This paper aims to find operational decisions and financing strategies in a closed-loop supply chain (CLSC) consisting of a financially constrained manufacturer and a retailer. Based on a benchmark model without financing, three different financing strategies for the capital-constrained manufacturer, bank financing (BF), retailer credit financing (RCF), and hybrid financing (HF), are respectively incorporated and investigated. Analytical results show that: (a) Depending on the initial working capital /and the increased cost of financing from the bank, the manufacturer will change remanufacturing strategy from Partial remanufacturing to Complete remanufacturing for capital constrained CLSC when the relative unit cost of the remanufactured product is moderate; RCF strategy only revises and charges a higher wholesale price of new and remanufactured products; (b) For a financially constrained manufacturer in the CLSC, it holds the prerequisite to implement external financing and a higher financing rate to bank clearly cuts down the profits of the manufacturer and the channel but improves the retailer’s profit under certain conditions; RCF strategy always redistributes the channel profit compared with the non-capital-constrained CLSC; c) A feasible financing rate to the bank of the manufacturer and an appropriate interest rate threshold of the retailer are potentially confirmed.

We study the evolution of cooperation in the spatial public goods game in the presence of third-party rewarding and punishment. The third party executes public intervention, punishing groups where cooperation is weak and rewarding groups where cooperation is strong. We consider four different scenarios to determine what works best for cooperation, in particular, neither rewarding nor punishment, only rewarding, only punishment or both rewarding and punishment. We observe strong synergistic effects when rewarding and punishment are simultaneously applied, which are absent if neither of the two incentives or just each individual incentive is applied by the third party. We find that public cooperation can be sustained at comparatively low third-party costs under adverse conditions, which is impossible if just positive or negative incentives are applied. We also examine the impact of defection tolerance and application frequency, showing that the higher the tolerance and the frequency of rewarding and punishment, the more cooperation thrives. Phase diagrams and characteristic spatial distributions of strategies are presented to corroborate these results, which will hopefully prove useful for more efficient public policies in support of cooperation in social dilemmas.

In this paper, we explore the impact of four different types of dissimilarity-driven behavior on the evolution of cooperation in the spatial public goods game. While it is commonly assumed that individuals adapt their strategy by imitating one of their more successful neighbors, in reality only very few will be awarded the highest payoffs. Many have equity or equality preferences, and they have to make do with an average or even with a low payoff. To account for this, we divide the population into two categories. One consists of payoff-driven players, while the other consists of dissimilarity-driven players. The later imitate the minority strategy in their group based on four different dissimilarity-driven behaviors. The rule that most effectively promotes cooperation, and this regardless of the multiplication factor of the public goods game, is when individuals adopt the minority strategy only when their payoff is better than that of their neighbors. If the dissimilarity-driven players adopt the minority strategy regardless of the payoffs of others, or if their payoff is the same, the population typically evolves towards a neutral state where cooperators and defectors are equally common. This may be beneficial when the multiplication factor is low, when defectors would otherwise dominate. However, if the dissimilarity-driven players adopt the minority strategy only when their payoff is worse than that of their neighbors, then cooperation is not promoted at all in comparison to the baseline case in the absence of dissimilarity-driven behavior. We explore the pattern formation behind these results, and we discuss their wider implications for the better understanding of cooperative behavior in social groups.