The Interplay of Financing and Trade-In Implementation Under Agency Selling

1. Introduction

A growing number of platforms, such as JD.com, Tmall, and Amazon, open their online marketplaces to manufacturers, letting them sell directly to consumers under agency selling in exchange for a commission on each sale. Most of these manufacturers are small and medium-sized businesses: on Amazon, for instance, about 73% of third-party sellers employ only one to five people, and another 10% employ five to ten [1]. Firms of this size often lack working capital and must rely on short-term financing to cover production and procurement before sales revenue comes in [2].

Such financing has traditionally come from banks. The platforms have since become lenders in their own right: because a platform observes its sellers’ sales and revenue in detail, it can evaluate and extend credit that an outside bank, lacking comparable information, cannot offer as readily. JD.com lends to its merchants through its own supply-chain finance program, Jingbaobei; Alibaba lends to its Taobao and Tmall sellers through MYbank, the online bank of its fintech affiliate Ant Group; and Amazon arranges credit for its sellers through partner lenders under Amazon Lending. We refer to this mode of financing, provided by the platform itself or by the platform in cooperation with external financial institutions, collectively as platform financing. A capital-constrained manufacturer can thus finance its production through either platform financing or a bank loan.

Beyond financing, these manufacturers face an increasingly saturated product market. Advances in technology have made many products, e.g., consumer electronics, ever more durable, so more and more consumers in the market already hold a used product. Trade-in programs, in which a consumer returns a used product for a rebate toward a new purchase, convert this stock of used products into replacement demand, and have therefore gained increasing favor among manufacturers and retailers [3]. Competitive pressure has extended the practice to the online marketplaces as well: JD.com, Amazon, and Taobao now offer trade-in services to consumers who purchase third-party products on their sites.

Trade-in implementation and financing have thus become a coupled pair of problems in the operation of platform supply chains. Policy makes the coupling explicit: China’s 2026 Government Work Report arranges RMB 250 billion of ultra-long-term special treasury bonds to subsidize consumer-goods trade-ins, alongside a RMB 100 billion fiscal–financial fund that supports enterprise financing through loan interest subsidies, financing guarantees, and risk compensation.1 This bundling underscores the need to treat the two issues within a unified decision framework. The literature, however, has typically studied the two dimensions separately: one stream examines trade-in programs, e.g., [4,5,6], and another examines financing choices, e.g., [1,7,8]. To address this gap, we investigate how the two dimensions interact. Specifically, we consider a capital-constrained manufacturer that sells a new durable product through an online retail platform under agency selling. The manufacturer can raise funds from either the platform or a bank, and the trade-in program can be implemented by either the manufacturer or the platform. Against this backdrop, we address the following questions.

(1) What are the equilibrium decisions—the interest rate, the new-product price, and the trade-in rebate—in each scenario?

(2) How do the financing source (platform versus bank) and the trade-in implementer (manufacturer versus platform) interact to shape these decisions and the resulting demand?

(3) From the perspectives of the manufacturer, the platform, the bank, and consumers, which trade-in implementer and which financing channel are preferred?

To answer these questions, we build four game-theoretic models in which a fraction of consumers own a used product while the others do not, the platform charges a fixed commission, and the manufacturer borrows to finance its production and procurement. Solving these models and comparing the equilibria across scenarios, we obtain the following main findings.

First, the financing channel and the trade-in implementer shape the equilibrium decisions in different ways. A platform-implemented trade-in raises the equilibrium interest rate relative to a manufacturer-implemented one, whereas whether platform or bank financing yields the higher rate depends on the production cost. The two dimensions’ effects on prices and demand are likewise largely cost-dependent, with two regularities under platform financing: a platform-implemented trade-in consistently pays a larger rebate, and total new-product demand is the same regardless of which party implements the trade-in.

Second, the financing channel reshapes who prefers to implement the trade-in. Under platform financing, both the manufacturer and the platform prefer to implement the program themselves, whereas under bank financing their preferences become mixed.

Third, we compare the preferences of the parties across the two dimensions. The bank consistently prefers the platform to implement the trade-in. The manufacturer’s preferred financing channel depends on the residual value of used products and the production cost, but in most cases it favors platform financing. Consumers prefer the platform financing channel when the manufacturer implements the trade-in, and prefer the manufacturer to implement the trade-in under platform financing; in the remaining cases their preference turns on the commission rate.

The remainder of the paper is organized as follows. Section 2 reviews the related literature. Section 3 describes the problem and assumptions. Section 4 presents the four scenarios and characterizes the equilibrium decisions. Section 5 compares the scenarios along the financing and implementation dimensions. Section 6 concludes and outlines directions for future research. All proofs are collected in Appendix A.

2. Literature Review

This paper relates to two research streams: (i) trade-in programs for durable goods; and (ii) financing for capital-constrained supply chains. We review these streams and position our contribution accordingly.

2.1. Trade-in Programs for Durable Goods

Within the scope of durable-goods operations, trade-in programs have been extensively studied; the literature falls into two substreams, one on the pricing of the program and the other on the choice of its implementer.

A majority of the studies in this substream focus on the pricing of the program and the associated strategy choices. For durable goods sold in a highly saturated market, Ray et al. [9] compare three pricing strategies: a uniform price for all consumers, prices differentiated by whether a consumer owns a used product, and prices further conditioned on the age of the used product. Yin and Tang [10] ask when a trade-in program should charge an up-front participation fee when consumers are uncertain about their valuation of the new product. Yin et al. [11] extend the pricing problem to two successive product generations whose incremental value is uncertain before introduction. Cao et al. [12] study how a retail platform implements its trade-in program and whether the program should cover the third-party stores it hosts. In a multi-period framework, Xiao et al. [13] evaluate the performance of fully dynamic pricing against semi-dynamic pricing, in which the new-product price is fixed and only the rebate adjusts. Cao and Choi [14] account for consumer returns and study the associated trade-in refund policy. Dong et al. [15] examine the trade-in strategies of two competing manufacturers when consumers incur switching costs. Ju et al. [16] embed trade-ins in a relief supply chain and study how a government procurement agency sets the reserve quantities of relief supplies. Tang et al. [6] examine how the government should design its subsidy scheme when a single firm implements the trade-in. Xu et al. [17] treat the trade-in as a collection channel and compare two pricing strategies for the remanufactured product, with and without price commitment.

