Manufacturer’s Incentive Strategies in a Dual-Channel Supply Chain with Moral Hazard: A Long-Term Perspective

Abstract

Moral hazard have a non-negligible impact on supply chain sustainability, especially from a long-term perspective. This influence is more complicated in a dual-channel supply chain with free riding. Therefore, it is necessary to explore how manufacturers design multi-period incentive strategies in a dual-channel supply chain to deal with moral hazard problems from retailers. In this study, we built a game theory model that contains a retailer (she) who is delegated by a manufacturer (he) to sell products in her offline and online channels and to provide experience services in a physical store. The retailer has the option of exerting effort when providing experience services to boost demand. We explored and compared the manufacturer’s strategies that cover a time horizon of multiple periods under two circumstances: full information and repeated moral hazard. The following conclusions were drawn from this study. In the repeated moral hazard game, the incentive constraints of the retailer are only related to her current and the next-period profits and independent from the profits in other periods. Moreover, the incentive strategies in each period are affected by the historical information in the previous period, while the strategies under information symmetry are not affected by history. Specially, the manufacturer can induce effort by charging an up-front payment from the retailer in the previous period and then returning a utility based on the achieved demand. Therefore, the manufacturer can postpone the payment of incentive costs and shift the risk to the next period. Furthermore, the manufacturer’s incentive strategies are also affected by the free-riding effect between channels. That is, compared with the low-state transfer payment, the high-state transfer payment was found to be more sensitive to free riding.

1. Introduction

Nowadays, dual-channel supply chains, which consist of both physical and online channels, are increasingly favored by manufacturers, retailers and consumers [1]. The structure of dual channels is better for the sustainable development of supply chains compared with single-channel supply chains. On the one hand, the advantages of online shopping have become more prominent due to the continuous development of information technology, e-commerce platforms, and mobile phones. Compared with physical channels, online channels have no spatial limitations in attracting consumers, and they hold the ability to quickly convey products and information to customers [2,3]. Simultaneously, sellers can conveniently collect rich first-hand sales data through online channels [4,5]. For example, Amazon’s Weblogs collect over 30 gigabytes of data every day, and the world’s largest commercial data warehouse at Walmart records more than 100 terabytes of data for 65-week historical transactions [6]. Therefore, more physical retailers and manufacturers, such as Walmart, Suning, Tesco, Metro, Sony, and IBM, are adopting dual channels by adding online stores to their traditional brick-and-mortar locations [7,8]. On the other hand, physical channels can offer both visual and tactile product experiences to consumers, which cannot be replaced by online channels. Furthermore, current consumers pay more attention to experience services during shopping, so some retailers who own online channels, such as JD, Warby Parker, Fab.com, and JD.com, have opened physical stores to cater to these consumers [8]. Therefore, dual-channel supply chains with both offline and online channels can better meet the requirements of the current market, in which the consumers have diverse purchasing preferences.

Moreover, manufacturers and retailers differ in their capability to promote products. Compared with retailers, manufacturers are far away from the terminal market in the supply chain, so it is more difficult for them to directly introduce or exhibit products to consumers, especially for the manufacturers who have no direct channels or want to enter a new market, such as oversea markets. In contrast, physical retailers can do a much better job of providing experience services to promote products [5,9,10]. In this situation, manufacturers prefer to cooperate with retailers and take advantage of their experience services to achieve products’ promotion and sales growth. Intuitively, these promotion effects are influenced by the effort that retailers exert when providing experience services [10,11,12]. For instance, it is more possible to achieve better promotion effects and higher demand if retailers introduce and more accurately explain products’ function, arrange enough booths for product display, or distribute enough samples to target customers. However, retailers need to pay higher costs to make efforts toward better experience services. In this situation, retailers may make no effort when providing services in order to save costs by reducing the numbers of samples or product booths. It is worth noting that in practice, information between manufacturers and retailers is always asymmetric [13,14,15]. Due to decentralized supply chain operations and the mature development of globalization, observing retailers’ actions in distant locations remains a significant challenge for many manufacturers [16]. Therefore, moral hazard occur when retailers exert no effort to save costs after signing contracts with manufacturers, which places manufacturers at a disadvantage [17,18].

Although some researchers have investigated the moral hazard problem in single-channel supply chains [16,19,20,21,22], little work has been conducted regarding multi-period strategies in the structure of dual channels. In practice, cooperation between manufacturers and retailers often occurs for more than one period. The existence of moral hazard may hurt the benefits of the players in supply chains, especially in a long-term operation. In long-term cooperation, manufacturers can update their beliefs about retailers’ “honesty” based on historical information and adjust their strategies in time to reduce the risk caused by asymmetric information. Furthermore, the interaction and competition between channels can also generate non-negligible effects on the strategies of both players and supply chain sustainability. Thus, it is necessary to investigate manufacturers’ multi-period incentive strategies in dual-channel supply chains with moral hazard.

Motivated by the popularity of dual-channel operations that can satisfy the requirements of the current market and the probable occurrence of moral hazard problems in long-term cooperation, we built a game theory model in this study and attempted to address the following research questions:

• How should manufacturers deal with moral hazard and design incentive mechanisms that are suitable for long-term cooperation to realize the sustainable development of the supply chain?
• In long-term cooperation, how does the retailers’ historical behavior influence the contracts provided by the manufacturers? Moreover, are the effects consistent in symmetric information and asymmetric information cases?
• How does free riding affect the incentive contracts and strategies of both manufacturers and retailers?

To answer these questions, we built a model of a dual-channel supply chain that consisted of an offline channel and an online channel. In the model, the online store could free ride the experience services provided by the conventional store. We started with a base model for a symmetric information case. Then, we investigated multi-period incentive strategies over a time horizon of finite length. We found that with the multi-period moral hazard problem, the manufacturer could induce effort by charging a “guarantee deposit”—which is an up-front payment—from the retailer and latterly refunding part of it according to the achieved demand, which was related to the retailer’s effort level. Moreover, the risk that the manufacturer bored in each period was deferred. Therefore, the main contribution of this paper is the model’s ability to derive multi-period contracts for manufacturers to overcome moral hazard in a dual-channel supply chain with a free-riding effect.

The rest of the paper is organized as follows. Section 1 provides a brief review. Section 2 outlines the model and assumptions. Section 3 considers a situation where the information between the manufacturer and retailer is symmetric. Section 4 discusses the manufacturer’s incentive strategies when he deals with repeated moral hazard. Section 5 concludes the study with some directions for further research.

2. Literature Review

There are two streams of research related to our paper. The first stream focuses on supply chain management in multi-period games. The second stream relates to contract design under moral hazard. In the following section, each stream is reviewed and related to our work.

