## 1 Introduction  
Extended producer responsibility (EPR) refers to the practice whereby manufacturing companies are responsible not only for designing, producing, and selling products but also for their recycling, dismantling, and reuse. EPR is also an indispensable part of zero waste management [1]. By reducing the amount of waste products, EPR can promote the full utilization of resources and facilitate the development of a circular economy. In China, EPR has been applied to various manufacturing industries, such as household appliances [2], automobiles [3], and electronic products [4]. It is now extending to more industries under the encouragement of national policies. According to the UN's 2020 Global E-waste Monitor Report, only 17.4% of the 53.6 million tons of global e-waste produced in 2019 were recycled [5]. EPR can effectively solve various social and environmental issues in e-waste recycling, such as handling heavy metals including lead, chromium, and mercury, in addition to addressing the problem of raw material shortages in manufacturing [6]. The main products involved in household appliance recycling are generally known as the \"four appliances and one brain\", namely televisions, refrigerators, washing machines,air conditioners, and computers [7]. Figure 1 shows the material circulation process in the manufacturing and recycling of household appliances. As shown in Figure 1, the industrial chain of household appliance recycling involves many participants, including producers, sellers, consumers, second-hand dealers, business recyclers, personal recyclers, disintegrators, and reproducers. Raw materials such as metal, plastic, and glass are sold to household appliance producers at a price of \(m_{i}\). Producers sell household appliances to sellers at a factory price of \(p_{i}\), and sellers sell them to consumers online or offline at a price of \(s_{i}\). Since household appliances that are replaced by consumers may be sold to second-hand dealers or directly to scrap dealers, there are two circulation pathways for waste household appliances. One is to sell them to second-hand dealers at a price of \(c_{i}\), then sell them to consumers at a price of \(rs_{i}\). The second is to sell them to scrap dealers at a price of \(c_{i}\). Scrap dealers can be divided into business recyclers and personal recyclers, and they are generally organized into multilevel networks according to their location. The selling price of the mth-level business recycler is denoted by \(b_{i}^{m}\), and the selling price of the nth-level personal recycler is denoted by \(p_{i}^{n}\). Personal recyclers usually do not have professional equipment, and they tend to dismantle waste household appliances privately, which not only exposes their employees to harmful substances and endangers their health [8] but also causes materials that cannot be recycled to flow out of the material circulation [9]. After dismantling, disintegrators sell the dismantled raw materials to reproducers at a price of \(d_{i}\), and some materials that cannot be recycled are treated for harmless disposal, then flow out of material circulation [10]. Reproducers process the waste raw materials into reusable raw materials and sell them to household appliance producers at a price of \(rp_{i}\), completing the internal circulation of materials in the manufacturing and recycling of household appliances. The pricing variables in the household appliance manufacturing and recycling process described above are summarized in Table 1.  
Research on the household appliance recycling chain includes recycling techniques, pricing strategies based on game theory, market competition and cooperation models, etc. [PERSON] et al. [7] introduced the 4R strategy in the household appliance recycling circular economy, which includes reduction, reuse, remanufacturing, and recycling. [PERSON] et al. [11] proposed the full recycling of various metal materials in electronic products by increasing reuse rates and enhanced recycling efficiency. [PERSON] et al.