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Random strategies are nearly optimal for generalized van der Waerden Games
dc.contributor.author | Kusch, C. |
dc.contributor.author | Rué Perna, Juan José |
dc.contributor.author | Spiegel, Christoph |
dc.contributor.author | Szabó, T. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-12-04T12:43:19Z |
dc.date.available | 2019-09-01T00:25:43Z |
dc.date.issued | 2017-08-01 |
dc.identifier.citation | Kusch, C., Rue, J., Spiegel, C., Szabó, T. Random strategies are nearly optimal for generalized van der Waerden Games. "Electronic notes in discrete mathematics", 1 Agost 2017, vol. 61, p. 1-7. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/111534 |
dc.description.abstract | In a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. Luczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], who studied biased H-games, we prove general winning criteria for Maker and Breaker and a hypergraph generalization of their result. Furthermore, we study the biased version of a strong generalization of the van der Waerden games introduced by Beck [Beck, J., Van der Waerden and Ramsey type games, Combinatorica, 1 (1981), 103–116] and apply our criteria to determine the threshold bias of these games up to constant factor. As in the result of [Bednarska, M., and T. Luczak, Biased positional games for which random strategies are nearly optimal, Combinatorica, 20 (2000), 477–488], the random strategy for Maker is again the best known strategy. |
dc.format.extent | 7 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa |
dc.subject.lcsh | Random variables |
dc.subject.other | General Winning Criteria |
dc.subject.other | Generalised van der Waerden games |
dc.subject.other | Maker-Breaker games |
dc.title | Random strategies are nearly optimal for generalized van der Waerden Games |
dc.type | Article |
dc.subject.lemac | Variables aleatòries |
dc.contributor.group | Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
dc.identifier.doi | 10.1016/j.endm.2017.07.037 |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S1571065317302020?via%3Dihub |
dc.rights.access | Open Access |
local.identifier.drac | 21554517 |
dc.description.version | Postprint (updated version) |
local.citation.author | Kusch, C.; Rue, J.; Spiegel, C.; Szabó, T. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 61 |
local.citation.startingPage | 1 |
local.citation.endingPage | 7 |
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