2.1. Supply Chain Management in Multi-Period Games

There has been a substantial amount of studies on multi-period game supply chain strategies under symmetric information, such as pricing strategies, and inventory strategies, quality strategies. For example, Zhou, J. et al. [5] investigated the two-period pricing strategies of retailers and manufacturers in a dual-channel supply chain, considering the interaction of information disclosure and price discrimination. They found that manufacturers should encourage new purchases in online stores when exercising BPD (behavior-based price discrimination) if retailers can disclose information offline, especially offering experience services. In another paper, Li, Z. et al. [23] explored the role of coupons on pricing strategies in a dual-channel supply chain by building a two-period model that included three coupon-issuing patterns: manufacturer issuing, the retailer issuing, and co-issuing. Anand, K. et al. [24] studied the two-period inventory strategies of a single-channel supply chain. Karray, S. et al. [25] developed two two-stage game models to analyze the long-term effects of retailers’ promotions on manufacturers’ cooperative advertising strategies. Their research showed that in some conditions, cooperative advertising can benefit both manufacturers and retailers even when retailers’ promotions negatively affect future sales. Different from the studies mentioned above, which only involved two-period games, Nana, W. [12] explored the role of option contracts in a multi-period VMI supply chain. This study proved that a supplier’s service level in each period is always higher with optional contracts than without them. In contrast to these studies, there has been a small amount of literature on multi-period games discussing the incentive strategies of supply chains under asymmetric information. Mobini, Z. et al. [26] investigated a supplier’s screening strategies when their retailer possessed private information about customer demand and his cost parameters. In a related paper, Zhou, J. et al. [27] studied the double moral hazard problem in a single-channel supply chain over multiple periods. Their research showed that a supplier shares more revenue with a retailer after they cooperate for longer time horizons.

2.2. Moral Hazard in Supply Chains

This paper is also related to the literature on moral hazard in supply chains. Besides the research of [27] mentioned above, researchers have extensively examined the problem of single and double moral hazard in supply chains. Corbett, C.J. et al. [19] explained that single moral hazard arises when a decision-maker does not fully internalize the costs and benefits resulting from his decisions, and those decisions are unobservable or at least unverifiable, so they cannot be contracted. Double moral hazard occurs when the same applies to both parties in a transaction. In a pioneering study, Laffont, J.-J. and Martimort, D. [17] analyzed moral hazard in detail from the principal–agent view. The authors of [21,28,29,30] analyzed the design of contracts when single moral hazard existed in supply chains. Moreover, refs. [16,31] explored the incentive strategies when supply chain members simultaneously deal with single moral hazard and adverse selection. Nikoofal, M.E. and Gümüş, M. [16] studied the effectiveness of auditing a supplier’s hidden actions for a buyer when the supplier is privately informed about the extent of supply risk. Different from these studies, refs. [19,32,33] described situations when double moral hazard occurred in a single-channel supply chain. Plambeck, E.L. and Taylor, T.A. [20] developed an optimal relational contract that does not depend on historical information. Unlike in previous studies that analyzed the problem of moral hazard in the framework of a single channel, Liang, L. and Atkins, D. [34] built a model with two suppliers and then extended the model to multiple suppliers. They found that retainage is an effective incentive mechanism to mitigate seller-side moral hazard problems in certain conditions.

2.3. Research Gap and Contribution

In summary, to the best of our knowledge, a large body of existing literature on moral hazard in supply chains has focused on the design of incentive contracts in single-channel supply chains within a one-period time horizon [16,19,21,22,28]. However, in practice, with the fast development of e-commerce, supply chains with both online and offline channels are more common and popular in operations. The behavior and decisions of supply chain members is affected by the competition and interaction between channels (such as the free-riding effect). Furthermore, cooperation among supply chain members always lasts for multiple periods, and the strategies of each member should be accordingly adjusted, which is also important in the management of supply chain sustainability. Although multi-period games in supply chain management have received a lot of attention, most studies have been focused on strategies, such as pricing and inventory, under the condition of symmetric information [5,12,23,24,25]. Unfortunately, the information among supply chain members is always asymmetric and moral hazard are unavoidable [22], which may hurt the profits of both a whole supply chain and its members [18]. We are aware of little work on multi-period strategies when supply chain members deal with moral hazard, especially in dual-channel supply chains. Therefore, this paper aimed to fill the gap by providing a mathematical model that shows a manufacturer’s multi-period incentive strategies to overcome moral hazard in a dual-channel supply chain with free riding.

Table 1. Summary of the major literature review.

Articles	Channel Type	Period	Information Type (A/S) 1	Decisions
Zhou, Zhao et al. (2020) [5]	Dual	Two	S	Pricing
Li, Yang et al. (2020) [23]	Dual	Two	S	Pricing
Nana (2020) [12]	Single	Multiple	S	Production and ordering policies
Zhou, Zhao et al. (2012) [27]	Dual	Two	A	Double moral hazard
Laffont and Martimort (2002) [17]	—	Two	A	Single moral hazard
Nikoofal and Gümüş (2020) [16]	Single	One	A	Single moral hazard
Walker, M.J., et al. (2022) [21]	Single	One	A	Single moral hazard
Corbett, DeCroix et al. (2005) [19]	Single	One	A	Double moral hazard
Plambeck and Taylor (2006) [20]	Single	Multiple	A	Double moral hazard
Choi, T.-M., et al. (2022) [22]	Single	One	A	Single moral hazard
Takemoto, Y. and I. Arizono (2020) [28]	Single	One	A	Single moral hazard
Liang, L. and D. Atkins (2021) [34]	Multiple	One	A	Single moral hazard
This paper	Dual	Multiple	A	Single moral hazard

¹ A represents asymmetric information; S represents symmetric information.

shows the main differences between this study and the most related literature.

3. Model Description and Assumption

3.1. Problem Description and Model Setup

We considered a two-tier supply chain with a manufacturer (he) and a retailer (she), who cooperate in $n$ periods, $n=1,2,3\dots$. The manufacturer has a constant marginal production cost, which, for simplicity, we normalized to zero [35,36,37,38]. The retailer is authorized to distribute the manufacturer’s goods through her own offline and online channels. The manufacturer is risk-neutral and the retailer is risk-averse [29,39]. As mentioned above, an offline store has more advantages to disclose product information by offering experience services. For simplicity, we assumed that the retailer can only provide experience services in her conventional store while the online store can disclose information by free riding on the offline services [40]. In other words, customers can experience a product offline and then purchase it online. Experience services can boost offline demand, and an online store can also realize demand growth through free riding to some extent. We assumed that the experience services can only affect the current-period demand, and the demand of each period is independent [17]. We use $\lambda$ to denote the free-riding effectiveness, where $\lambda \in \left(0,1\right)$. The greater the value of $\lambda$, the stronger the free-riding effect. The demand of offline and online store in period $T$ ($1\le T\le n$) is given by $Q_{Tr}^S=\alpha -p_{Tr}^S+\beta p_{Te}^S+{\varphi }_T^S$ and $Q_{Te}^S=\alpha -p_{Te}^S+\beta p_{Tr}^S+\lambda {\varphi }_T^S$, respectively [10,41,42,43,44]. The subscripts $r$ and $e$ denote the offline and online store, respectively. The state of the increased demand ${\varphi }_T^S$ is affected by the effort ($E_T$) exerted by the retailer. The retailer may make a positive effort ($E_T=1$) or no effort ($E_T=0$) when providing experience services. She pays a transfer payment $t_T^S$ to the manufacturer in each period. The model is shown in Figure 1.

