Maker-Maker and Maker-Breaker Games are PSPACE-Complete - Byskov, Jesper Makholm (BRICS Report Series, 2004)
We show that the problems of deciding the outcome of Maker-Maker and Maker-Breaker games played on arbitrary hypergraphs are PSPACE-complete. Maker-Breaker games have earlier been shown PSPACE-complete by Schaefer (1978); we give a simpler proof and show a reduction from Maker-Maker games to Maker-Breaker games.