I've been reading Games, Puzzles, and Computation which analyzes games through game theory and complexity theory.
The authors introduce something called "Constraint Logic" as a way of modeling games and proving their complexity class. For example, we can make a reduction from NP-Complete problems to a general Constraint Logic form to determine NP-Hardness. I mostly skipped to the proofs on 1- and 2-player games. Like most 2-player games, the 2-player games used are turn-based.
I was wondering if there is some mathematical reason for why most 2-player games are turn-based, instead of simultaneous move. Also, can it be proven that the order of turns does or doesn't affect the fairness of the game?