Quantum Information Processing (2020) 19:355 https://doi.org/10.1007/s11128-020-02860-w Cellular automaton simulation of the quantum war of attrition game Ramon Alonso-Sanz 1 · Andrew Adamatzky 2 Received: 19 April 2020 / Accepted: 3 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract The quantum war of attrition game is studied in this work via spatial numerical sim- ulation. It is found that the implemented simulation converges to the Pareto optimal solution, i.e. no fighting at all, when the resign times of the players are entangled with higher factor, whereas larger resign times would be got with weak entanglement. This finding is shown to apply also in a fiercer war game, the war of extermination, in which game the non-entangled (or classical) simulation leads to very high resign times and consequently to very high negative payoffs. Keywords War of attrition · Game theory · Simulation · Quantum 1 Introduction Entanglement plays an important role in quantum information theory. Two entangled particles have certain connections even if they are departed distantly. Interestingly, entangled particles can be used to play games, e.g. two players are each distributed with one particle and they make their movements by operating on his own particle. This idea supports the so-called quantum game theory, that was pioneered in a paper by Meyer [15], and shortly afterwards in a paper by Eisert et al. [9]. These papers, in par- ticular [9], induced a series of research works about playing games using the quantum approach [11]. The early works focused on discrete games, the Prisoner’s Dilemma in particular, and showed that even if players act non-cooperatively in quantum games, they could achieve results which could only be achieved through cooperation in the corresponding classical games. B Ramon Alonso-Sanz ramon.alonso@upm.es Andrew Adamatzky andrew.adamatzky@uwe.ac.uk 1 Complex Systems Group, Technical University of Madrid, C. Universitaria, 28040 Madrid, Spain 2 Unconventional Computing Laboratory, University of the West of England, Bristol BS16 1QY, UK 0123456789().: V,-vol 123