With　the　rapid　advancements　in　transportation　electrification,　the　proliferation　of　electric　vehicles　(EVs)　has　interconnected　power　and　transportation　networks,　forming　the　vehicle-traffic-power　nexus.　By　setting　charging　prices,　charging　station　operators　(CSOs)　can　effectively　guide　the　charging　behavior　of　EVs,　alleviate　grid　stress,　and　enhance　profitability.　This　paper　proposes　a　Nash-Stackelberg-Nash　(N-S-N)　game　model　to　investigate　the　competitive　charging　pricing　strategy　for　CSOs.　We　establish　the　stochastic　user　equilibrium　with　the　elastic　demand　traffic　assignment　problem　(SUE-ED-TAP)　model　to　account　for　users＇　incomplete　rationality　and　perception　errors　regarding　trip　costs.　Furthermore,　to　protect　the　privacy　of　both　CSOs　and　EV　users,　a　federated　multi-agent　deep　reinforcement　learning-based　solution　method　is　proposed　to　solve　this　problem.　In　this　method,　a　non-profit　aggregator　is　introduced　to　exchange　neural　network　parameters　among　agents,　enabling　privacy-preserving　and　collaborative　learning　without　sharing　CSOs＇　data.　Case　studies　on　two　test　systems　show　that　the　proposed　method　achieves　higher　profits　compared　to　existing　algorithms.　©　2023　IEEE.