That greatly depends on whether the medium is broadcast (like a radio) or broadcast-like (a shared copper wire) and if it has CSMA/CD logic. Many of the replies are losing that detail and thinking of how it would effect a 1000base-T network, which maps MAC addresses to specific ports.

For a broadcast network, the answer could be 'nothing' in the sense that both receivers would get the same traffic. The IP stack would then throw away packets destined for the other computer unless they were UDP broadcast or multicast, and even then it would only notice if someone was running Wireshark.

Advanced wifi devices/meshes will use beam forming and mesh allocation and might degrade if there were MAC duplicates, but I think they will generally operate in a non-exclusive basis due to end point movement and fading, so both computers will get a good data rate.

In summary: it's fine.