Quantum Game Theory and Ideal Quantum Strategies

Quantum principles can be applied to game theory, or the study of strategic interactions between rational actors. When games such as the prisoner's dilemma, penny flip, or chess are described through quantum formalism, players may use superposition and entanglement in their strategies as they attempt to maximize their payoff. In a seminal work of quantum game theory, Meyer [PRL 82, 1052 (1999)] claims that, within the PQ penny flip game, the use of quantum strategies rewards a player with a 100% chance of victory against a classical player. This game displays an extreme example of so-called quantum advantage. Employing IBM quantum simulators, I first investigate whether this quantum advantage is genuine or, in other words, solely attributable to the use of quantum strategies. I then investigate how an ideal quantum strategy evolves as the quantum player's awareness of the classical player's bias increases. Lastly, I display possible applications of quantum game theory.