This paper explores the impact of travel information sharing on road networks using a two-layer, agent-based, day-to-day traffic network model. The first layer (cyber layer) represents a conceptual communication network where travel information is shared among drivers. The second layer (physical layer) captures the day-to-day evolution in a traffic network where individual drivers seek to minimize their own travel costs by making route choices. A key hypothesis in this model is that instead of having perfect information, the drivers form individual groups, among which travel information is shared and utilized for routing decisions. The formation of groups occurs in the cyber layer according to the notion of percolation, which describes the formation of connected clusters (groups) in a random graph. We apply the novel notion of percolation to capture the disaggregated and distributed nature of travel information sharing. We present a numerical study on the convergence of the transport network, when a range of percolation rates are considered. The findings suggest a positive correlation between the percolation rate and the speed of convergence, which is validated through statistical analysis. A sensitivity analysis is also presented which shows a bifurcation phenomenon with regard to certain model parameters.