Stable Partitions in Networks with the Costs Dependent on Neighborhood Composition

Attend a 52-minute research seminar exploring discrete-time, infinite-horizon processes of partition formation in networks where link maintenance costs depend on neighborhood composition. Examine two distinct cost functions that determine the expense of maintaining connections between players based on their respective neighborhood structures. Analyze stable partition characterizations across various network topologies including star networks, complete networks, and balanced complete bipartite networks. Discover how the theoretical framework applies to real-world scenarios through the analysis of Zachary's karate club network, which demonstrates why certain individuals emerge as natural group leaders. Explore numerical simulations conducted on random networks that illustrate the partition formation process while highlighting the computational complexity and theoretical challenges inherent in solving such problems.