I run/develop an online game where many of our users are in southeast asia.

I recently went to southeast asia and made an alarming discovery. Anywhere I got internet access, whether it was via 3G, a LAN in a hotel, or wifi in a cafe, both in Singapore and the Philippines, I noticed that my IP address was changing CONSTANTLY. I mean the public IP address, not the private one. I could load a page like whatismyip.com and just hit reload and see a new IP address show up every 5-10 seconds!

This has lots of consequences for my online game, as many things "break" if the IP address changes for a given user. Basically, I would like to know more about this. Is there a name for the kind of network or router or paradigm that causes this, so I can read up on it? I don't understand WHY a network would function this way. Does it do this on purpose? Is it for security reasons? Is it to anonymize and protect the identity of the users? Or is it just an "old" method that is mostly obsolete in the rest of the world? Thanks for any info that will help me to understand.