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In deregulated electricity markets, market players have an important task of implementing the optimal offers, or bids, for each trading interval to maximize their profits. The major challenge of designing bidding strategies lies in that, it is difficult for a generator to predict competitive generators' behaviours because it only has incomplete information about its rivals. A novel approach of designing the optimal bidding strategies based on incomplete market information is proposed in this paper. This method predicts the expected bidding productions of each rival generator in the market based on publicly available bidding data. Moreover, the non-linear relationship between generators' bidding productions and the market clearing price (MCP) is also estimated from historical bidding and price data, using support vector machine (SVM). The optimal bidding problem is finally transformed into a stochastic optimization problem, which is solved with differential evolution (DE) and Monte Carlo simulation based on the predicted rivals' behaviour and MCP. The case studies using eleven coal-fired generators in the Australian National Electricity Market (NEM) are conducted to verify the effectiveness of the proposed method.