Because a trade-in naturally serves as a collection channel for used products, a growing body of work examines its interaction with used-product sales. Rao et al. [18] show that trade-ins can mitigate the lemons problem in used-goods markets. Agrawal et al. [19] study the trade-in rebate both as a price-discrimination device and as a means of collecting used products for remanufacturing. Zhao et al. [20] analyze how a manufacturer can deploy a trade-in program to compete with a third-party remanufacturer. Turning to used-product resale, Vedantam et al. [21] ask whether a manufacturer should run a trade-in program or open its own peer-to-peer marketplace; Hu et al. [22] examine when a manufacturer operating a trade-in program should refurbish the returned products; and Bai et al. [23] study the manufacturer’s implementation modes in the presence of a resale platform, distinguished by whether the rebate is paid in cash. Li et al. [24] consider hybrid manufacturing and remanufacturing with a trade-in program under a carbon tax. Hu et al. [25] incorporate time-varying customer choice behavior and changing secondary-market recycling prices into the pricing problem. Hu et al. [26] derive the pricing and resale strategies when a secondary market and a trade-in program coexist, and Srivastava et al. [27] identify when a manufacturer should cooperate with a third-party collection platform to implement the trade-in.

The other substream examines the choice of the trade-in implementer, which is closely related to our work. In a reselling supply chain, Tang et al. [3] study whether the manufacturer or the retailer should implement the trade-in program. Taking the resale of the collected products into account, Li et al. [28] ask whether the retailer or a collection platform should implement it. Wang et al. [5] compare the reselling and agency modes and investigate who should implement the program, the manufacturer or the platform, under each mode. Considering consumers’ quality preferences, Ma et al. [29] study the same choice between the manufacturer and the retail platform, and Zheng et al. [30] further examine it when the collected used products can be resold.

Although this stream has studied trade-in programs in depth, covering their pricing, their interplay with the used-product market, and who should implement them, it assumes a well-funded manufacturer. These studies do not consider a capital-constrained manufacturer that must finance production, nor who should provide that financing.

2.2. Financing for Capital-Constrained Supply Chains

Classic supply-chain finance contrasts an external bank with an upstream lender. Buzacott and Zhang [31] first incorporate asset-based financing into production decisions, showing that a firm’s inventory decisions and its access to asset-based credit are inseparable. Kouvelis and Zhao [32] characterize the optimal trade-credit contract for a newsvendor that can borrow from its supplier or a bank. Kouvelis and Zhao [33] further show that the firms’ credit ratings determine who should finance the chain’s inventory and at what rates, with a well-rated supplier offering interest-free trade credit and a poorly rated one setting a positive rate that pushes the retailer to combine trade credit with bank loans. Du et al. [34] examine how the manufacturer’s introduction of a direct channel interacts with the retailer’s choice between trade credit and bank credit.

With the development of the online economy, e-commerce platforms have emerged as a new source of financing and have drawn increasing research attention. Considering a manufacturer that sells through a traditional retailer and, under agency selling, an online platform, Zhen et al. [35] study the manufacturer’s financing choice among the retailer, the platform, and a bank. Yang et al. [36] identify the conditions under which a third-party retailer borrowing from the bank and the platform simultaneously achieves a Pareto improvement for the supply chain. Wang et al. [37] show how farmers’ social responsibility shapes their financing-channel choice between a bank and the platform. Mandal et al. [1] examine the bank-versus-platform financing choice of two competing sellers hosted on a platform. When carbon permits can serve as pledged assets, Xu et al. [7] study how the seller’s remanufacturing and carbon-abatement decisions interact with its financing choice between the platform and the bank. Zhang and Shang [38] likewise examine how the manufacturer’s platform-versus-bank financing choice interacts with its carbon-abatement decision. Lu et al. [8] investigate how the platform’s digital empowerment affects farmers’ loan choice between the platform and a bank. Liu et al. [39] study a supplier’s online selling-mode choice between agency and reselling when the platform offers financing, with the supplier also holding an offline reselling channel. Under exogenous and endogenous default risks, Huang et al. [2] analyze how a third-party seller should choose between trade credit from its supplier and platform financing. When third-party sellers trade through a platform, Hu et al. [40] examine the interplay between information sharing and financing services on the retail platform. For a low-carbon supply chain with an upstream supplier and two capital-constrained retailers, Zhang et al. [41] evaluate how supplier financing and hybrid financing affect the chain’s performance. Jiang et al. [42] study the financing choice of a retailer hosted on a platform between its upstream supplier and the platform. Liao et al. [43] examine how the sharing of farmers’ technology-investment costs affects their loan choice between the platform and a bank. Wang et al. [44] study how channel competition and consumers’ low-carbon preference drive the financing-channel choice of a capital-constrained manufacturer or retailer. Considering consumer-oriented advance-selling financing, Wang et al. [45] compare a retailer’s three financing options: trade credit alone, advance selling alone, or the two combined.

In recent years, governments have begun to intervene with subsidy and interest-subsidy policies to stimulate the economy, and a group of studies has accordingly turned to financing decisions under government subsidies. Luo et al. [46] study how the government should choose between risk compensation and guarantee-fee reduction when facing capital-constrained small and medium-sized businesses and a profit-maximizing guarantee company. When two competing farmers borrow from a bank, Yi et al. [47] examine the government’s choice between an interest subsidy and a direct subsidy. In an industrial-symbiosis setting with supply–demand mismatch, Cao et al. [48] compare purchase-order financing, factoring, and buyer direct financing in terms of supply-chain performance, and further analyze how an environmental tax and a recycling subsidy alter the value of each mode. Considering consumption-preference updating, Gao et al. [49] study the retailer’s mixed financing decision and the upstream manufacturer’s carbon-abatement decision when the government offers promotion subsidies and a carbon-quota financing channel. When the manufacturer raises green equity financing, Zhou et al. [50] compare three government subsidy targets, namely the manufacturer, the retailer, and consumers.