The retailer’s effort affects the state of the increased demand as follows: the probability that she makes a positive effort and realizes a high demand growth is ${\rho }_1$, i.e., $P\left({\varphi }_T^S={\varphi }_T^H|E_T=1\right)={\rho }_1$; the probability that she makes no effort and realizes a high demand growth is ${\rho }_0$, i.e., $P\left({\varphi }_T^S={\varphi }_T^H|E_T=0\right)={\rho }_0$, and ${\rho }_1>{\rho }_0$. Therefore, it is more possible to obtain a high demand growth if the retailer makes a positive effort, which costs $c$, to provide experience services. However, it is also possible that the retailer can realize a high demand growth without any effort and cost. In the face of information disadvantage, the retailer’s actions are not directly observable by the manufacturer. Therefore, the manufacturer cannot judge exactly whether the retailer exerts effort or not. Then, if moral hazard exists in the dual-channel supply chain, the manufacturer needs to design a menu of long-term incentive contracts $\left\{\left(t_1^H,t_1^L\right),\left(t_2^H,t_2^L\right),\cdot \cdot \cdot ,\left(t_n^H,t_n^L\right)\right\}$ with full commitment to encourage the retailer to make a positive effort when providing experience services in order to avoid the moral hazard.

3.2. Timing of the Game

According to our model setup, we considered the following n-period sequence of moves, as shown in Figure 2. At the beginning of the time horizon, the manufacturer offers a menu of long-term contracts $\left(t_T^H,t_T^L\right)$ for $n$ periods with full commitment, $T=1, 2, 3,\dots , n$. Then, the retailer decides whether to accept or refuse the contracts. If she accepts the contracts, the manufacturer and the retailer interact for multiple periods. At the beginning of period $T$, the retailer decides her effort level $E_T$, shown as stage 1 in Figure 2. At stage 2, the retailer decides the prices of both channels in period $T$, i.e., $p_{Te}^S$ and $p_{Tr}^S$. At stage 3, the output is realized and transfer payment $t_T^S$ is paid.

3.3. Notation and Assumptions

A summary of the model’s notation is shown in

Table 2. Model Notation.

Notation	Explanation
$t_T^S$	Transfer payment paid by retailer in period $T$, $1\le T\le n$
$\lambda$	Free-riding effectiveness
$p_{Tr}^S$ ($p_{Te}^S$)	Retail price for offline (online) store in period $T$, $1\le T\le n$
$S$	The state of valuation that customers realize after enjoying the experience services, $S\in \left\{H,L\right\}$
${\varphi }_T^S$	The demand increased by the experience services provided by the retailer in period $T$ when customer valuation is $S$, $S\in \left\{H,L\right\}$
$Q_{Tr}^S$ ($Q_{Te}^S$)	The demand of offline (online) store in period $T$
$\beta$	Substitution price elasticity between channels
$E_T$	The effort exerted by the retailer in period $T$, $E_T\in \left\{0,1\right\}$
$c$	The cost that the retailer needs to bear when she exerts effort
${\rho }_1$	Probability that a high demand growth is realized if the retailer makes a positive effort
${\rho }_0$	Probability that a high demand growth is realized if the retailer makes no effort
$O\in \left\{F, D\right\}$	Superscript for the case of “full information” (benchmark) and “repeated moral hazard”
${\pi }_{TM}^{SO}$ (${\pi }_{TR}^{SO}$)	The profit of the manufacturer (retailer) in period $T$ in case $O$
${\mathsf{\Pi }}_{TM}^{E,O}$ (${\mathsf{\Pi }}_{TR}^{E,O}$) 1	The expected profit of the manufacturer (retailer) in period $T$ in case $O$ when the retailer makes a positive effort ($E_T=1$) or no effort ($E_T=0$)
$U_{TR}\left({\varphi }_{T-1}^S\right)$	The expected utility that the manufacturer promises to give to the retailer in period $T$ $\left(T\ge 2\right)$ according to the increased demand realized in the previous period, i.e., ${\varphi }_{T-1}^S$ 2.

¹ The subscript “$T$ ” of $E_T$ in ${{{\displaystyle \prod }}^{ }}_{TM}^{E,O}$ (${{{\displaystyle \prod }}^{ }}_{TR}^{E,O}$) is omitted for simplicity. In the case of repeated moral hazard, the symbol ${{{\displaystyle \prod }}^{ }}_{TM}^{E,O}\left({\varphi }_{T-1}^S\right)$ is the same as ${{{\displaystyle \prod }}^{ }}_{TM}^{E,O}$. We use the symbol “ $\left({\varphi }_{T-1}^S\right)$ in ${{{\displaystyle \prod }}^{ }}_{TM}^{E,O}\left({\varphi }_{T-1}^S\right)$ to show the intertemporal relationship between the expected profit ${{{\displaystyle \prod }}^{ }}_{TM}^{E,O}$ in period $T$ and the increased demand ${\varphi }_{T-1}^S$ in period $T-1$; ² Since the value of $U_{TR}^{}\left({\varphi }_{T-1}^S\right)$ in period $T$ is related to the increased demand ${\varphi }_{T-1}^S$ in period $T-1$, we use the symbol “ $\left({\varphi }_{T-1}^S\right)$ in $U_{TR}^{}\left({\varphi }_{T-1}^S\right)$ to show the intertemporal relationship.

.

Furthermore, the authors of this paper proposed some assumptions in the model setup. For clarity, we summarize and list all the assumptions as follows:

• The manufacturer is risk-neutral and the retailer is risk-averse [29,39].
• Only the conventional store can provide experience services, and the online store can disclose information by free riding on the offline services [40].
• Experience services can only affect the current-period demand, and the demand of each period is independent [17].
• ${\varphi }_T^H>{\varphi }_T^L$, i.e., more demand can be increased if customers realize a high-state valuation than that when customers realize a low-state valuation.
• Moreover, we also assumed that the increased demand in each period is the same if the customers realize a high (low)-state valuation, i.e., ${\varphi }_T^H={\varphi }_1^H={\varphi }_2^H=\dots ={\varphi }_n^H\left({\varphi }_T^L={\varphi }_1^L={\varphi }_2^L=\dots ={\varphi }_n^L\right)$ (This assumption shows that the subscript “$T$” is meaningless in “${\varphi }_T^S$”. We keep the subscript because it will help us to analyze the strategies of both players in long-term cooperation).

4. Benchmark

Firstly, we analyzed a situation when the information between the manufacturer and the retailer is symmetric and used it as a benchmark case. In this situation, the manufacturer offers a menu of contracts $\left(t_T^{HF\ast },t_T^{LF\ast }\right)$ to the retailer. The superscript “$F$” denotes the case of “full information”.

