Quantum Game Simulation

Ramón Alonso‐Sanz

Panagiotis Vlachos, Ioannis G. Karafyllidis

Panagiotis Vlachos, Ioannis G. Karafyllidis

We present a general two-player quantum game simulator that can simulate any two-player quantum game described by a 2times2 payoff matrix (two strategy games).The user can determine the payoff matrices for both players, their strategies and the amount of entanglement between their initial strategies. The outputs of the simulator are the expected payoffs of each player as a function of the other player's strategy parameters and the amount of entanglement. The simulator also produces contour plots that divide the strategy spaces of the game in regions in which players can get larger payoffs if they choose to use a quantum strategy against any classical one. We also apply the simulator to two well known quantum games, the Battle of Sexes and the Chicken game.

A. Madrid S.

This paper provides some examples about quantum games simulated in Python’s programming language. The quantum games have been developed with the Sympy Python library, which permits solving quantum problems in a symbolic form. The application of these methods of quantum mechanics to game theory gives us more possibility to achieve results not possible before. To illustrate the results of these methods, in particular, there have been simulated the quantum battle of the sexes, the prisoner’s dilemma and card games. These solutions are able to exceed the classic bottle neck and obtain optimal quantum strategies. In this form, python demonstrated that is possible to do more advanced and complicated quantum games algorithms.

Karmela Padavic-Callaghan

Kolokoltsov Vasili