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Consider QBF, the Quantified Boolean Formula problem, as a combinatorial gameruleset. The problem is rephrased as determining the winner of the game wheretwo opposing players take turns assigning values to boolean variables. In thispaper, three common variations of games are applied to create seven new games:whether each player is restricted to where they may play, which values they mayset variables to, or the condition they are shooting for at the end of thegame. The complexity for determining which player can win is analyzed for allgames. Of the seven, two are trivially in P and the other five arePSPACE-complete. These varying properties are common for combinatorial games;reductions from these five hard games can simplify the process for showing thePSPACE-hardness of other games.

$2^3$ Quantified Boolean Formula Games and Their Complexities