According to the model we designed above, it is easy to obtain the manufacturer’s profit and retailer’s profit in period $T$, which is given by ${\pi }_{TM}^{SF}=t_T^{SF}$ and ${\pi }_{TR}^{SF}=p_{Tr}^{SF}{Q}_{Tr}^{SF}+p_{Te}^{SF}{Q}_{Te}^{SF}-t_T^{SF}$, respectively. The subscripts “$M$” and “$R$” denote the manufacturer and the retailer, respectively. Then, the expected profits of the manufacturer and the retailer are now, respectively, written as

$${\mathsf{\Pi }}_{TM}^{E=1,F}={\rho }_1{t}_T^{HF}+\left(1-{\rho }_1\right)t_T^{LF}$$

(1)

and

$${\mathsf{\Pi }}_{TR}^{E=1,F}={\rho }_1{\pi }_{TR}^{HF}+\left(1-{\rho }_1\right){\pi }_{TR}^{LF}-c$$

(2)

if the retailer makes a positive effort ($E_T=1$) with extra cost $c$ when providing experience services in period $T$. By the same token, if the retailer makes no effort ($E_T=0$) in period $T$, the expected profits of the both parties are given by:

$${\mathsf{\Pi }}_{TM}^{E=0,F}={\rho }_0{t}_T^{HF}+\left(1-{\rho }_0\right)t_T^{LF}$$

(3)

$${\mathsf{\Pi }}_{TR}^{E=0,F}={\rho }_0{\pi }_{TR}^{HF}+\left(1-{\rho }_0\right){\pi }_{TR}^{LF}$$

(4)

The retailer decides the offline and online sale prices in period $T$ to maximize her expected profits under two possible levels of effort. Then, we can derive the optimal offline and online prices, which are given by:

$$p_{Tr}^{SF\ast }=\frac{\alpha \left(1+\beta \right)+\left(1+\beta \lambda \right){\varphi }_T^S}{2\left(1-{\beta }^2\right)}$$

(5)

$$p_{Te}^{SF\ast }=\frac{\alpha \left(1+\beta \right)+\left(\beta +\lambda \right){\varphi }_T^S}{2\left(1-{\beta }^2\right)}$$

(6)

where the superscript “*” represents the equilibrium outcome in the rest of this paper. It is easy to prove $p_{Tr}^{SF\ast }>p_{Te}^{SF\ast }$, which is consistent with reality. In practice, offline stores need to bear more costs for operations and providing experience services, which leads to higher retail prices compared with online stores. Subsequently, we can obtain the optimal demands of both channels by:

$$Q_{Tr}^{SF\ast }=\frac{\alpha +{\varphi }_T^S}{2}$$

(7)

$$Q_{Te}^{SF\ast }=\frac{\alpha +\lambda {\varphi }_T^S}{2}$$

(8)

Obviously, the offline and online sale price $p_{Tr}^{SF\ast }$ and $p_{Te}^{SF\ast }$, respectively, are related to the state of the increased demand ${\varphi }_T^S$. Customers are willing to pay a higher price if they realize a high-state valuation when enjoying the experience services. In this circumstance, the retailer can set a higher sale price, i.e., $p_{Tj}^{HF\ast }>p_{Tj}^{LF\ast }$ ($j\in \left\{r,e\right\}$), and the offline and online channel can receive a higher demand, i.e., $Q_{Tj}^{HF\ast }>Q_{Tj}^{LF\ast }$. In this respect, the retailer has more bargaining power. Furthermore, it is easy to find that the pricing strategies are the same no matter whether or not the retailer exerts effort.

In the case of full information, the retailer’s action is observable. We assumed that $c<\widehat{c}$, which ensures that the problem of inducing the retailer’s effort is nontrivial. $\widehat{c}$ is given by:

$$\widehat{c}=\frac{\left({\rho }_1-{\rho }_0\right)\left({\varphi }^H-{\varphi }^L\right)\left(2\alpha \left(1+\beta \right)\left(1+\lambda \right)+\eta \left({\varphi }^H+{\varphi }^L\right)\right)}{4\left(1-{\beta }^2\right)}$$

(9)

where $\eta =1+2\beta \lambda +{\lambda }^2$. Proof is presented in Appendix A.

Therefore, both players in the supply chain make their decisions in the presence of $E_T=1$. Based on the direct revelation mechanism [17,45], under information symmetry, the optimal multi-period contract is the repetition of the optimal static contract. Therefore, in this section, we only analyze the manufacturer’s incentive strategies in one period. The manufacturer needs to solve the problem $\left(P^F\right)$ to induce effort:

$$\begin{array}{c}\left(P^F\right) \underset{\left\{t_T^{HF},t_T^{LF}\right\}}{\max } {\mathsf{\Pi }}_{TM}^{E=1,F}={\rho }_1{t}_T^{HF}+\left(1-{\rho }_1\right)t_T^{LF},\\ s.t. { \mathsf{\Pi }}_{TR}^{E=1,F}\ge 0 \left(I{R}_T\right)\end{array}$$

where $\left(I{R}_T\right)$ is the retailer’s participation constraint in period $T$. In the case of information symmetry, the retailer receives exactly her reservation utility, which we assumed to be zero. Thus, the retailer’s participation constraint is binding, i.e., ${\mathsf{\Pi }}_{TR}^{E=1,F}=0$. Then, we can derive the multi-period incentive contracts $\left(t_T^{HF\ast },t_T^{LF\ast }\right)$ offered by the manufacturer, as shown in Proposition 1. For notational simplicity, we assumed $f\left(x,y\right)$ is a function of $x$ and $y$, which can be expressed as:

$$f\left(x,y\right)=\frac{2\alpha \left(1+\beta \right)\left(\left(1+\lambda \right)x+\alpha \right)+\eta y}{4\left(1-{\beta }^2\right)}$$

(10)

Proposition 1.

When information is symmetric, the optimal long-term contract for n periods with full commitment is$\left(t_T^{HF\ast },t_T^{LF\ast }\right)$, where

$$t_T^{SF\ast }=f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c S\in \left\{H,L\right\}$$

(11)

$${\overline{\varphi }}_1={\varphi }^H{\rho }_1+{\varphi }^L\left(1-{\rho }_1\right)$$

(12)

$${\overline{\varphi }}_1^{\prime }={\left({\varphi }^H\right)}^2{\rho }_1+\left(1-{\rho }_1\right){\left({\varphi }^L\right)}^2$$

(13)

$$T=1,2,\dots ,n$$

Recall the assumption in Section 2. The increased demand in each period is the same if the customers realize a high (low)-state valuation, i.e., ${\varphi }_T^H={\varphi }_1^H={\varphi }_2^H=\dots ={\varphi }_n^H\left({\varphi }_T^L={\varphi }_1^L={\varphi }_2^L=\dots ={\varphi }_n^L\right)$, which indicates that the subscript “$T$” is meaningless in “${\varphi }_T^S$”. For ease of exposition, we drop the subscript “$T$” in “${\varphi }_T^S$” here. However, in the case of repeated moral hazard, we still keep the subscript “$T$” in “${\varphi }_T^S$” to show the intertemporal effect.