Rich as this body of work is, covering bank and trade credit, platform lending, and financing under government subsidies, the operation being financed is production, inventory, or green investment. These studies do not take a trade-in program as the operation that the capital-constrained firm must finance, nor let the financing decision interact with who implements that program.

Differing from the existing literature, we simultaneously consider the trade-in implementation responsibility and the financing responsibility of a capital-constrained manufacturer under agency selling. The manufacturer sells a durable product through a retail platform and offers a trade-in program; it finances production from either the platform or a bank, while the trade-in is implemented by either the manufacturer or the platform. Table 1 summarizes this positioning relative to representative studies; there, M, R, and P denote the manufacturer, the retailer, and the platform, respectively.

3. Problem Description and Assumptions

3.1. Problem Description

We consider a platform-based supply chain in which a capital-constrained manufacturer sells a durable product to consumers through a retail platform under agency selling. Under this mode, the manufacturer sets the new-product price $p_n$, while the platform charges a commission on the sales revenue at an exogenous rate $\varphi$ ($0<\varphi <1$). There are two types of consumers in the market: a fraction $\alpha$ ($0<\alpha <1$) own a used product and are referred to as replacement consumers ($C_R$), whereas the remaining fraction $1-\alpha$ do not own a used product and are referred to as primary consumers ($C_N$), as in [9]. The manufacturer lacks capital and needs financing in order to produce. We consider two financing channels, the platform and a bank; the manufacturer borrows from one of them and repays the loan at an interest rate r once demand is realized. For tractability, we assume that the manufacturer has zero initial capital and raises its unit production cost c entirely through external financing, a common assumption in the supply-chain finance literature (e.g., [1,7,47]). To encourage replacement consumers to replace their used product with the new one, we further allow a trade-in program, implemented either by the manufacturer or by the platform, that pays a replacement consumer a rebate $p_t$ for the used product upon repurchase. This setting mirrors the practice of leading platforms such as Taobao, JD.com, and Amazon, which simultaneously run a trade-in program and offer financing services to their capital-constrained sellers.

In this paper, we consider four scenarios, denoted $MP$, $MB$, $PP$, and $PB$, which arise from two dimensions: the trade-in implementer (the manufacturer M or the platform P) and the source of financing (the platform P or a bank B). In each two-letter label, the first letter identifies the trade-in implementer and the second the financing source; for instance, $MP$ denotes a manufacturer-implemented trade-in under platform financing. The platform may thus play up to two roles—financing production and implementing the trade-in program—in addition to operating the marketplace. For analytical convenience, we assume that the used products collected through the program have zero residual value to the collecting party, which is consistent with [19]. These four configurations form a $2\times 2$ design that allows us to study the interplay of financing and trade-in modes under agency selling. The supply chain structure of each scenario is depicted in Figure 1, and all notation is summarized in Table 2.

Throughout, we assume that the bank and the platform act as the leaders of the supply chain: they decide first and simultaneously, and the manufacturer decides afterward. This assumption is consistent with [1,7,30] and with practice, in which the manufacturer needs to know the interest rate before it produces and platforms are becoming increasingly powerful. The detailed decision sequence is as follows. In the first stage, the lender sets the interest rate r and, if the platform implements the trade-in program, the platform sets the rebate $p_t$. In the second stage, the manufacturer sets the new-product price $p_n$ and, if it implements the trade-in program, the rebate $p_t$.

To rule out degenerate outcomes, we focus throughout on the interior parameter region in which, in each scenario, the financing rate r, the new-product price $p_n$, and the rebate $p_t$ are positive; the manufacturer’s per-unit margin is positive on every consumer segment it serves, namely $(1-\varphi )p_n-(1+r)c>0$ on a primary unit in every scenario and, when the manufacturer funds the rebate (Scenarios $MP$ and $MB$), $(1-\varphi )p_n-p_t-(1+r)c>0$ on a replacement unit; and the segment demands $q_{nn}$ and $q_{nr}$ are positive, so that both segments are served.

3.2. Demand

We assume that each consumer’s valuation of the new product, $\theta$, is uniformly distributed on $[0,1]$, a standard assumption in this literature (e.g., [3,4]), and that the market size is normalized to one. For a replacement consumer, the used product still carries a residual value of $\delta \theta$, where $\delta$ ($0<\delta <1$) is the residual-value factor and $1-\delta$ captures its depreciation, referring to [23,28,51].

A replacement consumer obtains utility $U_{nr}=\theta -p_n+p_t$ from purchasing a new product, whereas keeping the used product yields $U_{ku}=\delta \theta$; the purchasing condition $U_{nr}\ge U_{ku}$ yields $q_{nr}^i=\alpha \left(1-{\displaystyle \frac{p_n-p_t}{1-\delta }}\right)$. A primary consumer obtains utility $U_{nn}=\theta -p_n$ from buying the new product and the purchasing condition $U_{nn}\ge 0$ yields $q_{nn}^i=(1-\alpha )(1-p_n)$, for $i\in \{MP,MB,PP,PB\}$.

4. Models and Optimal Decisions

This section constructs the model for each scenario and presents the optimal decisions of the supply chain members.

