To start with an infinitely repeated game of supply chains of public goods, a stout reciprocity mechanism is introduced into income games to build a matric dynamic equation. The conventional evolutionary game method is employed to propose a model called the evolutionary game for the cooperative strategy of both the manufacturer and the seller groups in the supply chain of public goods. Also, white Gaussian noise (WGN) is added to reflect random interference in the evolution process. Then, a stochastic dynamic system is established, and Ito\'s differential equation is used to analyze both sides\' strategy evolution in a game, interpret changes in system stability when random disturbance is added, and finally test the influence of different situations on the system stability by running a numerical simulation. The research shows that the stronger the reciprocity coefficient is, and the system is subjected to random interference, the greater the strategy choice change in players\' decision-making procedures when the repeated game of public goods is conducted.

Division of labor, where subpopulations perform complementary tasks simultaneously within an assembly, characterizes major evolutionary transitions of cooperation in certain cases. Currently, the mechanism and significance of mediating the interaction between different cell types during the division of labor, remain largely unknown. Here, we investigated the molecular mechanism and ecological function of a policing system for optimizing the division of labor in Bacillus velezensis SQR9. During biofilm formation, cells differentiated into the extracellular matrix (ECM)-producers and cheater-like nonproducers. ECM-producers were also active in the biosynthesis of genomic island-governed toxic bacillunoic acids (BAs) and self-resistance; while the nonproducers were sensitive to this antibiotic and could be partially eliminated. Spo0A was identified to be the co-regulator for triggering both ECM production and BAs synthesis/immunity. Besides its well-known regulation of ECM secretion, Spo0A activates acetyl-CoA carboxylase to produce malonyl-CoA, which is essential for BAs biosynthesis, thereby stimulating BAs production and self-immunity. Finally, the policing system not only excluded ECM-nonproducing cheater-like individuals but also improved the production of other public goods such as protease and siderophore, consequently, enhancing the population stability and ecological fitness under stress conditions and in the rhizosphere. This study provides insights into our understanding of the maintenance and evolution of microbial cooperation.

Dissimilatory metal-reducing bacteria (DMRB) can transfer electrons to extracellular insoluble electron acceptors and play important roles in geochemical cycling, biocorrosion, environmental remediation, and bioenergy generation. c-type cytochromes (c-Cyts) are synthesized by DMRB and usually transported to the cell surface to form modularized electron transport conduits through protein assembly, while some of them are released as extracellularly free-moving electron carriers in growth to promote electron transport. However, the type of these released c-Cyts, the timing of their release, and the functions they perform have not been unrevealed yet. In this work, after characterizing the types of c-Cyts released by Geobacter sulfurreducens under a variety of cultivation conditions, we found that these c-Cyts accumulated up to micromolar concentrations in the surrounding medium and conserved their chemical activities. Further studies demonstrated that the presence of c-Cyts accelerated the process of microbial extracellular electron transfer and mediated long-distance electron transfer. In particular, the presence of c-Cyts promoted the microbial respiration and affected the physiological state of the microbial community. In addition, c-Cyts were observed to be adsorbed on the surface of insoluble electron acceptors and modify electron acceptors. These results reveal the overlooked multiple roles of the released c-Cyts in acting as public goods, delivering electrons, modifying electron acceptors, and even regulating bacterial community structure in natural and artificial environments.

Expulsion has been found to promote cooperation in social dilemmas, but only if it does not incur costs or is applied unilaterally. Here, we show that removing both conditions leads to a spontaneous resolution of the costly expulsion problem. Namely, by studying the public goods game where cooperators and defectors can expel others at a personal cost, we find that public cooperation thrives as expulsion costs increase. This is counterintuitive, as the cost of other-regarding behaviour typically places an additional burden on cooperation, which is in itself costly. Such scenarios are referred to as second-order free-rider problems, and they typically require an additional mechanism, such as network reciprocity, to be resolved. We perform a mean field analysis of the public goods game with bilateral costly expulsion, showing analytically that the expected payoff difference between cooperators and defectors increases with expulsion costs as long as players with the same strategy have, on average, a higher frequency to interact with each other. As the latter condition is often satisfied in social networks, our results thus reveal a fascinating new path to public cooperation, and they show that the costs of well-intended actions need not be low for them to be effective.

In the current era of big data, it is critical to address people\'s demand for health literacy. At present, the traditional mode of communicating scientific health knowledge and information technology is interchangeable, resulting in the emergence of a new mode of communicating health literacy. To publicize health education and health literacy in a targeted way, to meet the public\'s needs, and to understand how the public\'s demand for subjects, contents, and forms of health literacy service has changed in the era of COVID-19, the investigation of public\'s demand for health information and health literacy was conducted.
This study aims to understand the differences in demand for health literacy service providers, contents, channels, forms, and facilities among Chinese citizens with different genders, ages, education levels, economic conditions, and living environments, and to provide reasonable recommendations for developing public health literacy.
Questionnaire Star was used to conduct a large sample of random online surveys. In Wuhan, Hubei Province, 2184 questionnaires were issued, 8 invalid questionnaires were eliminated, and 2176 were recovered, with an effective rate of 99.6%. IBM SPSS Statistics 20 was utilized to analyze the survey data.
(1) In health literacy service providers selected by the public, the proportion of government departments or government collaboration with other institutions exceeded 73%, indicating that health literacy services are public goods; (2) access to health literacy services was lower in township areas than in urban areas (P < 0.001, 3) internet media and communicating with acquaintances, which have the highest popularity rate, were also the two channels that were least trusted by the public; and (4) the differences in contents and service channels of health literacy among residents with different genders, ages, education levels, economic status, and living environments were statistically significant.
(1) It is recommended to establish an integrated health literacy service model with multi-center supply. Government departments, medical institutions, and media should cooperate effectively to provide health literacy services. (2) The government should pay attention to the fairness of health education and strengthen the supply of health literacy services in township areas. (3) It is critical to strengthen the public\'s ability to discriminate network information and pay attention to scientific thinking cultivation. (4) Health literacy service providers must focus on the differences between public demands and improve the connotation of health literacy services.