In the benchmark case, if the manufacturer decides to induce effort, he can extract the profit of the whole supply chain, i.e., ${\mathsf{\Pi }}_{TM}^{E=1,F\ast }=f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c$. Then, it is easy to derive that $f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)$ is the revenue of the whole supply chain, and the total cost of the supply chain is the cost $c$ which the retailer pays for making effort. Moreover, the profit of the manufacturer or the supply chain is the same in each period when information is symmetric. Hence, the manufacturer charges the same transfer payment from the retailer regardless of the realization of output. The parameter $\delta$ discounts the manufacturer’s profits obtained in $n$ periods into a present value in the first period, which is given by:

$${\Omega }_{1M}^{E=1,F\ast }=\left[f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c\right]{{\displaystyle \sum }}_{i=1}^n{\delta }^{i-1}$$

(14)

5. Repeated Moral Hazard

In the benchmark case, we analyzed the manufacturer’s incentive strategies when information is symmetric. However, the situation is different when information is asymmetric. In this circumstance, the manufacturer can only observe the demand growth brought by the retailer’s experience service, i.e., ${\varphi }_T^S$, instead of the retailer’s effort level. Therefore, a moral hazard may exist in the supply chain. The manufacturer needs to design a menu of contracts $\left(t_T^{HD\ast },t_T^{LD\ast }\right)$ to encourage the retailer to make effort. The superscript “$D$” denotes the moral hazard case. By following the same track in the benchmark, we can derive the online and offline pricing strategies in this case, i.e., $p_{Tr}^{SD\ast }=p_{Tr}^{SF\ast }$, $p_{Te}^{SD\ast }=p_{Te}^{SF\ast }$. For simplicity, we omit the analysis here. Under the condition of asymmetric information, the manufacturer’s multi-period information incentive strategies are different. Compared with the benchmark case, the manufacturer now needs to consider the incentive constraints of the retailer. By analyzing the pattern of the manufacturer’s profit maximization problem in a finite period of time horizon, i.e., $\left(P_{n=1}^D\right)$, $\left(P_{n=2}^D\right)$ and $\left(P_{n=3}^D\right)$, which is shown in the Appendix, we can obtain the optimization problem that the manufacturer must solve to induce effort in $n$ periods:

$$\begin{array}{c}\left(P_n^D\right) \underset{\left\{\left(t_1^H,t_1^L\right),\left(t_2^H,t_2^L\right),\cdot \cdot \cdot ,\left(t_n^H,t_n^L\right)\right\}}{max } {\rho }_1{t}_1^H+\left(1-{\rho }_1\right)t_1^L+{\displaystyle \sum }_{i=2}^n{\delta }^{i-1}{K}_{iM}^{E=1}\\ s.t. {\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^S\right)+\theta {\displaystyle {\displaystyle \sum }_{i=T+1}^n}{\delta }^{i-1}{K}_{iR}^{E=1,{\rho }_1}\\ \ge {\mathsf{\Pi }}_{TR}^{E=0}\left({\varphi }_{T-1}^S\right)\hfill \\ +\theta \left({\delta }^T{K}_{\left(T+1\right)R}^{E=1,{\rho }_0}+\chi {\displaystyle {\displaystyle \sum }_{i=T+2}^n}{\delta }^{i-1}{K}_{iR}^{E=1,{\rho }_1}\right) \left(I{C}_T\right)\\ {\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^S\right)+\theta {\displaystyle {\displaystyle \sum }_{i=T+1}^n}{\delta }^{i-1}{K}_{iR}^{E=1,{\rho }_1}\ge \mu U_{TR}\left({\varphi }_{T-1}^S\right) \left(I{R}_T\right)\end{array}$$

where

$$\begin{array}{c}\theta =\{\begin{array}{c}0 T=n\\ 1 T<n\end{array}\\ \chi =\{\begin{array}{c}0 T=n-1\\ 1 T<n-1\end{array}\\ \mu =\{\begin{array}{c}0 T=1\\ 1 T\ge 2\end{array}\end{array}$$

$$K_{TM}^{E=1}={\rho }_1{\mathsf{\Pi }}_{TM}^{E=1}\left({\varphi }_{T-1}^H\right)+\left(1-{\rho }_1\right){\mathsf{\Pi }}_{TM}^{E=1}\left({\varphi }_{T-1}^L\right)$$

(15)

$$K_{TR}^{E=1,{\rho }_1}={\rho }_1{\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^H\right)+\left(1-{\rho }_1\right){\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^L\right)$$

(16)

$$K_{TR}^{E=1,{\rho }_0}={\rho }_0{\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^H\right)+\left(1-{\rho }_0\right){\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^L\right)$$

(17)

$$T=1,2,\dots ,n, n\ge 2$$

where $\left(I{R}_T\right)$ and $\left(I{C}_T\right)$ denote the participation and incentive constraints of the retailer in period $T$, respectively. As noted earlier, the manufacturer always wants to implement a high level of effort in each period. Hence, there are $n$ incentive constraints of the retailer. By the same token, the amount of the participation constraints is $n$, too. For analysis, we can rewrite $\left(I{C}_T\right)$ as:

$${\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^S\right)+\theta \left({\delta }^T{K}_{\left(T+1\right)R}^{E=1,{\rho }_1}+{{\displaystyle \sum }}_{i=T+2}^n{\delta }^{i-1}{K}_{iR}^{E=1,{\rho }_1}\right)\ge {\Pi }_{TR}^{E=0}\left({\varphi }_{T-1}^S\right)+\theta \left({\delta }^T{K}_{\left(T+1\right)R}^{E=1,{\rho }_0}+\chi {{\displaystyle \sum }}_{i=T+2}^n{\delta }^{i-1}{K}_{iR}^{E=1,{\rho }_1}\right)$$

(18)

When $T<n-1$, $\chi =1$. By substituting $\chi =1$ in the inequality above, (17) is simplified as follows:

$${\mathsf{\Pi }}_{TR}^{E=1}\left({\varphi }_{T-1}^S\right)+\theta {\delta }^T{K}_{\left(T+1\right)R}^{E=1,{\rho }_1}\ge {\mathsf{\Pi }}_{TR}^{E=0}\left({\varphi }_{T-1}^S\right)+\theta {\delta }^T{K}_{\left(T+1\right)R}^{E=1,{\rho }_0}$$

(19)

Corollary 1.

When$T<n-1$, the incentive constraint$\left(I{C}_T\right)$in period$T$is only affected by the current and the next-period expected profits of the retailer (i.e., the expected profits in period$T$and$T+1$) but is irrelevant to the expected profits in the following periods (from period$T+2$to the end).

In long-term cooperation, the manufacturer offers incentive contracts at the beginning of the game. Thereby, both the manufacturer and the retailer need to consider intertemporal effects when making decisions. Intuitively, the strategies of the manufacturer and retailer in period $T$ are affected by their decisions and profits of each period in the future. However, when $T<n-1$, the incentive constraint of the retailer in period $T$ is only related to her expected profits in period $T$ and period $T+1$. The transfer payment that the retailer needs to pay in each period is relative to the increased demand realized in the previous period, i.e., ${\varphi }_{T-1}^S$, in other words, related to the retailer’s previous-period effort level. $\left(I{C}_T\right)$ affects the retailer’s decision of effort level in period $T$, which has an impact on ${\varphi }_T^S$, and then ${\varphi }_T^S$ makes a further impact on the expected profits of the retailer in period$T+1$. However, from period $T+2$, the transfer payments paid by the retailer are irrelevant to ${\varphi }_T^S$. Therefore, the retailer’s expected profits in the following periods (from period $T+2$) have no impact on $\left(I{C}_T\right)$.

Proposition 2 shows the manufacturer’s $n$-period incentive strategies when he deals with repeated moral hazard. For notational simplicity, we rewrite the function $f\left(x,y\right)$ as $g\left(x\right)$ when$y=x^2$, i.e.,

$$g\left(x\right)=f\left(x,x^2\right)$$

(20)

Proposition 2.

