Can Status Inequality Organize Cooperation in Multi-leader Systems? An Evolutionary Theory

Status hierarchies often emerge in small collective task groups. In these groups, clearly defined hierarchies facilitate and stabilize structured cooperative interactions among group members, supporting their evolutionary function in the real world. What the existing research in this field has failed to consider, however, is that cooperation matters in these hierarchies with clear status inequality, as well as in other more realistic, multiple-leader groups with less clear hierarchies. Multi-leadership is ubiquitous but, by definition, flattens status inequality and may, in turn, jeopardize its capacity to sustain cooperation. Leveraging the relationship between multi-leadership and cooperation, our evolutionary game model reveals that hierarchies, in general, promote cooperation in groups with multiple leaders, but these hierarchies only do that up to a point, after which multi-leadership backfires. Accordingly, the model provides not only a theoretical account for how multi-leadership coexists with cooperation but also the conditions under which the coexistence would break.

Containment Control of First-Order Multi-Agent Systems under PI Coordination Protocol

This paper investigates the containment control problem of discrete-time first-order multi-agent system composed of multiple leaders and followers, and we propose a proportional-integral (PI) coordination control protocol. Assume that each follower has a directed path to one leader, and we consider several cases according to different topologies composed of the followers. Under the general directed topology that has a spanning tree, the frequency-domain analysis method is used to obtain the sufficient convergence condition for the followers achieving the containment-rendezvous that all the followers reach an agreement value in the convex hull formed by the leaders. Specially, a less conservative sufficient condition is obtained for the followers under symmetric and connected topology. Furthermore, it is proved that our proposed protocol drives the followers with unconnected topology to converge to the convex hull of the leaders. Numerical examples show the correctness of the theoretical results.

Leadership Games: Multiple Followers, Multiple Leaders, and Perfection

Over the last years, algorithmic game theory has received growing interest in AI, as it allows to tackle complex real-world scenarios involving multiple artificial agents engaged in a competitive interaction. These settings call for rational agents endowed with the capability of reasoning strategically, which is achieved by exploiting equilibrium concepts from game theory.