I am playing a game on the 3G network using Android or Iphone. Suppose I am moving from one cell to another; Will the IP Address change? If yes, then how can I continue the same game while changing the base station, as my IP address is already registered in The game server? Is there something DHCP?
Just as @JustSid said, if you move from one cell to another the handover is handled transparently. The 3G network is just the method of transportation of your data packets, therefore it is a few layers below the IP layer, if you think in terms of the ISO/OSI stack. I worked on a push-to-talk application for mobile phones and all i can say is, that we never dealt with 3G cell changes. We just opened a TCP connection and started sending packets. One thing that also depends on your carrier is the 3G <-> 2G handover. With some carriers it worked fine, with some others we had disconnects.
A HTTP request from a mobile device is routed through a WAP Gateway. These are maintained by the mobile network operators. The WAP Gateway routes the request to the desired server and returns the response to the client.
As far as I know, IP routing on a mobile phone has nothing to do with cell tower base stations as everyone on the same network would be routed through these gateways.