Studying Bio-Inspired Coalition Formation of Robots for Detecting Intrusions Using Game Theory

In this paper, inspired by the society of animals, we study the coalition formation of robots for detecting intrusions using game theory. We consider coalition formation in a group of three robots that detect and capture intrusions in a closed curve loop. In our analytical model, individuals seek alliances if they think that their detect regions are too short to gain an intrusion capturing probability larger than their own. We assume that coalition seeking has an investment cost and that the formation of a coalition determines the outcomes of parities, with the detect length of a coalition simply being the sum of those of separate coalition members. We derive that, for any cost, always detecting alone is an evolutionarily stable strategy (ESS), and that, if the cost is below a threshold, always trying to form a coalition is an ESS (thus a three-way coalition arises).