If a man and a woman meet, decide that they prefer one another to their current partners, and consequently leave their current partners and marry one another, then this is an example of jointly intentional behaviour. The man and the woman have updated their strategies as a pair.
Hence we see that matching models will often feature collective agency on the part of the agents involved.
There are a considerable number of papers in this literature. A summary of work on rematching dynamics can be found in the following recent work:
The above paper considers matchings with non-transferable utility. A related literature considers matchings with transferable utility; that is, side payments. Recent works in this area are: