We study a network formation game in which agents sponsor links at a linear cost in order to maximize centrality, defined as a weighted sum of walk counts with positive and weakly decreasing weights. This class includes Katz Bonacich centrality and total communicability and captures environments in which access decays with distance. Our main result is a sharp equilibrium characterization: every Nash equilibrium network is core periphery, meaning there exists a set $C$ such that every node is linked to every node in $C$, and there are no other edges. The driving force is that linking to better connected agents generates many additional short connections at once, so incentives concentrate links on a dense subset. Finally, we show that the welfare maximizing network is always either empty or complete.
A planner in a network of strategic agents faces three entangled challenges: the optimum depends on agents'private information, queried agents may misreport to steer the outcome, and exact computation does not scale. We study these challenges in multi-activity network games with heterogeneous private technologies, in w...
Chenyu Zhang, R. Parasnis, Saurabh Amin· 0 citations
This paper forms two new metrics and establishes connections to a well-studied metric from the literature that was proposed and more studied for stochastic matrices, and then extended to graph-Laplacians, and proves that these three notions match for path-graphs and formulate an explicit expression for the metric both...
Karim Shahbaz, Madhu N. Belur, Chayan Bhawal et al.· International Journal of Con...· 0 citations
Katz centrality is a well-established measure to identify and rank the most important nodes in complex networks by means of a linear system solve. Recent works have developed notions of Katz centrality for temporal, i.e., time-evolving networks. Their drawback is that small changes in the network structure may drastica...
Kai Bergermann, Francesco Gravili, V. Simoncini et al.· 0 citations
It is proved that removing edges from these networks never decreases the maximum equilibrium latency, which establishes a necessary and sufficient condition: a network does not admit Braess's paradox for flow over time if and only if it is a chain of BPAs.
A mathematical framework incorporating degree-dependent inertia is developed, wherein the tendency to maintain one’s strategy is determined by node degree, and self-loops are permitted, and self-loops are permitted, and self-loops are permitted.
Nan Jiang, Xiaomeng Li, Qing-Hua Chen et al.· Journal of Mathematical Biol...· 0 citations
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