me and a friend had EXACTLY the same issue yesterday. we were playing against 2 computer players on the map "Backstab". for about 45 minutes into the game, everything went fine. but then we realized, that we were somehow out of sync. it was very strange. some of his actions were in sync, some werent.

e.g. we decided to take on a nearby enemy planet together. he ordered his ships to this planet, and i also saw his ships performing that command, BUT i didnt see all of his ships. for example i saw many ships still parked at his home system, but actually he had those ships already at the front with the rest of his army (on his game).

another example is that he saw an enemy invading one of my planets, while there were no enemy ships in that system in my game. so it also seemed, that the AI players were acting independently on each computer.

after a while his army wasn't doing anything anymore in my game, and my army wasn't doing anything in his game. e.g. he was invading an enemy planet, while i saw his army still "parked" and doing nothing.

after about 2:30h i had defeated both enemy players on my game, while he was still struggling with both of them.

exchanging credits and resources via diplomacy was working fine throughout the whole game.

we checked the network information (F4) several times and both players were always marked as "OK".

additionally, we had 2 crashes (i had one and a bit later he had one too), getting that minidump-error in windows. we then loaded a previous autosave, but the problem persisted.

we are both on v.1.05. i played several LAN-games with this and previous versions before, and its the first time we had such a problem.

i was playing on vista x64 and he on XP. we were not using any MODs.

maybe these symptoms are related to the known "Multiplayer Crashes", as described here :https://forums.sinsofasolarempire.com/307544, although the symptomatics with different courses of a multiplayer game aren't described in that thread.

check out this thread, its about the same problem:
https://forums.sinsofasolarempire.com/313535

it seems, the devs are already working on it.