Insufficient sewage treatment facility is one important reason for wastewater entering and affecting aquatic ecosystems. The PPP mode, serving as one of the fastest-growing mechanisms for public service provision in recent decades, is considered to be an effective way to alleviate the pressure of funding shortages and to improve the efficiency of sewage treatment. However, the performance of PPPs has been questioned, especially the service quality given the inherent nature of the private sectors\' pursuit of maximizing economic profit and the shortcoming of incomplete contracts. This paper evaluates the service quality, namely the environmental performance, of the PPP mode in China\'s urban sewage treatment sector. Based on detailed firm-level data in Jiangsu Province, China, we find that the PPP mode has improved the pollutant treatment performance, and increased operation cost and promoted sewage treatment efficiency serve as the main mechanism for the improvement of environmental performance. The research findings could help both developed and developing countries to apply and design a public-private partnerships mechanism.

Bacterial quorum sensing (QS) system regulates the production of most costly but sharable extracellular products (public goods) in a growth-phase-dependent manner, and the development of this energy-intensive process is susceptible to environmental changes. However, the role of nutrient factors in dominating the QS-mediated cooperative interaction and intracellular metabolism still remains less understood. Here we studied the performance of QS system by growing Pseudomonas aeruginosa under different nutrient and culture conditions. The results of comparative-transcriptomic analyses revealed that carbon source-limitation was the main factor suppressing the activation of QS system, and a substantial number of public-good-encoding genes were induced when phosphorus is limiting in short-term culture. By contrast, although the QS regulation of P. aeruginosa in all the cultures was generally decreased along with the enrichment of QS-deficient individuals during evolution, limitation of different nutrient factors had discrepant effects in directing the formation of population structure by coordinating the production of public goods and primary metabolism, especially the starch and sucrose metabolism. These findings demonstrate the pleiotropy of QS regulation in balancing the development of cooperative behavior and metabolism, and provide a reference for further understanding the role of QS system in causing persistent infections.

Public goods dilemmas are at the heart of some of the greatest challenges of our time, including climate inaction, growing inequality, and the overuse of natural resources. The public goods game in which cooperators contribute to a common pool that is then shared equally with defectors who contribute nothing captures the gist of the problem. Cooperators therefore cannot prevail, which ultimately leads to the tragedy of the commons. Actions such as punishment, rewards, and exclusion have been shown to help, but they are costly, therefore rendering cooperators second-order free-riders due to their lack of participation in these actions. In the search for a remedy, we study the public goods game with benevolent leaders who, at a personal cost, have the ability to exclude defectors from using common pool resources. We also consider bribers who can pay the leaders to relax their exclusion efforts. In a traditional setting, this setup yields the standard second-order free-rider problem, where, ironically, the leaders are overcome by cooperators, who then themselves succumb to defectors. We show, however, that the Singaporean model - where a leader\'s payoff is determined not only by the regular sharing income from the firm production but also by the success of gross firm production as an incentive - can resolve the second-order free-rider problem. We also show that the detrimental effect of bribery can always be, no matter how high the bribe, held in check as long as the number of individuals engaged in this activity is low compared to the number of benevolent leaders. Otherwise, an abrupt transition to a cooperator-less state becomes unavoidable. We discuss the implications of our research for designing successful cooperation and anti-corruption strategies in public goods dilemmas.

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.

Cooperation is the crux of many social problems, thus third-party sanction, as one of the most important ways to promote cooperation, is worth studying. The present study compared the effects of third-party punishment alone, third-party reward alone, and the combination of third-party reward and third-party punishment on cooperation in the context of a public goods experiment. In addition, we explored the characteristics of third-party sanctioning behaviors. A total of 280 students participated in the present study. The results showed that the operation of third-party sanctions did raise the level of cooperation and changed the discrete trend of cooperation-specifically, the differences between the cooperation level of every group member and the average level of the whole group. Furthermore, when third-party rewards and third-party punishments were used simultaneously in the public goods game (PGG), the level of cooperation was greatly enhanced, which meant that in the context of the third party, when punishment opportunities and reward opportunities coexist, they may have a \"compensatory effect.\" In terms of the characteristics of sanctioning behaviors, the frequency of third-party sanctions did not differ significantly under different conditions (third-party punishment alone, third-party reward alone, and a combination of third-party reward and third-party punishment), and neither did expenditures on third-party sanctions, but the strategies that third parties used changed under different conditions, thus their effects on other group members\' cooperative behavior varied under different conditions. The present study provides a comprehensive picture of how third parties behave in different conditions of third-party sanctions and how these sanctions exert influence on cooperation. Understanding these mechanisms can help us build more effective institutions.