A-Games: using game-like representation for representing finite automata

Non-determinism in automata theory allows us to model situations where given an input, one or more outputs are possible. Although this decision regarding which state to chose could be random, there are contexts where this decision is not random, for instance when modeling real life situations. Using game theory, we propose the representation of automata as a game of two players. This game is defined for languages of finite size. We characterize that this representation is suited for both deterministic and non-deterministic automata, and relate the former with perfect information games, and the latter with imperfect information games. We argue that this could help us in explaining concurrency in programming, for instance in novice programming environments.