Dynamic Taxes for Congestion Games with Polynomial Latencies

In this chapter, we consider the efficiency of taxation in congestion games with polynomial latency. By resorting to a novel application of the primal-dual method, we provide 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 well-studied polynomials in Combinatorics and Number Theory, such as the Touchard and the Geometric polynomials, arises (see Section 8.2 for further details).