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Knights and Merchants: The Peasants Rebellion doesn't work for multiplayer, the game becomes out of sync after not very long (so you see different things happening on your screen to your opponent, you might win while they also win)
Knights and Merchants: The Shattered Kingdom works ok for multiplayer but it still has problems like you can't save.
The best option is the
KaM Remake, a recreation of the game engine by fans. Install it on both of your computers (download/instructions on the website), then go to Multiplayer, type in your name and click Create Server, then Create Local Server on the popup. On the other computer, go the multiplayer screen, click Find Server By IP, type in the IP address of the computer you started the server on, then click connect.
Here are some instructions for finding the IP address of the computer if you don't know how to. Alternatively you can both join the same internet server from the multiplayer screen, but you will get more of a delay because the data will be sent out to the internet and back.
Let us know how it goes!
Lewin.