With a repeated moral hazard problem, the optimal long-term contract for n periods with full commitment is$\left(t_T^{HD\ast },t_T^{LD\ast }\right)$, where:

$$t_T^{\mathrm{HD}\ast }\left({\varphi }_{T-1}^S\right)=g\left({\varphi }^H\right)-\frac{\left(1-{\rho }_0\right)c}{{\rho }_1-{\rho }_0}-\mu U_{TR}\left({\varphi }_{T-1}^S\right)+\theta \delta U_{\left(T+1\right)R}\left({\varphi }_T^H\right)$$

(21)

$$\begin{array}{c}{t}_T^{\mathrm{LD}\ast }\left({\varphi }_{T-1}^S\right)=g\left({\varphi }^L\right)+\frac{{\rho }_{0}c}{\left({\rho }_1-{\rho }_0\right)}-\mu U_{TR}\left({\varphi }_{T-1}^S\right)+\theta \delta U_{\left(T+1\right)R}\left({\varphi }_T^L\right)\\ T=1,2,\dots ,n\end{array}$$

(22)

Specifically, when $T=1$, $t_T^{SD\ast }\left({\varphi }_{T-1}^S\right)=t_1^{SD\ast }\left({\varphi }_0^S\right)$. The symbol ${\varphi }_0^S$ is meaningless, i.e., $t_1^{SD\ast }\left({\varphi }_0^S\right)=t_1^{SD\ast }$. However, we keep the symbol so that we can easily observe and summarize the law of multi-period strategies.

Compared with the incentive contract $\left(t_T^{HF\ast },t_T^{LF\ast }\right)$ in the benchmark case, when moral hazard exists in a dual-channel supply chain, the transfer payment that the retailer pays to the manufacturer differs in terms of the state of demand growth achieved by the experience service. By comparing Proposition 1 and Proposition 2, we can derive Conclusion 1:

Conclusion  1.

In the game of repeated moral hazard, the incentive contract$\left(t_T^{HD\ast },t_T^{LD\ast }\right)$in period$T$is influenced by the historical information${\varphi }_{T-1}^S$, while the incentive contract$\left(t_T^{HF\ast },t_T^{LF\ast }\right)$in the information-symmetry case is just a repetition of the optimal static contract, which is unaffected by history.

When the information between the manufacturer and the retailer is symmetric, the retailer’s behavior is observable. During long-term cooperation, once the retailer does not exert effort, her behavior is discovered by the manufacturer. Therefore, the retailer has to make effort during the entire cooperation. Additionally, as time goes by, the information structure between the manufacturer and the retailer remains the same. Hence, the multi-period strategies under information symmetry are only the repetition of the optimal static strategies. When the information is asymmetric, although the manufacturer cannot know whether the retailer exerts effort or not when providing experience services, he can ask for the transfer payment $t_T^{SD}$ based on historical information ${\varphi }_{T-1}^S$. Both players’ expected profits in period $T$ are affected by the increased demand ${\varphi }_{T-1}^S$, brought by the experience services in the previous period. In other words, the effort level that the retailer exerts in each period has an impact on the next-period expected profits of both the manufacturer and the retailer.

Moreover, Proposition 1 and Proposition 2 indicate that both the incentive strategies in the benchmark case $\left(t_T^{HF\ast },t_T^{LF\ast }\right)$ and those in the repeated moral hazard case $\left(t_T^{HD\ast },t_T^{LD\ast }\right)$ are affected by the free-riding coefficient $\lambda$. It is easy to obtain $\partial t_T^{SF\ast }/\partial \lambda =\partial f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)/\partial \lambda$, $\partial t_T^{HD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda =\partial g\left({\varphi }^H\right)/\partial \lambda$, $\partial t_T^{LD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda =\partial g\left({\varphi }^L\right)/\partial \lambda$. Thereby, the free-riding coefficient $\lambda$ affects the transfer payments by influencing the function $f\left(x,y\right)$ and$g\left(x\right)$, as does the coefficient of competition intensity $\beta$.

To simplify the analysis, we can explore the impact of the free-riding coefficient $\lambda$ on the function$f\left(x,y\right)$ and $g\left(x\right)$ to figure out how $\lambda$ affects the transfer payments and the manufacturer’s expected profits. It is easy to obtain:

$$\frac{\partial t_T^{SF\ast }}{\partial \lambda }=\frac{\partial f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)}{\partial \lambda }=\frac{{\overline{\varphi }}_1\alpha \left(1+\beta \right)+{\overline{\varphi }}^{\prime }\left(\beta +\lambda \right)}{2\left(1-{\beta }^2\right)}$$

(23)

$$\frac{\partial t_T^{HD\ast }\left({\varphi }_{T-1}^S\right)}{\partial \lambda }=\frac{\partial g\left({\varphi }^H\right)}{\partial \lambda }=\frac{{\varphi }^H\left(\alpha \left(1+\beta \right)+{\varphi }^H\left(\beta +\lambda \right)\right)}{2\left(1-{\beta }^2\right)}$$

(24)

$$\frac{\partial t_T^{LD\ast }\left({\varphi }_{T-1}^S\right)}{\partial \lambda }=\frac{\partial g\left({\varphi }^L\right)}{\partial \lambda }=\frac{{\varphi }^L\left(\alpha \left(1+\beta \right)+{\varphi }^L\left(\beta +\lambda \right)\right)}{2\left(1-{\beta }^2\right)}$$

(25)

Formulas (23)–(25) are greater than 0. Therefore, free riding exerts a positive effect on the transfer payments under symmetric and asymmetric information. In other words, the larger $\lambda$ is, the higher the transfer payments that the manufacturer can receive. An online store can obtain more demand growth due to a better free-riding effect, and the supply chain can also obtain a higher revenue. Hence, the manufacturer has an incentive to charge higher transfer payments. To some extent, this can also explain that why the “experience in store, buy online” model is becoming more and more popular. Although experience services, such as presentation, offering samples, introduction, and product trial, may incur costs, they can also drive the demand for both offline and online channels, which is beneficial to both manufacturers and retailers. Therefore, more and more manufacturers and retailers are willing to adopt both offline and online sales channels. For example, JD has added physical stores to his online channels and Suning has launched online channels in addition to his traditional brick-and-mortar locations. Furthermore, by comparing Formulas (23)–(25), we can derive Corollary 2:

Corollary  2.

Compared with the benchmark case, in the repeated moral hazard case, the high-state transfer payment$t_T^{HD\ast }\left({\varphi }_{T-1}^S\right)$is more sensitive to free riding, while the low-state transfer payment$t_T^{LD\ast }\left({\varphi }_{T-1}^S\right)$is less sensitive to free riding, i.e.,$\partial t_T^{HD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda >\partial t_T^{SF\ast }/\partial \lambda >\partial t_T^{LD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda$.

