Artículo
Manfredi, J.J.; Parviainen, M.; Rossi, J.D. "Dynamic Programming Principle for tug-of-war games with noise" (2012) ESAIM - Control, Optimisation and Calculus of Variations. 18(1):81-90
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | Dynamic Programming Principle for tug-of-war games with noise |
| Autor: | Manfredi, J.J.; Parviainen, M.; Rossi, J.D. |
| Filiación: | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, 02015 TKK, Finland Departamento de Matemática, FCEyN UBA (1428), Buenos Aires, Argentina |
| Palabras clave: | 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 |
| Año: | 2012 |
| Volumen: | 18 |
| Número: | 1 |
| Página de inicio: | 81 |
| Página de fin: | 90 |
| DOI: | http://dx.doi.org/10.1051/cocv/2010046 |
| Título revista: | ESAIM - Control, Optimisation and Calculus of Variations |
| Título revista abreviado: | Control Optimisation Calc. Var. |
| ISSN: | 12928119 |
| CODEN: | ECOVF |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v18_n1_p81_Manfredi |
Referencias:
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- Manfredi, J.J., Parviainen, M., Rossi, J.D., An asymptotic mean value property characterization of p-harmonic functions (2010) Proc. Am. Math. Soc., 138, pp. 881-889
- Manfredi, J.J., Parviainen, M., Rossi, J.D., (2009) On the Definition and Properties of P-harmonious Functions, , Preprint
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Citas:
---------- APA ----------
Manfredi, J.J., Parviainen, M. & Rossi, J.D. (2012) . Dynamic Programming Principle for tug-of-war games with noise. ESAIM - Control, Optimisation and Calculus of Variations, 18(1), 81-90.http://dx.doi.org/10.1051/cocv/2010046
---------- CHICAGO ----------
Manfredi, J.J., Parviainen, M., Rossi, J.D. "Dynamic Programming Principle for tug-of-war games with noise" . ESAIM - Control, Optimisation and Calculus of Variations 18, no. 1 (2012) : 81-90.http://dx.doi.org/10.1051/cocv/2010046
---------- MLA ----------
Manfredi, J.J., Parviainen, M., Rossi, J.D. "Dynamic Programming Principle for tug-of-war games with noise" . ESAIM - Control, Optimisation and Calculus of Variations, vol. 18, no. 1, 2012, pp. 81-90.http://dx.doi.org/10.1051/cocv/2010046
---------- VANCOUVER ----------
Manfredi, J.J., Parviainen, M., Rossi, J.D. Dynamic Programming Principle for tug-of-war games with noise. Control Optimisation Calc. Var. 2012;18(1):81-90.http://dx.doi.org/10.1051/cocv/2010046
