# Unfair and Risky? Profit Allocation in Closed-Loop Supply Chains by Cooperative Game Approaches
## 2 Literature Review  
Considerable attention has been attracted to CLSCs in academia and practice. Remarkable studies have been conducted regarding two-echelon CLSCs [11; 12; 13; 14; 15] and three-echelon CLSCs [16; 17; 18]. Retailers of a CLSC frequently cooperate with manufacturers to collect preowned goods [19]. For instance, the Procter & Gamble company collects and resells used products through Loop, an online shopping platform which also sells new products. By forming strategic partnerships, enterprises in CLSCs can improve the profitability of individuals and distribution channels.  
In past research on CLSCs, agents were assumed to be of complete rationality. In actual fact, decision making agents often show different social preferences such as risk aversion. Research on CLSC coordination with risk aversion has been carried out. [PERSON] et al. [20] examined pricing and remanufacturing issues in a CLSC which is consisted of a dominant manufacturer and a risk-averse retailer. [PERSON] et al. [21] constructed and analyzed a risk-averse multi-stage model of a CLSC which include several functional entities. [PERSON] et al. [22] examined a bike-sharing operation network to study a multi-product, multi-agent, single-stage CLSC system under risk-averse criterion. [PERSON] et al. [23] studied a two-period risk-averse model of a CLSC for reusable packaging materials.  
Fairness concerns also widely exist in CLSCs. Along this research line, [PERSON] et al. [24] investigated reverse-channel CLSCs where retailers serve as collectors of preowned products while retailers have distributional fairness concern. [PERSON] et al. [25] incorporated fairness concern into a three-echelon CLSC composed of one manufacturer, one distributor and one retailer, and examined the impact of the retailer's fairness concern. [PERSON] and [PERSON] [26] analyzed the coordination of a CLSC in the presence of fairness concerns with a constant wholesale price contract. [PERSON] et al. [27] studied the impact of fairness concern in e-commerce CLSCs and showed that the fairness concern of the e-commerce platform reduces individual profit and systematic efficiency.  
Limited research has been carried out on CLSCs regarding both risk aversion and fairness concern. [PERSON] et al. [28] examined pricing strategies of a CLSC consisting of one manufacturer and one retailer considering the factors of risk aversion and fairness concern. [PERSON] et al. [29] investigated the price decisions in a CLSC with a risk-averse retailer with fairness concern and a risk-neutral manufacturer. [PERSON] and [PERSON] [30] studied a CLSC composed of two suppliers, a manufacturer, a risk-averse retailer and a fairness-concerned third-party under supply disruptions. These studies show that risk aversion and fairness concerns bring complexities to the coordination of a CLSC, and past research is limited to non-cooperative game setups. Differing from existing studies, this paper investigates the impact of risk aversion and fairness concern in a CLSC by cooperative game approaches. As summarized in Table 1, this paper differs from other existing CLSC literature in subject areas.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multicolumn{4}{c}{**Subject Areas**} \\ \cline{2-5}  & **CLSCs** & **Risk Aversion** & **Fairness Concern** & **Cooperative Game** \\ \hline Refs. [11; 12; 13; 14; 16; 17; 18] & Yes & No & No & No \\ \hline Ref. [15] & Yes & No & No & Yes \\ \hline Refs. [19; 20; 21; 22; 23] & Yes & Yes & No & No \\ \hline Refs. [24; 26; 27] & Yes & No & Yes & No \\ \hline Ref. [25] & Yes & No & Yes & Yes \\ \hline Refs. [28; 29; 30] & Yes & Yes & Yes & No \\ \hline This paper & Yes & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table}
Table 1: An overview of characteristics of the literature and this paper.