When information is symmetric, the high-state and low-state transfer payments are the same, so free riding exerts the same effect on $t_T^{HF\ast }$ and $t_T^{LF\ast }$. However, free riding was found to have different effects on the high-state and low-state transfer payments in the repeated moral hazard case. If free-riding effect grows stronger, i.e., the value of $\lambda$ becomes greater, the online store can receive more demand growth when customers realize high valuations than that when customers realize low valuation, i.e., $\lambda {\varphi }^H>\lambda {\varphi }^L$. Accordingly, the manufacturer charges higher transfer payments from the retailer. We use $\mathrm{\Delta }t$ to denote the increase in the transfer payments brought by every unit increase in the free-riding coefficient, and we have $\mathrm{\Delta }{t}_T^{HD\ast }\left({\varphi }_{T-1}^S\right)>\mathrm{\Delta }{t}_T^{SF\ast }>\mathrm{\Delta }{t}_T^{LD\ast }\left({\varphi }_{T-1}^S\right)$, which can be simplified to $\mathrm{\Delta }g\left({\varphi }^H\right)>\mathrm{\Delta }f\left(\overline{\varphi },{\overline{\varphi }}^{\prime }\right)>\mathrm{\Delta }g\left({\varphi }^L\right)$ (see Figure 3). Therefore, in the repeated moral hazard case, the high-state transfer payments are more sensitive to the free-riding coefficient. Although the incentive strategies of the manufacturer under information symmetry and asymmetry situations have different sensitivities to free riding, the expected profits of the manufacturer in period $T$ have the same sensitivity to the free-riding coefficient in both cases, i.e., $\partial {\mathsf{\Pi }}_{TM}^{\mathrm{E}=1,F\ast }/\partial \lambda =\partial {\mathsf{\Pi }}_{TM}^{\mathrm{E}=1,D\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda =\partial f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)/\partial \lambda$.

As mentioned before, we found that $\partial t_T^{SF\ast }/\partial \lambda =\partial f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)/\partial \lambda$, $\partial t_T^{HD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda =\partial g\left({\varphi }^H\right)/\partial \lambda$, $\partial t_T^{LD\ast }\left({\varphi }_{T-1}^S\right)/\partial \lambda =\partial g\left({\varphi }^L\right)/\partial \lambda$ according to Formulas (23)–(25). To simplify the analysis, we explore the impact of the free-riding coefficient $\lambda$ on the function$f\left(x,y\right)$ and $g\left(x\right)$ to figure out how $\lambda$ affects the transfer payments. Therefore, the values on the vertical axis are the values of $f\left(x,y\right)$ and $g\left(x\right)$, which can represent transfer payments.

In the benchmark case, the expected profit of the manufacturer in each period is ${\mathsf{\Pi }}_{TM}^{E=1,F\ast }\left({\varphi }_{T-1}^S\right)=f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c$. When moral hazard exists in the supply chain, the present value of the manufacturer’s expected profit in period $T$ is given by:

$${\Omega }_{TM}^{\mathrm{E}=1,D\ast }\left({\varphi }_{T-1}^S\right)=\left[f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c\right]{{\displaystyle \sum }}_{i=0}^{n-T}{\delta }^i-\mu U_{TR}\left({\varphi }_{T-1}^S\right)$$

(26)

The expected profit of the manufacturer in period $T$ is:

$$\begin{array}{c}{\mathsf{\Pi }}_{TM}^{E=1,D\ast }\left({\varphi }_{T-1}^S\right)=f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c-\mu U_{TR}\left({\varphi }_{T-1}^S\right)\\ +\theta \delta \left[{\rho }_1{U}_{\left(T+1\right)R}\left({\varphi }_T^H\right)+\left(1-{\rho }_1\right)U_{\left(T+1\right)R}\left({\varphi }_T^L\right)\right]\end{array}$$

(27)

It is easy to prove $f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)=\left(1-{\rho }_1\right)g\left({\varphi }^L\right)+{\rho }_{1}g\left({\varphi }^H\right)$.

Conclusion 2 can be drawn by analyzing the expected profit of the manufacturer in period $T$.

Conclusion  2.

In the repeated moral hazard case, the manufacturer can induce effort by charging the present value of the retailer’s$\left(T+1\right)$-period expected utility in period$T \left(T<n\right)$and then returning part of it to the retailer in period$T+1$according to the increased demand achieved in period$T$.

From (27) we can find that in the repeated moral hazard case, the manufacturer’s expected profit in period $T$, ${\mathsf{\Pi }}_{TM}^{E=1,D\ast }\left({\varphi }_{T-1}^S\right)$, consists of three parts. The first part is $f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c$, which is identical to the manufacturer’s excepted profit in the benchmark case, i.e., ${\mathsf{\Pi }}_{TM}^{E=1,F\ast }\left({\varphi }_{T-1}^S\right)$. The second part is $\mu U_{TR}\left({\varphi }_{T-1}^S\right)$, which is the utility that the manufacturer promises to pay back to the retailer according to the demand growth realized in the previous period, i.e., ${\varphi }_{T-1}^S$. The third part is $\delta \left[{\rho }_1{U}_{\left(T+1\right)R}\left({\varphi }_T^H\right)+\left(1-{\rho }_1\right)U_{\left(T+1\right)R}\left({\varphi }_T^L\right)\right]$, which is the present value of the expected utility that the retailer may obtain in the next period (period $T+1$). The manufacturer charges this from the retailer in period $T$. Then, similar to the above analyses, in period $T+1$, the manufacturer returns the utility $U_{\left(T+1\right)R}\left({\varphi }_T^S\right)$ to the retailer according to the demand growth achieved in period $T$, i.e., ${\varphi }_T^S$. In this respect, we can regard the third part as a “guarantee deposit”. To make the retailer exert effort in the next period, the manufacturer asks the retailer to pay a “guarantee deposit” in period $T$, which is an ex ante payment. Then, in period $T+1$, the manufacturer refunds part of the deposit to the retailer according to ${\varphi }_T^S$. Figure 4 depicts the manufacturer’s incentive strategies.

Since $U_{\left(T+1\right)R}\left({\varphi }_T^H\right)>U_{\left(T+1\right)R}\left({\varphi }_T^L\right)$, it is easy to derive:

$$U_{\left(T+1\right)R}\left({\varphi }_T^H\right)>{\rho }_1{U}_{\left(T+1\right)R}\left({\varphi }_T^H\right)+\left(1-{\rho }_1\right)U_{\left(T+1\right)R}\left({\varphi }_T^L\right)>U_{\left(T+1\right)R}\left({\varphi }_T^L\right)$$

(28)

If the achieved demand growth in period $T$ is at a high state, the retailer can obtain the utility $U_{\left(T+1\right)R}\left({\varphi }_T^H\right)$ in period $T+1$, which is higher than the “guarantee deposit” that she previously paid, i.e.,$U_{\left(T+1\right)R}\left({\varphi }_T^H\right)>{\rho }_1{U}_{\left(T+1\right)R}\left({\varphi }_T^H\right)+\left(1-{\rho }_1\right)U_{\left(T+1\right)R}\left({\varphi }_T^L\right)$. If the retailer exerts effort, she can achieve high-state demand growth ${\varphi }_T^H$ with the possibility ${\rho }_1$. Although there is also a possibility of ${\rho }_0$ to realize ${\varphi }_T^H$ if the retailer makes no effort, she prefers to exert effort due to ${\rho }_1>{\rho }_0$. In other words, it is more possible to achieve high-state demand growth and obtain a higher refund if the retailer makes effort. In contrast, if the retailer makes no effort, she probably obtains a refund $U_{\left(T+1\right)R}\left({\varphi }_T^L\right)$ that is lower than the “guarantee deposit”, i.e., ${\rho }_1{U}_{\left(T+1\right)R}\left({\varphi }_T^H\right)+\left(1-{\rho }_1\right)U_{\left(T+1\right)R}\left({\varphi }_T^L\right)>U_{\left(T+1\right)R}\left({\varphi }_T^L\right)$. Therefore, the manufacturer can encourage the retailer to exert effort by offering a refund that is higher than the “guarantee deposit” she paid previously if high-state demand growth is achieved and can punish the retailer by offering a lower refund if low-state demand growth is achieved.

