Determinacy of infinite games is one of oldest result in
Friedman-Simpson's reverse mathematics and have been investigated by a
lot of researchers.
[Veldman 09] formulated determinacy in intuitionistic mathematics. His
unpublished note also consider it from the viewpoint of reverse
mathematics in intuitionistic setting.
In this talk, we see some similarity and dissimilarity between
determinacy in two kinds of reverse mathematics.
[Nemoto, Medsalem and Tanaka 09] Infinite games in the Cantor space
and subsystems of second order arithmetic, Mathematical Logic
Quarterly, Volume 53, Issue 3 (2007), pp. 226 - 236.
[Veldman 09] The Problem of Determinacy of Infinite Games from an
Intuitionistic Point of View,
Games: Unifying Logic, Language, and Philosophy, Logic, Epistemology,
and the Unity of Science Volume 15, 2009, pp 351-370