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In evolutionary game theory, the emergence and maintenance of cooperative behavior in a population often face challenges posed by the temptation of free-riding behavior, which offers high individual payoff. Recently, apart from a range of mechanisms that promote the formation of cooperation, individual learning abilities under limited information have emerged as a key factor in adjusting agents' strategies. This paper introduces q-learning and particle swarm optimization into the realm of evolutionary dynamics. The primary focus is on investigating the impact of Exploration-based Particle Swarm Optimization (EPSO) and Q-learning-based Particle Swarm Optimization (QPSO) on the evolution of cooperation in a continuous version of the spatial public goods game (SPGG) with punishment. EPSO defines a rule for updating agents' strategies based on individual and limited population information. It also integrates an exploration mechanism to increase the diversity and directionality of the strategies. Additionally, QPSO serves to adaptively optimize the parameters of EPSO, addressing the issue of parameter control limiting the EPSO's performance. Leveraging experiential learning and iterative adjustment, QPSO progressively refines system parameters, thus rationally assimilating knowledge and updating individual strategies to attain optimal payoff. Through extensive simulation studies, it has been observed that employing QPSO's adaptively optimized parameters in EPSO significantly promotes the cooperative evolution in the SPGG with punishment. Furthermore, individual learning coefficients, when too low or too high, both facilitate the occurrence of cooperation. Simultaneously, higher inertia weight coefficients strengthen the system's cooperation level, while lower punishment intensity coefficients and higher gain intensity coefficients effectively promote the cooperation emergence and exert a significant influence on the overall cooperation level of the system. This research provides a new perspective for designing real-world schemes that encourage cooperation and offers insights into the intricate dynamics of cooperation in complex systems. • The cooperative evolution in SPGG with punishment is investigated. • A novel strategy updating rule, EPSO, is proposed. • A new optimization algorithm, QPSO, is proposed to optimize the EPSO's parameters. • The intricate dynamics of system behavior under varying parameter conditions is studied. • The effectiveness of both EPSO and QPSO are confirmed by empirical results. [ABSTRACT FROM AUTHOR]

To explore transboundary pollution games with network externalities, this study develops a multi-region differential game which investigates the interaction and co-evolution of multiple pollution stocks across a continuous horizon. Pollution transmission networks are incorporated into the model via an adjacency matrix, detailing transmission paths of pollution across regions. Equilibrium strategies for emissions and investments in pollution control are obtained through a system of coupled differential equations. Our study demonstrates that these equilibrium strategies and the corresponding discounted net welfare of regions depend crucially on the structure of pollution transmission networks. The spectral properties of networks can effectively discern the evolutionary stability of equilibrium strategies. Through a numerical simulation of multiregional pollution dynamics, we also show that regions' motivation for pollution control decreases continuously as their influence in pollution transmission networks (i.e., network influence) increases; Nevertheless, an increase in a region's network influence can significantly reduce local pollution stocks in cycle networks but increase them in tree networks. [ABSTRACT FROM AUTHOR]

The rational utilization of the characteristics of sediment resources to achieve the optimal allocation of sediment resources is a key problem that must be solved urgently for ecological governance. On the basis of determining the allocation mode of sediment resources, this study established the multi-objective optimal allocation model of sediment resources, which aimed at the maximum ecological, economic, and social benefits and used the ε-constraint method and Kuhn–Tucker condition to obtain the non-inferior solution. Moreover, the optimal equilibrium solution of the model was obtained by using the subjective trade-off method from the perspective of preference. The Weishan and Bojili irrigation areas in China were then chosen as a case study to verify the feasibility and validity of the model. Results corroborate that, compared with the present situation, the proportions of sediment transport into the field in Weishan and Bojili irrigation areas are significantly increased and that the proportions of the main and branch canal sediment detention in the two irrigation areas are reduced. Compared with the results of the non-inferior solution, ecological and social benefits have been improved, and economic benefit has been decreased. The coordinated optimization of ecological, economic, and social benefits has been realized, instead of blindly pursuing economic benefit. Image 1 • Ecological, economic, and social benefits brought by different allocation modes are analyzed. • The model of multi-objective optimal allocation of sediment resources is established. • The optimal equilibrium solution of the model is obtained by using the subjective trade-off method. • The optimal allocation scheme of sediment resources is put forward to realize the coordinated development. [ABSTRACT FROM AUTHOR]

• We investigate the role of shared punishment cost in the evolution of cooperation in public goods game. • The punishment with shared cost can promote and stabilize cooperation in both well-mixed and structured populations. • Population structure can promote the emergence of cooperation and allow cooperators and defectors to coexist stably. • The joint effect of networks and punishment will not always promote cooperation and even inhibits the evolution of cooperation. Both experimental and theoretical studies have shown that punishment plays an important role in promoting cooperation. Various forms of punishment are proposed to explain why costly punishment could be maintained in the population and stabilize cooperation. Here we consider an altruistic behavior that cooperators perform cooperation and punishment simultaneously and share the punishment cost. We investigate the role of punishment cost shared among cooperators in the evolution of cooperation in public goods game. We show that the punishment can promote and stabilize cooperation when the penalty imposed on defectors is large enough compared to the punishment cost incurred by cooperators in well-mixed populations. In structured populations, cooperation could emerge under lower fine threshold and coexist with defection. However, as the penalty increases, cooperation will have a larger basin of attraction in the well-mixed population than that in the structured population. Our analytical and simulated results indicate that punishment indeed can effectively promote the evolution of cooperation. We also find that population structure can promote the coexistence of cooperation and defection but not always be beneficial to cooperation. [ABSTRACT FROM AUTHOR]

