Linking Micro- to Macro-level Behavior in the Aggressor-Defender-Stalker Game

In many multiagent systems, small changes in individual-level rules may lead to very large changes at the group-level. This phenomenon is striking in the “aggressor-defender game,” a simple participative game in which each participant randomly selects two others from the group (A and B). In the aggressor game, everyone tries to position themselves so that A is always between themselves and B. In the defender game everyone tries to position themselves between A and B. Despite these exceedingly simple rules and the seemingly small difference between them, the two games exhibit very different dynamics. The aggressor game produces a highly dynamic group that rapidly expands over time whereas the defender game quickly collapses to a tight knot. I analyze these games and provide some insight as to how these two group level behaviors arise, thereby linking the micro- and macro-levels. I also introduce and analyze a new, related and simpler game, the stalker game, in which each participant selects and pursues a single participant, and which also produces a collapsing group. It is suggested that such a geometrical analysis may be applicable for other multiagent systems such as insect societies and collective robotics.