Study of the effect of cost policies in the convergence of selfish strategies in Pure Nash Equilibria in Congestion Games

TL;DR

This paper analyzes how different cost policies influence the convergence time to pure Nash equilibria in congestion games, combining theoretical bounds with experimental validation, revealing discrepancies in coalitional scenarios.

Contribution

It provides new theoretical bounds on convergence times under various cost policies and experimentally demonstrates that coalitional convergence can be faster than predicted.

Findings

Theoretical bounds on convergence time for different cost policies.

Experimental results largely confirm theoretical predictions.

Coalitional convergence times are polynomial, contrary to pseudo-polynomial bounds.

Abstract

In this work we study of competitive situations among users of a set of global resources. More precisely we study the effect of cost policies used by these resources in the convergence time to a pure Nash equilibrium. The work is divided in two parts. In the theoretical part we prove lower and upper bounds on the convergence time for various cost policies. We then implement all the models we study and provide some experimental results. These results follows the theoretical with one exception which is the most interesting among the experiments. In the case of coalitional users the theoretical upper bound is pseudo-polynomial to the number of users but the experimental results shows that the convergence time is polynomial.