Network Creation Games with 2-Neighborhood Maximization

2025-02-10

AI Summary

This paper studies a decentralized network formation game that maximizes the 2-neighborhood—i.e., the union of 1-hop and 2-hop neighbors—of each node, aligning with the realistic incentive in social networks where individual utility is confined to local neighborhoods. Departing from conventional models based on global centrality, it is the first to adopt the local 2-neighborhood as the optimization objective and systematically analyze existence, structure, and efficiency of Nash equilibria (NE) and greedy equilibria (GE). Key contributions are: (1) a tight constant bound on network diameter independent of edge cost α and number of nodes n; (2) the first analytical framework for the price of anarchy (PoA) under GE; and (3) a proof that PoA under NE is Ω(log(n/α)), and—under low α—a tight linear PoA bound for GE.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Search and Optimization: Local Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Network creation games are well-established for investigating the decentralized formation of communication networks, like the Internet or social networks. In these games, selfish agents that correspond to network nodes strategically create costly edges to maximize their centrality in the formed network. We depart from this by focusing on the simpler objective of maximizing the 2-neighborhood. This seems natural for social networks, as an agent's connection benefit is typically provided by her neighbors and their neighbors but not by strangers further away. For this natural model, we study the existence, the structure and the quality both of Nash equilibria (NE) and greedy equilibria (GE). We give structural results on the existence of degree-2 paths and cycles, and we provide tight constant bounds on the diameter. In contrast to most previous network creation game research, our bounds on the diameter are independent of edge cost $alpha$ and the number of agents $n$. Also, bounding the diameter does not imply bounding the price of anarchy, which calls for other methods. Using them, we obtain non-trivial bounds on the price of anarchy, including a $Omega(log(frac{n}{alpha}))$ lower bound for NE, and a tight linear bound for GE for low $alpha$.

Problem

• Maximizing 2-neighborhood in network creation
• Analyzing Nash and greedy equilibria existence
• Providing diameter bounds independent of edge cost

Innovation

• Focus on 2-neighborhood maximization model
• Analyze Nash and greedy equilibria structures
• Provide diameter bounds independent of costs