The Calculation and Simulation of the Price of Anarchy for Network Formation Games

TL;DR

This paper models network formation as a strategic game among selfish players, introduces an Integer Program to compute the price of anarchy, and finds that the inefficiency in such networks tends to be low.

Contribution

It presents a novel Integer Program for calculating the price of anarchy in network formation games considering strategic player behavior.

Findings

Simulated price of anarchy is generally low.

The model effectively captures strategic decision-making in network formation.

Provides a computational framework for analyzing network efficiency.

Abstract

We model the formation of networks as the result of a game where by players act selfishly to get the portfolio of links they desire most. The integration of player strategies into the network formation model is appropriate for organizational networks because in these smaller networks, dynamics are not random, but the result of intentional actions carried through by players maximizing their own objectives. This model is a better framework for the analysis of influences upon a network because it integrates the strategies of the players involved. We present an Integer Program that calculates the price of anarchy of this game by finding the worst stable graph and the best coordinated graph for this game. We simulate the formation of the network and calculated the simulated price of anarchy, which we find tends to be rather low.