4.1. Scenario MP

In Scenario $MP$, the manufacturer implements the trade-in program and chooses platform financing. The platform first sets the interest rate r, and the manufacturer then jointly sets the new-product price $p_n$ and the rebate $p_t$. The manufacturer and the platform solve

$$\underset{p_n,p_t}{max}{\Pi }_m^{MP}=(1-\varphi )p_n{q}_n-p_t{q}_{nr}-(1+r)c{q}_n,$$

(1)

and

$$\underset{r}{max}{\Pi }_p^{MP}=\varphi p_n{q}_n+rc{q}_n,$$

(2)

respectively.

Theorem 1.

In Scenario $MP$, a unique equilibrium exists when $0<\varphi <\overline{\varphi }$: the interest rate is $r^{MP\ast }={\displaystyle \frac{A^{MP}}{4c(1-\alpha )(1-\delta )(2-\varphi )(1-(1-\alpha \left)\delta \right)}}$, the new-product price is $p_n^{MP\ast }={\displaystyle \frac{B^{MP}}{4(1-\alpha )(1-\delta )(2-\varphi )(1-(1-\alpha \left)\delta \right)}}$, and the trade-in rebate is $p_t^{MP\ast }={\displaystyle \frac{C^{MP}}{4(1-\alpha )(2-\varphi )(1-\delta )}}$, where the aggregates $A^{MP}$, $B^{MP}$, $C^{MP}$ are given in Appendix B and the threshold is $\overline{\varphi }={\displaystyle \frac{2}{\alpha }}(\sqrt{(1-\alpha )(1-\delta )(1-(1-\alpha \left)\delta \right)}-(1-\alpha )(1-\delta ))$.

In Theorem 1, the restriction on $\varphi$ indicates that the commission rate cannot be too high. This is consistent with both practice and the literature: on JD’s open platform the transaction fee is about 0.6% and the operation-support service fee ranges from 0 to 10%2, while Mandal et al. [1] assume $\varphi <{\displaystyle \frac{1}{2}}$.

4.2. Scenario MB

In Scenario $MB$, the manufacturer implements the trade-in program and chooses bank financing. The bank first sets the interest rate r, and the manufacturer then jointly sets the new-product price $p_n$ and the rebate $p_t$, while the platform only collects commission. The manufacturer and the bank solve

$$\underset{p_n,p_t}{max}{\Pi }_m^{MB}=(1-\varphi )p_n{q}_n-p_t{q}_{nr}-(1+r)c{q}_n,$$

(3)

and

$$\underset{r}{max}{\Pi }_b^{MB}=rc{q}_n,$$

(4)

respectively.

Theorem 2.

In Scenario $MB$, a unique equilibrium exists when $\varphi <\overline{\varphi }$, with $\overline{\varphi }$ as in Theorem 1: the interest rate is $r^{MB\ast }={\displaystyle \frac{2(1-\delta )-\varphi (2-(2-\alpha \left)\delta \right)-2c(1-(1-\alpha \left)\delta \right)}{4c(1-(1-\alpha \left)\delta \right)}}$, the new-product price is $p_n^{MB\ast }={\displaystyle \frac{A^{MB}}{4(1-(1-\alpha )\delta )(4(1-\alpha )(1-\delta )(1-\varphi )-\alpha {\varphi }^2)}}$, and the rebate is $p_t^{MB\ast }={\displaystyle \frac{B^{MB}}{4(4(1-\alpha )(1-\delta )(1-\varphi )-\alpha {\varphi }^2)}}$, where $A^{MB}$ and $B^{MB}$ are given in Appendix B.

4.3. Scenario PP

In Scenario $PP$, the platform implements the trade-in program, and the manufacturer chooses platform financing. The platform first jointly sets the interest rate r and the rebate $p_t$, and the manufacturer then sets the new-product price $p_n$. The manufacturer and the platform solve

$$\underset{p_n}{max}{\Pi }_m^{PP}=(1-\varphi )p_n{q}_n-(1+r)c{q}_n,$$

(5)

and

$$\underset{r,p_t}{max}{\Pi }_p^{PP}=\varphi p_n{q}_n+rc{q}_n-p_t{q}_{nr},$$

(6)

respectively.

Theorem 3.

In Scenario $PP$, there exists a unique equilibrium: the interest rate is $r^{PP\ast }={\displaystyle \frac{A^{PP}}{2c(2-\varphi )(1-(1-\alpha \left)\delta \right)}}$, the new-product price is $p_n^{PP\ast }={\displaystyle \frac{B^{PP}}{2(2-\varphi )(1-(1-\alpha \left)\delta \right)}}$, and the rebate is $p_t^{PP\ast }={\displaystyle \frac{\delta }{2}}$, where $A^{PP}$ and $B^{PP}$ are given in Appendix B.

4.4. Scenario PB

In Scenario $PB$, the platform implements the trade-in program, and the manufacturer chooses bank financing. The bank sets the interest rate r and the platform sets the rebate $p_t$ simultaneously in the first stage, and the manufacturer then sets the new-product price $p_n$. The manufacturer, the bank, and the platform solve

$$\underset{p_n}{max}{\Pi }_m^{PB}=(1-\varphi )p_n{q}_n-(1+r)c{q}_n,$$

(7)

$$\underset{r}{max}{\Pi }_b^{PB}=rc{q}_n,$$

(8)

and

$$\underset{p_t}{max}{\Pi }_p^{PB}=\varphi p_n{q}_n-p_t{q}_{nr},$$

(9)

respectively.

Theorem 4.

In Scenario $PB$, there exists a unique equilibrium: the interest rate is $r^{PB\ast }={\displaystyle \frac{A^{PB}}{c(1-(1-\alpha )\delta )H^{PB}}}$, the new-product price is $p_n^{PB\ast }={\displaystyle \frac{B^{PB}}{2(1-\varphi )(1-(1-\alpha )\delta )H^{PB}}}$, and the rebate is $p_t^{PB\ast }={\displaystyle \frac{C^{PB}}{(1-\varphi )H^{PB}}}$, where $A^{PB}$, $B^{PB}$, $C^{PB}$, and $H^{PB}$ are given in Appendix B.

