Link Biased Strategies in Network Formation Games

We show a simple method for constructing an infinite family of graph formation games with link bias so that the resulting games admits, as a $\mathit{\text{pairwise}}\mathit{\text{stable}}$ solution, a graph with an arbitrarily specified degree distribution. Pairwise stability is used as the equilibrium condition over the more commonly used Nash equilibrium to prevent the occurrence of ill-behaved equilibrium strategies that do not occur in ordinary play. We construct this family of games by solving an integer programming problem whose constraints enforce the terminal pairwise stability property we desire.