(y) ud y, end equation* for x Ω with u(y) = F(y) when y Ω. This principle implies the existence of quasioptimal Markovian strategies. © 2010 EDP Sciences, SMAI. |
| author |
Rossi, Julio Daniel |
| author_facet |
Rossi, Julio Daniel |
| author_sort |
Rossi, Julio Daniel |
| title |
Dynamic Programming Principle for tug-of-war games with noise |
| title_short |
Dynamic Programming Principle for tug-of-war games with noise |
| title_full |
Dynamic Programming Principle for tug-of-war games with noise |
| title_fullStr |
Dynamic Programming Principle for tug-of-war games with noise |
| title_full_unstemmed |
Dynamic Programming Principle for tug-of-war games with noise |
| title_sort |
dynamic programming principle for tug-of-war games with noise |
| publishDate |
2012 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v18_n1_p81_Manfredi http://hdl.handle.net/20.500.12110/paper_12928119_v18_n1_p81_Manfredi |
| work_keys_str_mv |
AT rossijuliodaniel dynamicprogrammingprinciplefortugofwargameswithnoise |
| _version_ |
1768546034237046784 |