In the same model, both distributional fairness concern and peer-induced fairness concern are considered, so are the absolute fairness concern and the relative fairness concern. When there are multiple recycling markets, collectors attach importance not only to the fairness distribution of profit with the manufacturer (distributional fairness concern), but also to the fairness distribution of profit with the peer collector (peer-induced fairness concern). On the basis of the perspective of the collectors, this paper introduces distributional and peer-induced fairness concern into the closed-loop supply chain (CLSC). The impact of the collectors’ different fairness concerns on the CLSC pricing decisions is discussed under five models.The research shows that: (1) When the manufacturer considers the collectors’ fairness concern, the manufacturer’s profit and distributional fairness concern coefficient change inversely, and the collectors’ profit and distributional fairness concern coefficient move together, that is, the distributional fairness concern is of advantage to the collectors but not good for the manufacturer. On the contrary, the manufacturer’s profit and peer-induced fairness concern coefficient move in the same direction, while the profit of the collectors and peer-induced fairness concern coefficient change in opposite direction; (2) As long as the manufacturer considers the fairness of the collectors, the profit of the collector who pays attention to both fairness is always lower than that of the collector who only concerns distributional fairness, so peer-induced fairness concern is not a self-interest behavior. However, when the appeal of the two collectors for fairness distribution is not considered by the manufacturer, peer-induced fairness concern benefits himself; (3) The two-part Tariff contract has realized the coordination of the CLSC. Additionally, our findings provide some managerial insights on the pricing decision when the collectors consider multiple fairness concerns.

The importance of behavioral factors in the process of decision making is widely recognized in literature and practice. The aim of this paper is to examine the influence of collectors’ multiple fairness concerns on pricing decisions in a closed-loop supply chain (CLSC), which consists of one manufacturer, one retailer, and two collectors. Specifically, the collectors are concerned with both distributional fairness and peer-induced fairness. By considering fairness concerns and selecting Nash bargain solution as the reference point of fairness distribution, this paper studies the equilibrium solution of Stackelberg game models in the CLSC with symmetrical and asymmetrical information of fairness concerns, respectively. The results show that in the former case, distributional fairness is always at the cost of sacrificing the manufacturer’s profits, which is a means of gaining more benefits for the collectors. In the latter case, the profits of both the manufacturer and the collectors turn into a loss. No matter in which case, the collector who is concerned with both distributional and peer-induced fairness is always in a passive position. Generally speaking, whether the decision maker concerns fairness and whether it can be perceived by the CLSC members both impact the members’ decision making. Additionally, the utilities of both the manufacturer and the collectors receive Pareto improvement under the proposed incentive contract.

This study focuses on evolutionary game analysis of supply chain (SC) strategies with fairness concerns. First, the equilibrium solutions under the eight combined strategies are obtained through the Stackelberg game. Subsequently, evolutionary game theory is applied to analyze the stability of these equilibrium solutions and to discuss the evolutionary stability strategy of the tripartite game. The study suggests that the effect of distributional fairness concerns on SC pricing differs from that of peer-induced fairness concerns in the short term. Implanting fairness concerns into SC pricing decisions is always detrimental to the supplier and not always beneficial to retailers. From a long-term perspective, only one evolutionarily stable equilibrium point exists. Retailers do not pay attention to the fairness of the channel profit distribution, and the supplier does not consider the fairness of retailers. The results help enterprises understand the influence of fairness preferences on pricing decisions and provide a reference for the efficient operation of SCs.

Based on the Shapley value fairness concern framework, a fairness concern utility system is established for the closed-loop supply chain (CLSC) with one manufacturer, one retailer, and two competitive collectors. Under the five models (one centralized and four decentralized), the influence of competitive strength and fairness concern degree of collectors on the pricing decisions is analyzed. The following conclusions can be obtained: (1) When the manufacturer considers the fairness concern of the collectors, fairness concern is a way for the collectors to obtain more profit. Whether the manufacturer “proactively” considers the fairness concern of the collectors is an approach to benefiting the collectors but only in the case of “active” consideration, there is less self-loss to the manufacturer. (2) When the collectors’ fairness concern cannot be considered by the manufacturer, the equilibrium recycling price sets lower for the purpose of achieving more profit by the collectors. At this point, the profit of the collectors and the manufacturer is the lowest, and so is the return rate of the CLSC. (3) When the collectors do not care about whether they are being fairly treated but the manufacturer “actively” takes the fairness of the collectors into consideration, the collectors get “unexpected” attention from the manufacturer, which makes the performance of the collectors more positive than it is when their fairness concerns are taken into account. The profit increased by the collectors is more than that lost by the manufacturer, so the profit of the CLSC is the largest. Additionally, our findings provide some managerial insights on the pricing decision in the case where the collectors consider fairness concern.

This article investigates the stability of evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. In the real environment, players interact simultaneously while the return of their choices may not be observed immediately, which implies one or more time-delays exists. In addition to using the method of classic characteristic equations, we also apply linear matrix inequality (i.e., LMI) to discuss the stability of the mixed evolutionarily stable strategy in replicator dynamics of two-community with multi-delays. We derive a delay-dependent stability and a delay-independent stability sufficient conditions of the evolutionarily stable strategy in the two-community replicator dynamics with two delays, and manage to extend the sufficient condition to n time delays. Lastly, numerical trials of the Hawk–Dove game are given to verify the effectiveness of the theoretical consequences.

Purpose: This study explores the impact of EN's (venture entrepreneurs, simplified as EN) jealousy fairness concerns coefficient on two-stage venture capital decision-making in cases of symmetrical and asymmetrical information. It discusses the equilibrium solution of two-stage venture.Design/methodology/approach: The principal-agent model was established based on multiple periods, and differentiated contracts were established at different stages. The validity of the models and the contract was verified by numerical simulation.Findings: The results suggest that with the increase in the EN fairness concerns coefficient, the effort level of EN decreases continuously and decreases faster in the second stage because this is the last stage. The level of VC's (venture capitalist, simplified as VC) effort declines first and then increases; that is, VC will increase the effort level when the fairness concerns coefficient increases to a certain threshold. To motivate EN to pay more effort, VC will increase the incentive to EN in the first stage. However, it will reduce the level of incentive to EN in the second stage. In the limited stage of venture investment, consider that the fairness concerns of EN do not make the profits of EN and VC achieve Pareto improvement simultaneously.Originality/value: First, the authors implanted fairness concerns into multi-stage venture capital and discussed the impact of fairness concerns on the efforts and returns of both parties. Second, among the influencing factors of the project output, the authors consider the bilateral efforts of EN and VC, the working capacity of EN, the initial investment scale, and the external uncertain environment.