For a long time, the best results and the bulk of the research into AIs playing video game environments were around genetic algorithms. This approach involves creating a set of modules that take parameters to control the behavior of the AI. The range of parameter values is then set by a selection of genes. A group of agents would then be created using different combinations of these genes, which would be run on the game.
The most successful set of agent's genes would be selected, then a new generation of agents would be created using combinations of the successful agent's genes. Those would again be run on the game and so on until a stopping criteria is reached, normally either a maximum number of iterations or a level of performance in the game. Occasionally, when creating a new generation, some of the genes can be mutated...