  In this paper, a nonlinear revision protocol is proposed and embedded into
the traffic evolution equation of the classical proportional-switch adjustment
process (PAP), developing the present nonlinear pairwise swapping dynamics
(NPSD) to describe the selfish rerouting evolutionary game. It is demonstrated
that i) NPSD and PAP require the same amount of network information acquisition
in the route-swaps, ii) NPSD is able to prevent the over-swapping deficiency
under a plausible behavior description; iii) NPSD can maintain the solution
invariance, which makes the trial and error process to identify a feasible
step-length in a NPSD-based swapping algorithm is unnecessary, and iv) NPSD is
a rational behavior swapping process and the continuous-time NPSD is globally
convergent. Using the day-to-day NPSD, a numerical example is conducted to
explore the effects of the reaction sensitivity on traffic evolution and
characterize the convergence of discrete-time NPSD.
