Internet-related　markets　have　transformed　the　traditional　means　of　production/service,　consumption,　and　executing　transactions　and　prompted　the　restructuring　of　traditional　multisided　markets.　Against　this　background,　this　paper　presents　a　multilevel　agent　framework　method　to　model　Internet-platform　markets　and　simulate　the　evolution　during　their　initiation　and　competition　periods　from　the　perspectives　of　e-travel,　e-commerce,　e-food,　and　e-manufacturing.　Furthermore,　this　paper　discusses　the　interaction　mechanism　of　market　agents,　particularly　the　core　mechanism,　in　two-sided　Internet　markets　using　a　multilevel　agent　model.　The　financing,　pricing　and　innovation　instruments,　are　integrated　in　the　model.　A　venture　capital　mechanism　with　stage　financing　and　venture　value　decision　model　is　used　to　model　investment.　Concerning　network　externality　and　platform　motivation,　new　user　utility　functions　and　adaptive　learning　rules　are　established　to　describe　user　(producer　and　consumer)　choice.　©　2020　IEEE.