On Dynamics of Basic Network Creation Games With Non-Uniform Communication Interest

Abstract

We consider the network construction process by selfish players. Each player is associated with a vertex of a communication graph and can simultaneously remove one incident edge and add a new incident edge. Each player is interested in a subset of players and the goal of each player is to minimize the average or maximum distance to these players. Starting from a given initial communication graph, a sequence of selfish edge swaps generates an evolution of the communication graph. Due to non-uniform communication interest, this game may converge to a disconnected Nash equilibrium, which may attain infinite social costs. In this paper, we focus on the dynamics of this game. We first give theoretical analysis such as the existence of a best response cycle and a sufficient condition for keeping connectivity in dynamics. We then present simulation results to show the ratio of Nash equilibria with infinite cost, diameters of Nash equilibria, social cost, price of anarchy, price of stability, and convergence time.