With the advent of the fighting game AI competition, there has been recent interest in two-player fighting games. Monte-Carlo Tree-Search approaches currently dominate the competition, but it is unclear if this is the best approach for all fighting games. In this paper we study the design of two- player fighting games and the consequences of the game design on the types of AI that should be used for playing the game, as well as formally define the state space that fighting games are based on. Additionally, we also characterize how AI can solve the game given a simultaneous action game model, to understand the characteristics of the solved AI and the impact it has on game design.