By MLL + MIX we usually refer to the multiplicative fragment of linear logic, extended with the MIX rule, viz.
Please expand.
AJM games are fully complete for MLL+MIX [Abramsky and Jagadeesan 1994].
Abramsky, Samson, and Radha Jagadeesan. 1994. ‘Games and Full Completeness for Multiplicative Linear Logic’. The Journal of Symbolic Logic 59 (2): 543. https://doi.org/10.2307/2275407. arXiv
@article{abramsky_1994,
title = {Games and {Full} {Completeness} for {Multiplicative} {Linear} {Logic}},
volume = {59},
doi = {10.2307/2275407},
number = {2},
journal = {The Journal of Symbolic Logic},
author = {Abramsky, Samson and Jagadeesan, Radha},
year = {1994},
pages = {543}
}