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}
}