Conclusion  3.

In the repeated moral hazard case, in period$T$ ($T\ge 2$), the manufacturer needs to pay the information incentive cost $C_T^{D\ast }$ for the previous period, i.e., period $T-1$, where:

$$C_T^{D\ast }\left({\varphi }_{T-1}^S\right)={\rho }_1{U}_{TR}\left({\varphi }_{T-1}^H\right)+\left(1-{\rho }_1\right)U_{TR}\left({\varphi }_{T-1}^L\right)-U_{TR}\left({\varphi }_{T-1}^S\right)$$

(29)

According to Conclusion 2 and Figure 4, we know that the utility the manufacturer pays to the retailer in period $T$ is based on the achieved demand in period $T-1$, so the incentive cost of period $T-1$ is paid in period $T$. When the state of the demand growth in period $T-1$ is high, i.e., ${\varphi }_{T-1}^S={\varphi }_{T-1}^H$, we have $C_T^{D\ast }\left({\varphi }_{T-1}^H\right)>0$, which means the manufacturer needs to pay positive information incentive costs. On the contrary, when the state of the demand growth in period $T-1$ is low, i.e., ${\varphi }_{T-1}^S={\varphi }_{T-1}^L$, we have $C_T^{D\ast }\left({\varphi }_{T-1}^L\right)<0$, which indicates that the manufacturer needs to pay negative information incentive costs. Therefore, in the $n$-period moral hazard case, from period 2 to period $n$, the manufacturer pays the information incentive costs of period 1 to period $n-1$, respectively. That is, the payment of the information incentive costs is deferred. Then, Corollary 3 is obtained.

Corollary  3.

In the multi-period moral hazard case, the risk that the manufacturer bears in period$T-1$ ($T\ge 2$) is deferred to period $T$.

Charging a “guarantee deposit” one period ahead lowers the risk that the manufacturer needs to bear under information asymmetry to some extent. Besides the deferred payment of the information incentive costs mentioned in Conclusion 3, the utility that the manufacturer pays to the retailer for her services, from another perspective, is also deferred. Therefore, the impact of the uncertainty or risk brought by the retailer’s behavior of period $T-1$ on the manufacturer’s profit occurs in period $T$. That is, the risk is deferred. Especially when $T=1$, ${\mathsf{\Pi }}_{1M}^{E=1,D\ast }=f\left({\overline{\varphi }}_1,{\overline{\varphi }}_1^{\prime }\right)-c+\delta \left[{\rho }_1{U}_{2R}\left({\varphi }_1^H\right)+\left(1-{\rho }_1\right)U_{2R}\left({\varphi }_1^L\right)\right]$. The manufacturer obtains a higher expected profit in period one than that in the benchmark case. In other words, the risk in the first period is transferred to the second period. Therefore, the risk that the manufacturer bears in the current period is deferred to the next period.

6. Conclusions and Discussion

The authors of this paper explored the manufacturer’s multi-period incentive strategies when dealing with moral hazard to achieve supply chain sustainability by building a dual-channel supply chain model in which the retailer operates both the offline and online channels. The following conclusions and managerial insights can be drawn from this study.

6.1. Conclusions

(1)

Influence of long-term interaction

In the multi-period moral hazard game, the incentive constraints for the retailer are only affected by her expected profits of the current and the next period but are irrelevant to the expected profits in the following periods. In other words, the incentive contract is influenced by historical information. In contrast, the contract in the information-symmetry case is unaffected by historical information. Therefore, when information is asymmetric, the contract offered to the retailer in each period is different depending on the retailer’s different behavior in the previous period.

(2)

Manufacturer’s incentive strategies

In the multi-period moral hazard case, the manufacturer can induce effort by charging a “guarantee deposit” one period ahead and refunding parts of it later according to the realized demand growth. Then, the manufacturer can postpone the payment of the incentive costs and transfer the risk to the next period. In this way, the manufacturer can protect himself from the risk of moral hazard to some extent and the retailer can exert effort to maintain cooperation, which is also beneficial for the sustainable development of the supply chain.

(3)

Influence of free-riding effect

Since the online channel can free ride on the experience services of the physical store, the manufacturer’s incentive strategies are also affected by free riding. We found that the high-state transfer payments are more sensitive to the free-riding coefficient than the low-state ones, which indicates that the stronger the free-riding effect is, the higher the transfer payments that the manufacturer can receive. The online store can obtain more demand growth due to a stronger free-riding effect, and the supply chain can also obtain a higher revenue. Therefore, the manufacturer is able to charge higher transfer payments. From this perspective, “experience in store, buy online” is a good choice for the manufacturer when making use of free riding.

6.2. Managerial Insights

The above-mentioned conclusions shed some managerial insights into long-term supply chain management under information asymmetry.

Firstly, in long-term cooperation, the behavior of retailers in each period will affect the contracts that they can obtain in next period. Retailers exert effort and take appropriate action for better offers and more cooperation opportunities. Thus, it is better to choose long-term contracts for manufacturers and retailers, which can help to reduce short-sighted decision making and moral hazard risk. Furthermore, long-term cooperation is also beneficial for supply chain sustainability.

Secondly, manufacturers can consider charging a “guarantee deposit” when designing the incentive contracts that are offered to retailers. This kind of contract can avoid the risk of moral hazard and information asymmetry to some extent.

Thirdly, in supply chain operation, manufacturers, retailers and other supply chain managers should take advantage of both online and offline channels due to their different features. As we mentioned before, conventional stores are good at providing experience services and online stores can obtain demand growth by free-riding the experience services, which is also beneficial for the whole supply chain. Therefore, manufacturers and retailers can promote the mode of “experience in store, buy online” in operation.

6.3. Limitations and Future Research Suggestions

Although this paper has significant contributions to current literature and important empirical implications, the insights obtained from our analysis are to be understood in the context of the model’s assumptions and the study still has limitations that must be addressed in future studies. Firstly, this study only examined single moral hazard situation between manufacturers and retailers in a dual-channel supply chain. However, double moral hazard situations always exist in the cooperation between manufacturers and retailers [19,20,27], and relevant strategies are more complicated in long-term cooperation. Thus, further studies could explore the multi-period strategies of manufacturers and retailers when a double moral hazard exists in the dual-channel supply chain. Secondly, for simplicity, this study assumed that online stores cannot offer experience services. In practice, live-stream selling is becoming an increasingly popular in e-commerce platforms, which has nonnegligible impacts on consumer valuation and purchase decisions [46,47,48]. Hence, investigating moral hazard strategies in a dual-channel supply chain with live-stream selling is a worthy endeavor.