5. Comparative Analysis

In this section, we compare the four scenarios along two dimensions: fixing the trade-in implementer while switching the financing source, and fixing the financing source while varying the trade-in implementer. Because Scenarios $MP$ and $MB$ require $\varphi <\overline{\varphi }$ (Theorems 1 and 2), we maintain this condition throughout, with $\overline{\varphi }$ as in Theorem 1. All comparisons are made over the feasible region defined in Section 3. For each analytical result, we provide both a proof and numerical evidence to ensure that it is realized within the feasible region.

5.1. Interest Rate

Proposition 1.(1) Under a fixed trade-in implementer, platform versus bank financing:

(i) under a manufacturer-implemented trade-in, $r^{MP\ast }\ge r^{MB\ast }$ if $c\le c_1^I$, and $r^{MP\ast }<r^{MB\ast }$ otherwise;

(ii) under a platform-implemented trade-in, $r^{PP\ast }\ge r^{PB\ast }$ if $c\le c_2^I$, and $r^{PP\ast }<r^{PB\ast }$ otherwise.

(2) Under a fixed financing source, manufacturer versus platform trade-in:

(i) under platform financing, $r^{PP\ast }>r^{MP\ast }$;

(ii) under bank financing, $r^{PB\ast }>r^{MB\ast }$.

The thresholds $c_1^I$ and $c_2^I$ are given in Appendix B.

Proposition 1(1) fixes the trade-in implementer and compares the interest rate under platform versus bank financing. The ranking of the two rates is cost-dependent. Two forces underlie this. First, the two lenders earn differently: the platform collects both a commission on the manufacturer’s sales and interest on the loan, whereas the bank earns interest alone. Second, when the platform lends, the supply chain is more concentrated and the platform holds greater channel power within it. Which force dominates depends on the production cost. When the cost is high, the new-product demand is fragile, and the platform—to protect the commission it would lose if a high rate suppressed output—holds its rate below the bank’s. When the cost is low, demand is ample and the commission base is secure even at a high rate, so the platform exercises its power and charges a rate above the bank’s.

Proposition 1(2) fixes the lender and compares the interest rate under a manufacturer- versus platform-implemented trade-in. Under either lender, a platform-implemented trade-in carries the higher rate, and the reason is who bears the rebate. When the manufacturer implements the trade-in (Scenarios $MP$ and $MB$), it funds the rebate on top of repaying the production loan, so the lender cuts the rate to avoid overburdening the manufacturer and suppressing output. When the platform implements it (Scenarios $PP$ and $PB$), the manufacturer is shielded from the rebate and the lender charges more. The party that bears the trade-in cost thus pulls the financing rate down.

5.2. Prices and Demands

In this section, we compare the new-product price first, the rebate next, and the total output they induce last.

5.2.1. New-Product Price

Proposition 2.(1) Under a fixed trade-in implementer, platform versus bank financing:

(i) under a manufacturer-implemented trade-in, $p_n^{MP\ast }\ge p_n^{MB\ast }$ if $c\le c_1^I$, and $p_n^{MP\ast }<p_n^{MB\ast }$ otherwise;

(ii) under a platform-implemented trade-in, $p_n^{PP\ast }\ge p_n^{PB\ast }$ if $c\le c_1^P$, and $p_n^{PP\ast }<p_n^{PB\ast }$ otherwise.

(2) Under platform financing, $p_n^{MP\ast }<p_n^{PP\ast }$.

The threshold $c_1^P$ is given in Appendix B.

Proposition 2(1) fixes the trade-in implementer and compares the new-product price under platform versus bank financing. As with the rate, the ranking is cost-dependent. The reason is pass-through: the manufacturer funds production with the loan, so a higher financing rate lifts its marginal cost and the price it sets. The new-product price therefore tracks the rate ordering of Proposition 1(1). When the cost is low, the platform charges a higher rate than the bank—exercising its channel power once the commission base is secure—so platform financing carries the higher new-product price. When the cost is high, the platform lowers its rate to protect the commission it would lose if output were suppressed, and bank financing becomes the more expensive channel.

Proposition 2(2) fixes platform financing and compares the new-product price under a manufacturer- versus platform-implemented trade-in. The platform-implemented program carries the higher price. The rationale is that pricing under a platform-implemented trade-in is more decentralized. When the manufacturer implements the trade-in, it sets the new-product price and the rebate jointly and coordinates the two, holding the price down. When the platform implements it, the two levers split: the platform sets the rebate, the manufacturer the new-product price. Earning a commission $\varphi p_n$ on every unit, the platform values volume more than the manufacturer and sets a more generous rebate (Proposition 3); facing the stronger replacement demand this creates, the manufacturer best-responds with a higher price. Splitting the two levers across firms thus lifts the new-product price—a redistribution, not a loss of output, since the deeper rebate offsets the higher price and total sales are unchanged (Proposition 4).

Since it is hard to compare $p_n^{MB\ast }$ and $p_n^{PB\ast }$ analytically, we use a numerical experiment to illustrate their relationship at $\alpha =0.4$ and $\varphi =0.15$, as shown in Figure 2. Contrary to Proposition 2(2), under bank financing a manufacturer-implemented trade-in no longer always carries the lower new-product price. Once the bank makes the loan, the platform earns only its commission $\varphi p_n$ and not the interest that an expanded demand would generate, so it has little incentive to offer a deep rebate (Figure 3). The manufacturer’s incentive, by contrast, moves with the value of the trade-in. When that value is high—a large residual value and a low production cost, so the margin on each replacement is high—the manufacturer offers a more generous rebate, which lifts the new-product price through the same mechanism as in Proposition 2(2); over most of the feasible region the manufacturer-implemented program then carries the higher price. Only when the trade-in is worth little—a low residual value and a high production cost—does the manufacturer’s rebate incentive fade, letting the financing rate take over. Under bank financing, a platform-implemented trade-in carries the higher rate (Proposition 1(2)(ii)). With the rebate playing little role, this higher rate passes through to a higher new-product price. The ordering thus reverts to the platform, $p_n^{PB\ast }$ overtaking $p_n^{MB\ast }$.

