Core war

"Core War (or Core Wars) is a programming game in which two or more battle programs (called warriors) compete for the control of the MARS virtual computer (Memory Array Redcode Simulator). These battle programs are written in an abstract assembly language called Redcode. The object of the game is to cause all processes of the opposing program(s) to terminate, leaving your program in sole possession of the machine.

...The game was introduced to the public in May 1984, in an article written by Dewdney in Scientific American (Computer Recreations)."
Wikipedia

Info about at: corewars (including links to tutorials/guides, math of the game and even the use of genetic algorithms to evolve core war programs).

Sodarace

"Sodarace is the online olympics pitting human creativity against machine learning in a competition to design robots that race over 2D terrains using the Sodaconstructor virtual construction kit."

Sodarace

Wodka info.

NERO

NERO, which stands for Neuro-Evolving Robotic Operatives is an experimental game of the University of Texas at Austin.
Train your soldiers!