On the interpretation of quantum theory as games between observers and nature played in Minkowski spacetime
<|reference_start|>On the interpretation of quantum theory as games between observers and nature played in Minkowski spacetime: In 2019, we introduced games in Minkowski spacetime as a generalization of game theory to special relativity that subsumes games in normal form (spacelike separation) and games in extensive form (timelike separation). Many concepts of the game theory literature, including Nash equilibria and flattened strategic forms, naturally extend to spacetime games. We also emphasized the importance of these games to model quantum experiments, such as Bell experiments and more generally any adaptive measurements, from a decision theory perspective. Subsequent work, named causal contextuality scenarios, suggested formalizing a special case of such games in terms of strategy presheaves. If a natural cover is taken, we show that spacetime games recover causal contextuality scenarios as a special case. Spacetime games provide a visual and intuitive framework that captures the distinction between joint experiments and either-or experiments, so that they are rich enough in their causal structure to imply a natural cover for the corresponding causal contextuality scenario. Based on this observation, we suggest defining the strategy presheaf directly based on the pure strategies (and restrictions thereof) in the reduced strategic form of the spacetime game, and we show that the sheaf property obtains for the games at hand. The argument is simple and similar to event sheaves for the flat case. Finally, we explain how, in the other direction, the failure of the sheaf property on strategy distribution presheaves is consistent with our previous argument that Nash game theory is incompatible with quantum physics. This shows that the insights of spacetime games and causal contextuality scenarios, taken together, can contribute positively to the advancement of the field of quantum foundations.<|reference_end|>
@article{fourny2024on,
    title={On the interpretation of quantum theory as games between observers and
  nature played in Minkowski spacetime},
    author={Ghislain Fourny},
    journal={arXiv preprint arXiv:2405.20143},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.20143},
    primaryClass={quant-ph cs.GT}
}