5.2.2. Trade-In Rebate

Proposition 3.(1) Under a fixed trade-in implementer, platform versus bank financing:

(i) under a manufacturer-implemented trade-in, $p_t^{MP\ast }\ge p_t^{MB\ast }$ if $c\le c_1^I$, and $p_t^{MP\ast }<p_t^{MB\ast }$ otherwise;

(ii) under a platform-implemented trade-in, $p_t^{PP\ast }\ge p_t^{PB\ast }$ if $c\le c_1^T$, and $p_t^{PP\ast }<p_t^{PB\ast }$ otherwise.

(2) Under platform financing, $p_t^{MP\ast }<p_t^{PP\ast }$.

The threshold $c_1^T$ is given in Appendix B.

Proposition 3(1) fixes the trade-in implementer and compares the rebate under platform versus bank financing. The ranking is again cost-dependent and tracks the rate ordering of Proposition 1(1). The manufacturer sets the price and the rebate jointly: a higher financing rate raises the price it posts (Proposition 2(1)) and, to keep replacement demand intact, a matching rebate. So at low cost, where platform financing carries the higher rate, it also carries the larger rebate; at high cost the larger rebate shifts to bank financing, exactly as the price does.

Proposition 3(2) fixes platform financing and compares the rebate under a manufacturer- versus platform-implemented trade-in. The platform-implemented program pays the larger rebate. This is the deeper rebate already at work in Proposition 2(2): when the platform controls it, the commission $\varphi p_n$ makes the platform value the extra volume more than a manufacturer paying out of its own margin, so it is the more generous. The decentralization that raises the price also widens the rebate.

Comparing $p_t^{MB\ast }$ and $p_t^{PB\ast }$ analytically is again hard; Figure 3 plots their ordering at $\alpha =0.4$ and $\varphi =0.15$. The rebate reverses much as the price does. Where the trade-in is valuable, the manufacturer-implemented program is the more generous over most of the region; where it is not—a low residual value and a high production cost—the platform-implemented program regains the larger rebate, in almost the same corner where it sets the higher price. Price and rebate broadly move together: the implementer that sets the higher price tends to fund the deeper rebate as well.

5.2.3. Total Demand

Proposition 4.(1) Under a manufacturer-implemented trade-in, platform versus bank financing: $q_n^{MP\ast }<q_n^{MB\ast }$ if $c<c_1^D$, and $q_n^{MP\ast }\ge q_n^{MB\ast }$ otherwise.

(2) Under a fixed financing source, manufacturer versus platform trade-in:

(i) under platform financing, $q_n^{MP\ast }=q_n^{PP\ast }$;

(ii) under bank financing, $q_n^{MB\ast }\ge q_n^{PB\ast }$ if $c\le c_2^D$, and $q_n^{MB\ast }<q_n^{PB\ast }$ otherwise.

The thresholds $c_1^D$ and $c_2^D$ are given in Appendix B.

Proposition 4(1) fixes a manufacturer-implemented trade-in and compares total output under platform versus bank financing. The ranking is cost-dependent, and output moves inversely with the financing rate: a higher rate lifts the price and contracts output, so the channel with the higher rate produces the smaller output. When the cost is low, the platform’s rate exceeds the bank’s (Proposition 1(1)(i)) and platform financing yields the smaller output; when the cost is high, the platform’s rate is the lower of the two, and platform financing yields the larger output.

Proposition 4(2) fixes the financing source and compares the two implementers. Under platform financing, part (2)(i) delivers the notable result: total output is the same regardless of the implementer. The two programs are far from identical in their prices—a platform-implemented trade-in sets a higher price and pays a larger rebate (Propositions 2 and 3)—yet these differences cancel in the aggregate: the higher new-product price contracts primary demand $q_{nn}$, while the deeper rebate lowers the effective price $p_n-p_t$ and expands replacement demand $q_{nr}$ by exactly the same amount, leaving $q_n$ unchanged. When the platform both lends and earns the commission, the choice of implementer is a pure redistribution of who buys the new product, primary consumers versus replacement consumers, rather than of how many are sold. This cancellation is special to platform financing: the platform’s whole return, interest and commission alike, rises with total output. Output is then pinned down by the platform’s stake in it and is the same regardless of the implementer, the platform simply reaching that level through different levers (the rate under $MP$, the rate and rebate under $PP$). Under bank financing the interest accrues to the bank instead, so the supply chain is more decentralized and no single party’s stake pins output down: the platform loses the lending lever that absorbed the implementer’s impact, the gap between the two programs is no longer netted out but passes through to output, and part (2)(ii) turns cost-dependent.

Comparing $q_n^{PP\ast }$ and $q_n^{PB\ast }$ is again analytically intractable; Figure 4 plots their ordering at $\alpha =0.9$ and $\varphi =0.2$. Platform financing yields the larger output over almost the entire region, driven by the rebate rather than the rate. Under platform financing the platform sets a generous rebate (Proposition 3(1)(ii)), lowering the effective price and expanding replacement demand; this rebate channel, not the financing rate, keeps platform financing ahead, so output here does not follow the rate as it does in part (1). Only in a narrow band along the high-residual-value frontier, where the platform’s rebate advantage narrows, does bank financing yield the larger output.

5.3. Trade-In Preference

5.3.1. Preferences of the Trade-In Implementers

Proposition 5.

Under platform financing, for the manufacturer, ${\Pi }_m^{MP\ast }>{\Pi }_m^{PP\ast }$; for the platform, ${\Pi }_p^{PP\ast }>{\Pi }_p^{MP\ast }$.

