Link Biased Strategies in Network Formation Games

TL;DR

This paper introduces a method to design network formation games with link bias that guarantees the existence of pairwise stable graphs with any desired degree distribution, using integer programming.

Contribution

It presents a novel approach to construct network formation games with specific stable degree distributions via integer programming, focusing on pairwise stability.

Findings

Successfully constructs infinite families of stable graphs with arbitrary degree distributions.

Demonstrates the use of integer programming to enforce stability constraints.

Provides a framework for designing network games with predictable equilibrium structures.

Abstract

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 \textit{pairwise 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.