Random Tug-of-War games and the infinity Laplacian
In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/106761 |
| Acceso en línea: | https://hdl.handle.net/2117/106761 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Elliptic Infinity Laplacian Tug-of-War Viscosity solutions Comparison principle Equacions diferencials el·líptiques Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials |
| Sumario: | In this work we introduce and analyze a new random Tug-of-War game in which one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value and identify the partial differential equation to which it is related. This is the first time that such equation is found to have a relation with game theory. Moreover, our analysis relies on comparison and viscosity tools, in contrast to probabilistic arguments which are more common in the literature. The work also includes a review of the infinity Laplacian and its connection to the classical random Tug-of-War game, as well as an introduction to the theory of viscosity solutions. Furthermore, some explicit examples of the new game are considered. |
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