Conventional lead bullets won't do much good against armoured robots. Better start stockpiling SMAWs and Javelins.
I've toyed around with the thought of fully robotic warfare (no humans put in harms way). It sort of takes a lot of the horror out of war. I mean, it might as well be a sporting event after...
Sadly, if you aren't killing your enemies there seems to be no point in fighting wars. Crowded as the world is, killing is unlikely to stop now.
OTOH, robot battles as sporting events (to quote you) ...
YEAHHHHHH!!!