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The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game.

In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop.

Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior.

In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.

The managerial questions of this paper are as follows, and the authors are trying to solve them: How revenue sharing contract (CSR) degree and government subsidy affect the agri-food quality? What kind of model (WPC, revenue-sharing contract [RSC] and cooperative) would be more effective in motivating manufacturers and retailer to increase effort and improve agri-food quality? What kind of model (WPC, RSC and cooperative) would make manufacturer and retailer better off?

Considering the jointing quality effort and contract decision in green agri-food supply chain, this paper proposes six models that consider CSR of manufacturer and retailer, and then the obtained optimal solutions are compared and analyzed. At the same time, the impact of government subsidies is analyzed, and corresponding conclusions are drawn.

The results show that, first of all, whether the increasing CSR of the manufacturer or the retailer can motivate both parties to improve the agri-food quality effort investment. Second, the WPC and RSC contract may play different role in different cases. Finally, under the model with government subsidies, regarding positive influence of government subsidies on efforts of manufacturer and retailer, quality and profits of members is investigated. Based on these conclusions, this study puts forward the following policy suggestions. Firstly, governments should formulate reasonable subsidy policies to support manufacturer and retailer to improve the agri-food quality, thereby promoting green industries' development. Secondly, manufacturer and retailer should actively improve CSR and strengthen the effort of agri-food so as to advance quality. Finally, manufacturer and retailer can choose cooperative model or WPC contract.

In this paper, one manufacturer and one retailer are considered. Since the agri-food supply chain structure in reality is more complicated, the future research direction can consider the supply chain structure with one manufacturer and multiple retailers. In addition, this paper only considers the subsidy, and future research can classify the subsidy into different types.

The study makes two substantive contributions to the body of knowledge in the field of sustainable operations:(1) incorporating quality-based demand function in supply chain and dynamic process of agri-food quality; (2) exploring the impact of CSR awareness of members and subsidy of government on agri-food quality, and comparing the influence in different models.

This study aims to focus on the optimal green R&D of a capital-constrained supply chain under different channel power structures as well as the impact of capital constraint, financing cost, channel power structure and cost-reducing efficiency on green R&D and supply chain profitability.

A two-echelon supply chain is considered. The upstream firm engages in green R&D but has capital constraints that can be overcome by external financing. Green R&D is beneficial to reduce production costs and increase consumer demand. Based on whether or not the upstream firm is capital constrained and dominates the supply chain, four models are developed.

Capital constraints significantly lower green R&D and supply chain profitability. Transferring leadership from the upstream to the downstream firms leads to higher green R&D levels and downstream firm profitability, whereas the upstream firm's profitability is increased (decreased) if green R&D investment efficiency is high (low) enough. Greater financing costs reduce green R&D and downstream firm profitability; however, the upstream firm's profitability under the model in which it functions as the follower increases if the initial capital is sufficient. More importantly, empirical analysis based on practice data is used to verify the theoretical results reported above.

This study reveals how upstream firms in supply chains decide green R&D decisions in situations with capital constraints, providing managers and governments with an understanding of the impact of capital constraint, channel power structure, financing cost and cost-reducing efficiency on supply chain green R&D and profitability.

The major contributions are the exploration of supply chain green R&D by taking into consideration channel power structures and cost-reducing efficiency and the validation of theoretical results using practice data.