Proposition 5 shows that, under platform financing, each member strictly prefers to implement the trade-in itself, unconditionally—independent of the commission rate $\varphi$—so the assignment is a persistent conflict between the two. It is financing that produces this conflict: without it, in the agency-selling benchmark of [5], neither member holds a margin on the product, so each one’s preferred format turns on the commission, and the two move in lockstep: a high commission has the platform implement the program and the manufacturer defer to it, a low commission reverses both—so the implementer shifts with the commission, yet the two never disagree. Platform financing removes that dependence for both. The interest the platform charges on the loan is a margin on output, a return earned on every unit sold like the retail margin a reseller keeps, so neither member’s preference now hinges on the commission; as under reselling, both always want to run the trade-in themselves. The driver is that the implementer internalizes one extra pricing decision—the rebate—and coordinates it with the lever already in hand: the manufacturer sets $p_n$ and $p_t$ jointly, the platform sets r and $p_t$ jointly. Each is better off as the implementer, so the program becomes a point of conflict rather than a task either side will delegate.

Once the bank, rather than the platform, earns the lending return, the platform loses its output margin and the preferences revert to the commission-driven pattern of agency selling; neither is unconditional any longer. Figure 5 maps them over the cost–commission $(c,\varphi )$ plane at $\alpha =0.4$. At a low residual value (panel (a)), all four configurations appear, set by two forces. The first is which implementer generates the larger output: the manufacturer at low cost and the platform at high cost (Proposition 4(2)(ii)). The second is who must fund the rebate, a burden that weighs more heavily the smaller the funding party’s own revenue share: the manufacturer’s margin $(1-\varphi )p_n$ when the commission is high, and the platform’s commission $\varphi p_n$ when it is low (as in [5]). At a low cost, the manufacturer-run program sells the most and both members favor it. Raising the commission turns this into mutual free-riding at a low cost, since neither side will fund a rebate that buys little extra output, and into both favoring the platform at an intermediate cost, where the platform by then produces more. Only at a high cost and a modest commission does each prefer to run the program itself, so the platform-financing conflict resurfaces in only one of the four regions. At a high residual value (panel (b)) the trade-in is costly to run and the feasible commissions shrink, collapsing the free-riding and both-favor-platform regions: only the cost-dependent split survives, with the manufacturer-run program preferred at low cost and conflict at high cost. The bank thus reinstates the commission logic of [5] in part. This occurs because the bank now captures the lending return that platform financing would keep inside the chain. With this profit transferred outside the manufacturer-platform dyad, the preference gaps narrow, and small movements in c and $\varphi$ suffice to reverse them, fragmenting the two members’ choices across the plane rather than aligning them on the commission alone.

5.3.2. The Bank’s Preference over the Trade-In Implementer

It is hard to rank the bank’s two profits in closed form, so we compare them numerically over the feasible region. Figure 6 reports the comparison in the $(c,\delta )$ plane at $\alpha =0.4$ and $\varphi =0.15$. Over the entire feasible region the bank strictly prefers the platform to implement the trade-in, ${\Pi }_b^{PB\ast }>{\Pi }_b^{MB\ast }$. This preference is unconditional, in sharp contrast to the two trade-in implementers in Section 5.3.1: the one party that does not implement the trade-in has an unambiguous preference over the implementer, while the two that do are divided.

The bank’s interest rises with both the rate it charges and the output it finances. The rate favors the platform unambiguously—a platform-implemented trade-in carries the higher rate, $r^{PB\ast }>r^{MB\ast }$ (Proposition 1(2)(ii))—whereas the output does not, since $q_n^{MB\ast }$ and $q_n^{PB\ast }$ cross at the cost threshold $c_2^D$ (Proposition 4(2)(ii); the red curve in Figure 6, magnified in the inset). The rate proves decisive: even below $c_2^D$, where the manufacturer-run program finances the larger output, the higher rate the bank earns under platform implementation more than offsets that small output advantage.

5.4. Manufacturer’s Financing Channel Choice

The manufacturer now chooses its financing channel—platform (P) or bank (B)—taking the trade-in implementer as given. It is hard to rank its profit across financing channels in closed form, so we proceed numerically over the feasible region. Figure 7 reports the two comparisons in the $(c,\delta )$ plane at $\alpha =0.9$ and $\varphi =0.2$ (blue: platform financing preferred; red: bank). Under both implementers, platform financing is preferred over most of the region, the manufacturer turning to the bank only at very low cost when it implements the trade-in itself (panel a) and along the high-residual-value frontier when the platform implements it (panel b). We find that the manufacturer’s financing-channel choice coincides with the total-output comparison of Section 5.2.3—panel a matching Proposition 4(1), panel b matching Figure 4. This indicates that the larger output drives the manufacturer’s choice; the forces behind the output comparison in Section 5.2.3 therefore carry over.

5.5. Consumers’ Preference

Following [3], we measure consumers’ preference by the consumer surplus accruing to buyers of the new product: a primary consumer who buys obtains $\theta -p_n$, and a replacement consumer who repurchases obtains $(1-\delta )\theta -(p_n-p_t)$. Consumer surplus is given by the following, evaluated at each scenario’s equilibrium:

$$C{S}^{i\ast }=(1-\alpha )\underset{\mathrm{primary}\mathrm{consumers}}{\underbrace{{\int }_{p_n^{i\ast }}^1\left(\theta -p_n^{i\ast }\right)d\theta }}+\alpha \underset{\mathrm{replacement}\mathrm{consumers}}{\underbrace{{\int }_{{\displaystyle \frac{p_n^{i\ast }-p_t^{i\ast }}{1-\delta }}}^1\left((1-\delta )\theta -p_n^{i\ast }+p_t^{i\ast }\right)d\theta }},i\in \{MP,MB,PP,PB\}.$$

(10)

We examine consumers’ preference along two dimensions—the trade-in implementer and the financing channel—holding one fixed and varying the other, and report the comparisons in the $(c,\varphi )$ plane at $\alpha =0.6$ and $\delta =0.4$.

