A Quantum Battle of the Sexes Cellular Automaton with Probabilistic Updating

The dynamics of a spatial quantum formulation of the iterated battle of the sexes (BOS) game with probabilistic updating of strategies is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The effect of spatial structure and variable entangling on the evolving dynamics are assessed in fair and unfair contests, both in the two and three parameter strategy spaces. It is concluded that the intrinsic asymmetry of the BOS game induces a very interesting modification in the payoffs that the players achieve when varying the degree of entanglement of the player's strategies.