Stars and Celebrities: A Network Creation Game

TL;DR

This paper introduces a new network creation game model called celebrity games, where players aim to connect with high-weight celebrities within a critical distance, analyzing equilibrium existence, structure, and efficiency bounds.

Contribution

It presents the celebrity game model with weighted players and critical distance, proves the existence of pure Nash equilibria, and characterizes star celebrity subgames with bounds on the price of anarchy.

Findings

Celebrity games always have pure Nash equilibria.

Connected Nash equilibria are characterized in star celebrity subgames.

Bounds on the price of anarchy are provided, especially for tree structures.

Abstract

Celebrity games, a new model of network creation games is introduced. The specific features of this model are that players have different celebrity weights and that a critical distance is taken into consideration. The aim of any player is to be close (at distance less than critical) to the others, mainly to those with high celebrity weights. The cost of each player depends on the cost of establishing direct links to other players and on the sum of the weights of those players at a distance greater than the critical distance. We show that celebrity games always have pure Nash equilibria and we characterize the family of subgames having connected Nash equilibria, the so called star celebrity games. We provide exact bounds for the PoA of celebrity games. The PoA can be tightened when restricted to particular classes of Nash equilibria graphs, in particular for trees.