We propose a concept of quantum extensive-form games, which is a quantum extension of classical extensive-form games. Extensive-form games is a general concept of games such as Go, Shogi, and chess, which have triggered the recent AI revolution, and is the basis for many important game theoretic models in economics. Quantum transitions allow for pairwise annihilation of paths in the quantum game tree, resulting in a probability distribution that is more likely to produce a particular outcome. This is similar in principle to the mechanism of speed-up by quantum computation represented by Grover's algorithm. A quantum extensive-form game is also a generalization of quantum learning, including Quantum Generative Adversarial Networks. As an new example of quantum extensive-form games, we propose a quantum form of the Angel problem originally proposed by Conway in 1996. The classical problem has been solved but by quantizing it, the game becomes non-trivial.

15 pages