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.

Purpose Members in a supply chain account for corporate social responsibility (CSR) in different ways. This paper considers a socially responsible supply chain in which the manufacturer innovates in a sustainable product while the retailer exhibits CSR concerns. This paper aims to investigate how socially responsible behavior, namely, sustainable innovations or CSR concerns, affects the pure profit, environmental impact and social welfare, in such a socially responsible supply chain. Design/methodology/approach This paper first constructs an integrated case as a benchmark and then develops a Manufacturer-Stackelberg game in a decentralized scenario. The pure profit, environmental impact and social welfare are confirmed and analyzed in centralized and decentralized cases. Moreover, two unique coordinating contracts, i.e. wholesale price discount contract and revenue-sharing contract, are used in this socially responsible supply chain. Findings Analytical analysis shows that, under certain conditions, the optimal CSR strategies hold for maximizing pure channel profit, minimizing environmental impact and maximizing social welfare. Whether the performance in a centralized case outnumbers that in a decentralized case depends on the CSR concerns level and environment-friendly degree of the product. In addition, it is found that a wholesale price discount contract is better for the retailer whereas a revenue-sharing contract is better for the manufacturer in pure profit to improve coordinating efficiency. Practical implications These results can offer managerial implications to the socially responsible supply chain in terms of pricing decisions, CSR strategies and sustainability innovations. Specifically, under certain conditions, placing more CSR concerns level increases pure channel profit and the social welfare. A balance between the pure profit and the social welfare is hereby achieved for the two socially responsible individuals by designing a proper contract. Originality/value To the best of the authors’ knowledge, this paper is among the first studies so far to combine the CSR concerns strategy and sustainability innovation into a socially responsible supply chain.

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.

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