Quantum Mechanics, Free Will and the Game of Life

Adrian P. Flitney, Derek Abbott

Henry Pierce Stapp

Adrian P. Flitney, Derek Abbott

A version of John Conway's game of Life is presented where the normal binary values of the cells are replaced by oscillators which can represent a superposition of states. The original game of Life is reproduced in the classical limit, but in general additional properties not seen in the original game are present that display some of the effects of a quantum mechanical Life. In particular, interference effects are seen.

Henry Margenau

Adrian P. Flitney, Derek Abbott

A version of John Conway’s game of Life is presented where the normal binary values of the cells are replaced by oscillators which can represent a superposition of states. The original game of Life is reproduced in the classical limit, but in general additional properties not seen in the original game are present that display some of the effects of a quantum mechanical Life. In particular, interference effects are seen.

Kaytki Chakankar, Xinhui Tang, Yiguo Zhang

The centipede game is a two-player non-zero-sum game. Each turn, a player can choose whether they want to take or pass a growing reward. The classical, rational solution of this game shows defection in the first round, when in reality, players cooperate much more often. Inspired by prior work employing quantum strategies in the prisoners dilemma, we showed that when similar quantum mechanics principles are applied to the centipede game, it leads to two new quantum Nash equilibria that are superior to the classical solution. Furthermore, by implementing our algorithm on Qiskit, we confirmed that leveraging quantum strategies, rather than strategies like backward induction, to solve the centipede game provided better payoffs for both players and more accurately modeled the games real-life outcomes. Ultimately, we propose a generalized conjecture for similarly structured quantum games.