Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the efficiency of taxation in congestion games with polynomial latency functions along the line of research initiated by [Caragiannis et al., ACM Transactions on Algorithms, 2010] who focused on both pure and mixed Nash equilibria in games with affine latencies only. By exploiting the primal-dual method [Bilo, Proceedings of the 10th Workshop on Approximation and Online Algorithms, 2012],  obtain interesting upper bounds with respect to a variety of different solution concepts ranging from approximate pure Nash equilibria up to approximate coarse correlated equilibria, and including also approximate one-round walks starting from the empty state. Our findings show a high beneficial effect of taxation which increases more than linearly with the degree of the latency functions. In some cases, a tight relationship with some ll-studied polynomials in Combinatorics and Number Theory, such as the Touchard and the Geometric polynomials, arises. In these cases  can also show matching lor bounds, albeit under mild assumptions; interestingly, our upper bounds are derived by exploiting the combinatorial definition of these polynomials, while our lor bounds are constructed by relying on their analytical characterization.
['Vittorio Bilò', 'Cosimo Vinci']
I am writing a research paper on a idea Dynamic Taxes for Polynomial Congestion Games
[{"from": "human", "value": "I am writing a research paper on a idea Dynamic Taxes for Polynomial 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:  consider the efficiency of taxation in congestion games with polynomial latency functions along the line of research initiated by [Caragiannis et al., ACM Transactions on Algorithms, 2010] who focused on both pure and mixed Nash equilibria in games with affine latencies only. By exploiting the primal-dual method [Bilo, Proceedings of the 10th Workshop on Approximation and Online Algorithms, 2012],  obtain interesting upper bounds with respect to a variety of different solution concepts ranging from approximate pure Nash equilibria up to approximate coarse correlated equilibria, and including also approximate one-round walks starting from the empty state. Our findings show a high beneficial effect of taxation which increases more than linearly with the degree of the latency functions. In some cases, a tight relationship with some ll-studied polynomials in Combinatorics and Number Theory, such as the Touchard and the Geometric polynomials, arises. In these cases  can also show matching lor bounds, albeit under mild assumptions; interestingly, our upper bounds are derived by exploiting the combinatorial definition of these polynomials, while our lor bounds are constructed by relying on their analytical characterization."}]