Endogenous default risk in supply chain and non-linear pricing

Based on incomplete contract theories, we studied the strategic behaviors of up-stream and down-stream manufacturers by option game model and obtain some conclusions. First, the down-stream's pay-off function is a concave function of its investment in fixed assets, so there is an optimal investment, which ensures the down-stream's maximal pay-off and prevents it from being holdup. Second, in presence of endogenous default risks, the up-stream can improve its pay-off level through non-linear pricing. Last, increasing business risks of the down-stream may lead to an increased price fluctuation of the up-stream, while the down-stream's technological advancement can make such fluctuation less.