Holding the implementer fixed, we first compare the two financing channels; in Figure 8, blue marks where consumers prefer platform financing and red where they prefer bank financing.

Figure 8 shows consumers preferring platform financing when the manufacturer implements the trade-in (panel a), and shifting their preference with the commission when the platform implements it (panel b). The driving factor in both is the new-product price: consumers favor the cheaper channel. When the manufacturer implements, the platform—earning a commission as well as interest—lends more cheaply here than a bank that maximizes interest alone, so platform financing carries the lower price. When the platform implements, the comparison turns on the lender’s response to the commission. The bank earns interest alone, so its rate is steadier than the platform’s and, at a low commission, lower; with little commission yet passing into the price, bank financing is then the cheaper channel and consumers are best off under it, $C{S}^{PB\ast }>C{S}^{PP\ast }$. As the commission rises this reverses: under bank financing the manufacturer, squeezed by the commission, lifts its price steeply, while under platform financing the platform cuts its rate sharply to protect the commission it now earns, holding its price down. At a high commission platform financing is therefore the cheaper channel and, reinforced by its deeper rebate, delivers the larger surplus, $C{S}^{PP\ast }>C{S}^{PB\ast }$.

Holding the financing channel fixed, we then compare the two implementers; in Figure 9, blue marks where consumers prefer the manufacturer-implemented scenario and red where they prefer the platform-implemented one.

Figure 9 shows consumers preferring the manufacturer-implemented trade-in under platform financing (panel a), and shifting their preference with the commission under bank financing (panel b). Again it is the new-product price that decides, here against the rebate. Under platform financing the platform earns on both the loan and the commission, so its return rises with sales and total output is the same regardless of the implementer (Proposition 4(2)(i)); a manufacturer- versus platform-implemented trade-in then only trades a lower price (Proposition 2(2)) against a deeper rebate, and since the price moves consumers more than the rebate, the manufacturer-implemented scenario is the one they favor. Under bank financing the cheaper scenario changes with the commission. A platform-implemented trade-in leaves the manufacturer setting only the price (the platform fixes the rebate, the bank the rate), so a rising commission passes straight through into a steeply higher price. A manufacturer that also sets the rebate holds two levers and keeps the chain more coordinated, so its price climbs far less. At a low commission the platform-implemented scenario is thus the cheaper and consumers prefer it, $C{S}^{PB\ast }>C{S}^{MB\ast }$; at a high commission its price overtakes the other and the ranking reverses, $C{S}^{MB\ast }>C{S}^{PB\ast }$.

6. Conclusions

This study examines the interplay of financing (by the platform or a bank) and trade-in implementation (by the manufacturer or the platform) in an agency supply chain with a capital-constrained manufacturer, and the interaction of the two dimensions yields four scenarios. Under these four scenarios, we develop a game-theoretic framework with replacement and primary consumers, in which the platform and/or the bank act as leaders and the manufacturer acts as the follower. We then derive the equilibrium interest rate and pricing decisions in each scenario, and combine analytical comparisons with numerical experiments to investigate how the two dimensions interact in shaping prices, demand, and the parties’ trade-in and financing preferences.

Our analysis yields several findings. First, the robustness of the equilibrium comparisons differs across the two dimensions: switching the financing channel generally reverses the ranking of the decisions as the production cost varies, whereas switching the trade-in implementer leaves several comparisons unchanged or pinned down by the equilibrium structure, particularly under platform financing. Second, under platform financing a platform-implemented program embeds a cross-subsidy: it raises the new-product price and enlarges the rebate; counterintuitively, the two effects offset, and total new-product demand is independent of the implementer; once a bank finances production, this neutrality disappears. Third, financing reshapes the contest over implementation. Under platform financing, both the manufacturer and the platform want to run the program themselves, a preference that does not hinge on the commission rate, so the trade-in becomes an object of contention rather than delegation; under bank financing, where the lending return accrues to an outside bank, this alignment dissolves and the willingness to run the program varies with the production cost and the residual value of used products. Finally, the remaining preferences follow identifiable levers. The manufacturer’s channel choice tracks total output over the feasible region, favoring platform financing except for products with a high residual value and a low production cost, and the bank prefers a platform-implemented program, which sustains the higher lending rate. Consumers’ preference is fixed in two of the four comparisons, namely platform financing when the manufacturer implements the trade-in and manufacturer implementation when the platform finances production; in the other two comparisons it shifts with the commission: when the platform implements, consumers prefer bank financing at a low commission and platform financing at a high one, and under bank financing they prefer platform implementation at a low commission and manufacturer implementation at a high one.

These results offer guidance for firms and policymakers. (1) A capital-constrained manufacturer should make its financing and trade-in decisions jointly: different trade-in implementers and different lenders lead it to different choices. (2) A platform that both lends and charges a commission should manage the interest rate, the commission, and, when it implements the program, the rebate as one system: optimizing one lever while ignoring the others can overturn the intended outcome. (3) For policymakers, trade-in promotion and financing support are complements: rebate-oriented subsidies work best when designed together with financing measures, in line with China’s 2026 policy package that pairs the two. (4) The financing channel itself deserves policy attention: the manufacturer gains from platform financing in most cases, and consumers fare better under it when the manufacturer implements the program, so financing-support measures should cover platform lending as well as bank credit.

This study can be extended in several directions. First, we assume deterministic demand; incorporating demand uncertainty would let the financing and trade-in decisions hedge against random replacement volumes and clarify how risk shifts the financing-channel and implementation choices. Second, we take the new product’s improvement as fixed; endogenizing the product-upgrade level would link the trade-in rebate to the manufacturer’s innovation decision and to consumers’ upgrade incentives. Third, given the prominence of trade-in subsidies in practice, a natural extension is to add a government interest subsidy on the production loan and to study how subsidizing the cost of capital, rather than the rebate, reshapes the equilibrium and the choice between platform and bank financing.