Bisection-based trial-and-error implementation of marginal cost pricing and tradable credit scheme

The purpose of this paper is three fold: First, it demonstrates the non-convergence of the bisection method proposed in the literature for the trial-and-error implementation of the marginal-cost pricing in the absence of a demand function. Second, it provides a modified version of the bisection method and establishes its convergence. Third, it adapts the modified bisection method for the trial-and-error implementation of the tradable credit scheme proposed recently, which can emulate a congestion pricing system in a revenue-neutral manner.