Interesting games through stage complexity and topology

In (Yannakakis and Hallam, 2004) we saw that the online learning (OLL) mechanism proposed is a robust approach which manages to emerge opponents (i.e Ghosts) that increase the interest of the prey-predator, multiagent Pac-Man computer game. It also demonstrated high adaptability to changing types of Pac-Man player (i.e. playing strategies) in a relevantly simple playing stage. In the work presented here we attempt to test the OLL mechanism over more complex stages and furthermore to explore the relation between the interest measure and the topology of the stage. In order to distinguish between stages of different complexity, we require an appropriate measure to quantify this feature of the stage. This measure is as follows