In this study, we suggest a multi-generation Lotka-Volterra model, which is a competition model using game theory and complex system theory. The suggested model shows many improvements to weakness of a well known Bass model to forecast new technology in competitive markets. We show that the Lotka-Volterra model has strong power to forecast mobile communication services when it is used for competition of 1st generation mobile phone service and 2nd generation phone service in Korea. We finally use the model to forecast IMT-2000 service, the 3rd generation mobile communication service.