We consider a two-stage newsvendor model in which the retailer orders a product and sells it at the full price in the first stage, and sells the leftover stock, if any, at a discounted price in the second stage. The customers are strategic, who are boundedly rational and risk averse, and their valuations of the product decrease with time. The customers make purchase decisions based on their beliefs of the product's availability and their expected utility in the two stages. The customers who purchase in the second stage may not get the product. Characterising the retailer's optimal inventory policy, we show that the retailer's optimal profit decreases with the rate of the customers' decreasing product valuation. Moreover, as the customers become less rational or more risk averse, the retailer's profit vary with the model parameters. We conduct numerical studies to examine the impacts of the customers' bounded rationality on the retailer's order quantity and optimal profit. In addition, considering the value of the quick response (QR) strategy, we show that the QR strategy can increase the retailer's profit, while the customers' bounded rationality may increase or decrease the value of QR to the retailer.