Applications of limited information strategies in Menger's game

summary:As shown by Telgársky and Scheepers, winning strategies in the Menger game characterize $\sigma$-compactness amongst metrizable spaces. This is improved by showing that winning Markov strategies in the Menger game characterize $\sigma$-compactness amongst regular spaces, and that winning strategies may be improved to winning Markov strategies in second-countable spaces. An investigation of 2-Markov strategies introduces a new topological property between $\sigma$-compact and Menger spaces