Reciprocal Market Access Act of 2018 This bill requires that reductions in tariff rates for imports into the United States are accompanied by reciprocal trade barrier reductions for the same U.S.-produced goods exported to the same foreign country. Before the President agrees to reduce or eliminate a rate of duty for any product to carry out a trade agreement between the United States and a foreign country, the President must certify to Congress that the foreign country has also reduced or eliminated tariff and non-tariff barriers for imports of the same goods from U.S. producers. Violations of a trade agreement by the foreign country are immediately enforceable under the bill. If the foreign country has not reduced a trade barrier as previously agreed, or has imposed a new one, the U.S. Trade Representative (USTR) shall withdraw the duty reduction for the same goods from that country. The bill allows interested parties to petition the USTR to investigate violations of trade agreements. Interested parties include manufacturers and wholesalers of the goods involved in the alleged violation, as well as unions and trade associations. The bill requires the U.S. International Trade Commission to investigate possible market access opportunities when the President seeks to reduce a rate of duty for an imported good.