A Review of Quantum Games

expanded to include unitary operators (termed “quantum strategies”), or (iii) both of the above occur. These quantum mechanical applications in games produce various novel and interesting results. In this review, the term “novel” refers to a result in quantum game theory that is favorable and could not be realized in classical game theory. Quantum game theory literature focuses on a number of such results to establish the topic’s significance. Pareto efficiency refers to an outcome in a game such that there are no other possible outcomes that give higher payoffs to a non-zero number of players without decreasing any player’s payoff. Conversely, Pareto inefficiency is observed when the Nash equilibrium of the game – an outcome where all players of a game do not have an incentive to change their strategies – does not exhibit Pareto efficiency (Nash, 1951). Games that are Pareto inefficient under the classical paradigm can be made efficient through the use of quantization, which is a novel result beneficial to the players (Eisert, Wilkens, and Lewenstein, 1999). Another key result is higher payoffs for players in the game, which directly indicates that they have benefitted from quantization (Meyer, 1999). Quantization can also lead to new coalitions among players in the game that gives higher payoffs to a greater number of players (Chen, Hogg, and Beausoleil, 2002). These results, obtained uniquely in quantum games, are significant as they expose a deep and rich econophysical connection wherein quantization is conducive to strategic coordination. Although the current lack of quantum technology imposes significant limitations on immediate practical applications of the theory, the accuracy of a few simple quantum games has been supported with experimental evidence through computer science, suggesting the potential relevance of the theory once necessary technological advances are made (Du et al., 2002; Prevedel et al., 2007; Schmid et al., 2010). Research conducted on quantum game theory may be clasA Review of Quantum Games