  We establish a network formation game for the Internet's Autonomous System
(AS) interconnection topology. The game includes different types of players,
accounting for the heterogeneity of ASs in the Internet. We incorporate
reliability considerations in the player's utility function, and analyze static
properties of the game as well as its dynamic evolution. We provide dynamic
analysis of its topological quantities, and explain the prevalence of some
"network motifs" in the Internet graph. We assess our predictions with
real-world data.
