Quantum Game Theory — I

Zhi Wang

Wenjie Liu, Jingfa Liu, Mengmeng Cui +1 more

With utilizing some quantum mechanism into the game theory, quantum game theory provides us with the ability to achieve results not otherwise possible. In this paper, a brief overview of classical game theory and some game-theoretic terms are depicted. Then, an introduction to quantum theory is presented as well as some correlative works in this field. Finally, some well-known quantum games are analyzed and discussed, which shows its predominant effect on some games problems (the Prisoners' Dilemma, Parrondo's Games, etc.).

Indranil Ghosh

Indranil Ghosh

David M. Schneider

With nearly one decade of life, the theory of quantum games has nowadays become a very reach and prolific field of research. Multiplayer and multistrategy setups, a quantum approach to Evolutionary Game Theory, quantum game-like simulations of market phenomena, quantum duels, the effect of decoherence and noise during the implementation of a quantum game, are just some of the many scenarios where the quantum aspects of games were analyzed [2–4, 6, 7, 11–13, 16–18, 23]. Here we do not attempt to review the vast universe of quantum game theory, but just to give a comprehensive and didactic introduction to the pioneering work of Eisert [5]. This introduction will allow us to expose a recent approach developed to geometrically understand quantum games [20, 21], which represents the main focus this chapter. For a complete review of quantum games, we refer the reader to [9].

Edward W. Piotrowski, Jan Sładkowski