Spatial Quantum Game Simulation

Ramón Alonso‐Sanz

Panagiotis Vlachos, Ioannis G. Karafyllidis

Ramón Alonso‐Sanz, Andrew Adamatzky

Azhar Iqbal, Derek Abbott

Abstract We propose a scheme for a quantum game based on performing an EPR-type experiment and in which each player’s spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the players’ choices to specific spatial trajectories. We show that for players’ directional choices for which the Bell-CHSH inequality is violated, the players’ payoffs in the quantum game have no mapping within the classical mixed-strategy game. The scheme provides a more direct link between classical and quantum games.

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.

Hong Mei Guo, Juheng Zhang, Gary J. Kœhler