Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the existence of approximate pure Nash equilibria in ighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically,  show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players  obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.
['Christoph Hansknecht', 'Max Klimm', 'Alexander Skopalik']
I am writing a research paper on a idea Approximate Pure Nash Equilibria in Weighted Congestion Games
[{"from": "human", "value": "I am writing a research paper on a idea Approximate Pure Nash Equilibria in Weighted Congestion Games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the existence of approximate pure Nash equilibria in ighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically,  show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players  obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions."}]