Sharp thresholds for half-random games II
| Autor: | Tibor Szabó, Jonas Groschwitz |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Computer Science::Computer Science and Game Theory
Institut für Mathematik 0211 other engineering and technologies Complete graph ComputingMilieux_PERSONALCOMPUTING 021107 urban & regional planning Randomized strategy 0102 computer and information sciences 02 engineering and technology 01 natural sciences Upper and lower bounds Theoretical Computer Science Combinatorics Set (abstract data type) Asymptotically optimal algorithm 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Enhanced Data Rates for GSM Evolution Combinatorics (math.CO) ddc:510 Focus (optics) Mathematics |
| DOI: | 10.48550/arxiv.1602.04628 |
| Popis: | We study biased Maker-Breaker positional games between two players, one of whom is playing randomly against an opponent with an optimal strategy. In this work we focus on the case of Breaker playing randomly and Maker being "clever". The reverse scenario is treated in a separate paper. We determine the sharp threshold bias of classical games played on the edge set of the complete graph $K_n$, such as connectivity, perfect matching, Hamiltonicity, and minimum degree-$1$. In all of these games, the threshold is equal to the trivial upper bound implied by the number of edges needed for Maker to occupy a winning set. Moreover, we show that the clever Maker can not only win against an asymptotically optimal bias, but can do so very fast, wasting only logarithmically many moves (while the winning set sizes are linear in $n$). Comment: This is the second part of our work on this subject, the first part can be found here: arXiv:1507.06688 . Originally, both parts were contained in the same paper. This original version can be found here: arXiv:1507.06688v2 |
| Databáze: | OpenAIRE |
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