A Review of Quantum Games

Authors: Gaon Kim and Eung-won Nho

Institution Information: K. International School Tokyo, 1-5-15 Shirakawa, Koto-ku, Tokyo, Japan

Department of Economics, Chungnam National University, 99 Daehak-ro, Gung-dong, Yuseong-gu, Daejon, South Korea


Over the past two decades, the quantum mechanical concepts of superposition and entanglement have been applied in game theory to produce novel and interesting results. Quantization offers significant improvements to classical games that cannot be realized using purely classical strategy spaces. Because quantum game theory is a recent development with both merits and limitations, this review attempts to critically evaluate existing research as well as gaps in the literature requiring further research. The literature is classified into four categories of games based on differences in quantization schemes and results: quantum simultaneous non-zero-sum games, quantum simultaneous zero-sum games, quantum coalitional games and quantum sequential games. The first two categories exhibit the results of Pareto efficiency and improved payoffs, but the literature reviewed does not sufficiently analyze the role of strategic coordination in bringing about such improvements. Quantum coalitional games also have improvements over their classical counterparts, often leading to cores that yield higher payoffs to a greater number of players, given a quantization scheme that encompasses all players’ strategy spaces. However, the mechanism through which these improvements are realized is generally unclear. Finally, quantum sequential games exhibit cooperative behavior among players that is absent in the corresponding classical games. This review concludes that quantum games have significant advantages over their classical counterparts and suggests the role of strategic coordination in quantum games as a fruitful direction for future research.

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