Abstract: In recent years, the rapid development of remanufacturing industry has promoted the transformation of traditional supply chain to closed-loop supply chain. Due to the lack of market supervision and the lack of corporate integrity, price cheating in the remanufactured product market emerges one after another. In order to obtain more profit, the sellers of remanufactured products usually spend some camouflage cost. They camouflage remanufactured products as new products and sell camouflaged remanufactured products at the price of new products in the market. This behavior of the sellers is the price cheating on remanufactured products. It not only severely damages the benefits of the consumers, but also hinders the healthy development of the remanufactured product market. In order to protect the benefits of the consumers and promote the healthy development of the remanufactured product market, we study the price cheating on remanufactured products in the back-to-sale link of closed-loop supply chain and discuss its internal mechanism and solution in this paper. We first consider the camouflage cost in the narrow sense, and then consider the camouflage cost in the broad sense. Also, the results under two cases are compared.
Firstly, considering the camouflage cost in the narrow sense, we construct an evolutionary game model composed of the seller and the consumer, and analyze the evolutionary stability of mixed strategies through Jacobi matrix. The results show that when the difference between the camouflaged selling price and the camouflage cost of the remanufactured products is smaller than the non-camouflaged selling price of the remanufactured products, the seller chooses not to camouflage and the consumer chooses to buy. At this time, the remanufactured product market is effective. So in the evolutionary game between the seller and the consumer, increasing the camouflage cost can prompt the system evolve to an effective state that the seller chooses not to camouflage and the consumer chooses to buy. In fact, the increase of camouflage cost will lead to the decrease of the income of the seller in selling camouflaged remanufactured products. If the income of the seller in selling camouflaged remanufactured products is smaller than the income of the seller in selling non-camouflaged remanufactured products, the seller will not have the need to camouflage, and the seller will choose not to camouflage. Once the seller chooses not to camouflage, it prompts the consumer to choose to buy. In the end, the two sides evolve into an effective state that the seller chooses not to camouflage and the consumer chooses to buy, and form a benign development.
Secondly, considering the rewards and punishments of the government for the seller, that is considering the camouflage cost in the broad sense, we establish an evolutionary game model composed of the seller, the consumer and the government, and analyze the evolutionary stability of mixed strategies through Jacobi matrix. To be specific, by using the step-by-step analysis method, the three-party evolutionary game is transformed into two two-party evolutionary games. On the basis of the results of the two two-party evolutionary games, the evolutionary stability strategy of the three-party evolutionary game is obtained by comprehensive analysis. The results show that when the difference between the camouflaged selling price and the camouflage cost of the remanufactured products is smaller than the non-camouflaged selling price of the remanufactured products, the seller chooses not to camouflage, the consumer chooses to buy and the government chooses not to inspect. At this time, the market allocation is effective. Obviously, the results obtained in the three-party evolutionary game is same to that obtained in two-party evolutionary game, so we can prompt the market to evolve to an effective state only by adjusting the camouflage cost. But in the three-party evolutionary game among the seller, the consumer and the government, the retail price of new products and remanufactured products are determined by the market, and the camouflage cost is an uncontrollable parameter. Therefore, in order to push the remanufactured product market to an effective state, we can increase the probability of government inspection of the remanufactured product market and increase the government’s rewards and punishments for the seller. When the government’s intervention plays a positive role in promoting the effective allocation of the market, the government can not achieve the Nash equilibrium at that time. This shows that the government needs to pay a certain price to promote the healthy development of the remanufactured product market.
Finally, we verify the correctness of the corresponding results in the above models through numerical simulation. In this paper, the numerical analysis is carried out in the case of pure simulation and does not combine with the actual data of the remanufactured product market. In the future, we can collect big data of the remanufactured product market and use econometrics and data mining to conduct empirical analysis. So we can improve the research on the behavior of relevant participants in the remanufactured product market.

Key words: remanufactured product, price cheating, evolutionary game, dynamic replication equation, Jacobi matrix

摘要： 由于市场监管缺乏和企业诚信缺失,再制品市场的价格欺骗事件层出不穷,严重损害了消费者的利益和市场配置的有效性。本文研究闭环供应链中的再制品价格欺骗问题。首先,构建一个由销售商和消费者组成的双方演化博弈模型,通过Jacobi矩阵分析混合策略的演化稳定性。结果表明:当再制品伪装之后的销售价格与伪装成本的差小于再制品不伪装的销售价格时,销售商选择不伪装,消费者选择购买,再制品市场是有效的。其次,考虑政府对销售商奖励或惩罚的措施,构建一个由销售商、消费者和政府组成的三方演化博弈模型,通过Jacobi矩阵分析混合策略的演化稳定性。结果表明:政府积极检查再制品市场,加大奖励和惩罚力度,均能促使销售商选择不伪装且消费者选择购买,市场达到有效配置。最后,通过数值分析验证相关结论的正确性。

关键词: 再制品, 价格欺骗, 演化博弈, 复制动态方程, Jacobi矩阵