How does DHCP work on a direct ethernet link between hosts?

I plugged in an ethernet cable between my desktop and laptop for faster, direct, file transfer. Both run Linux Mint, and both are connected to the same WiFi (probably WiFi is irrelevant here). Both have only dhcp client package installed but, AFAICT from dpkg -l, neither has dhcp server installed. Yet, each managed to configure 10.0.0.1 and .2 by itself without any prodding. How does this work, without any dhcp server installed? Which host initiates the connection, and how do they negotiate and reach consensus? dmesg only tells me the link is up but nothing much else.