Topologies and Price of Stability of Complex Strategic Networks with Localized Payoffs : Analytical and Simulation Studies
Rohith Dwarakanath Vallam, C. A. Subramanian, Ramasuri Narayanam, Y., Narahari, and Srinath Narasimha

TL;DR
This paper studies how strategic individuals form networks with localized payoffs, analyzing the stability and efficiency of various network topologies through analytical proofs and simulations, revealing conditions under which optimal networks emerge.
Contribution
It introduces a simple local payoff-based network formation model and analytically characterizes the stability and efficiency of key network structures, extending findings with simulations.
Findings
Complete bipartite and cycle networks are pairwise stable under certain conditions.
The Turan graph is often the unique efficient network configuration.
Price of stability is typically 1, indicating near-optimal stability in most cases.
Abstract
We analyze a network formation game in a strategic setting where payoffs of individuals depend only on their immediate neighbourhood. We call these payoffs as localized payoffs. In this game, the payoff of each individual captures (1) the gain from immediate neighbors, (2) the bridging benefits, and (3) the cost to form links. This implies that the payoff of each individual can be computed using only its single-hop neighbourhood information. Based on this simple model of network formation, our study explores the structure of networks that form, satisfying one or both of the properties, namely, pairwise stability and efficiency. We analytically prove the pairwise stability of several interesting network structures, notably, the complete bi-partite network, complete equi-k-partite network, complete network and cycle network, under various configurations of the model. We validate and…
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Taxonomy
TopicsOpinion Dynamics and Social Influence · Game Theory and Applications · Complex Network Analysis Techniques
