  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. In this network
formation game, the utility of a player depends on the network structure, e.g.,
the distances between nodes and the cost of links. We also consider the case
where utility (or monetary) transfers are allowed between the players. 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 topological quantities, and explain the prevalence
of some "network motifs" in the Internet graph. We assess our predictions with
real-world data.