Abstract Understanding and explaining the widespread emergence of cooperation in social dilemmas remains a great challenge. Previous researches have shown that complex networks with high heterogeneity especially scale-free networks can remarkably facilitate cooperation in the case of accumulated payoff, but fail in the case of average payoff. In this paper, we investigate the role of particle swarm optimization (PSO) strategy update rules in the evolution of cooperation in the prisoner's dilemma (PD) on scale-free networks, when each player obtains the average payoff normalized with its degree. In the meantime, considering whether goods and resources are divisible, PSO strategy update rules based on continuous and mixed strategy systems are proposed respectively. The simulation results show that the PSO strategy update rules can promote cooperation in the continuous strategy system, but lead to the severe collapse of cooperation in the mixed strategy system. The nodes with low or medium degree play an important role to facilitate cooperative behaviors. [ABSTRACT FROM AUTHOR]

Retailer can continuously gather market demand information during the planning horizon, and dynamically updates her demand forecast. The demand forecast is more precisely when it is nearer to the sales season, but the unit procurement cost is higher. The retailer has two order opportunities. She orders at the beginning of the planning horizon through normal channel with a low unit procurement cost. According to the demand forecast evolution process, she can also dynamically order once through emergency channel with a higher unit procurement cost at any time in the planning horizon. When the demand forecast evolution process is MMFE (martingale model of forecast evolution) and there's different fixed ordering costs at different time epochs, we prove the optimal policy is state dependent basestock and (s,S), and analytically characterize that the base-stock level depends on the market demand forecast at current time point in a linear fashion. The meaning of ordering thought normal and emergency channels is analyzed, and sensitive analyses are carried out to show how retailer tradeoffs between normal and emergency channels, market demand information and procurement cost. Using a lot of numerical examples, we find that full balance is made by dual souring. [ABSTRACT FROM AUTHOR]

The emergence of cooperation between competing agents has been commonly studied through evolutionary games, but such cooperation often requires a mechanism or a third party to be activated and kept alive. To investigate how a mechanism affects the evolution of cooperation, this paper proposes an innovative reinforcement learning-based strategy updating model. The model consists of two symmetrical sets of convolutional neural networks. Besides, the agents' strategies updating rules are defined: firstly, the agents learn and predict the environment and the behaviors of neighboring agents, then estimate their future payoffs based on this information, and finally determine their strategies based on these estimated payoffs. Through investigating the behavior characteristics and the stable states of the network for highly intelligent agents with memory learning and prediction ability in the evolution of the prisoner's dilemma game, the results demonstrate that the game initiators who adopt the mixed optimal payoff approach can increase the number of cooperators and facilitate "global cooperation" and "repaying kindness with kindness". Although the temptation factor has little effect on the population, increasing the discount factor can expand the scale of the cooperative cluster and even achieve dynamic stability. Additionally, a smaller size of minibatch is beneficial for the evolution of cooperation in a smaller experience replay pool. A larger size of minibatch is more conducive to the evolution of cooperation with an increasing capacity of the experience replay pool. This research provides a novel perspective from reinforcement learning to understand the evolution of cooperation. • An innovative RLSUM is proposed to investigate the PDG. • The behavioral characteristics and the steady state of the network are studied. • The RLSUM can facilitate "global cooperation" and "repaying kindness with kindness". • The research provides a novel perspective from RL to understand the cooperative evolution. [ABSTRACT FROM AUTHOR]

This paper studies the evolution of cooperation in the Prisoner’s Dilemma (PD) and the Snowdrift (SD) game on a square lattice. Each player interacting with their neighbors can adopt mixed strategies describing an individual’s propensity to cooperate. Particle Swarm Optimization (PSO) is introduced into strategy update rules to investigate the evolution of cooperation. In the evolutionary game, each player updates its strategy according to the best strategy in all its past actions and the currently best strategy of its neighbors. The simulation results show that the PSO mechanism for strategy updating can promote the evolution of cooperation and sustain cooperation even under unfavorable conditions in both games. However, the spatial structure plays different roles in these two social dilemmas, which presents different characteristics of macroscopic cooperation pattern. Our research provides insights into the evolution of cooperation in both the Prisoner’s Dilemma and the Snowdrift game and maybe helpful in understanding the ubiquity of cooperation in natural and social systems. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a two-period model in which an OM decides the remanufacturability level of products in product design in the first period, and a remanufacturer enters the product market to compete with the OM in the second period. The OM can control the supply of used remanufacturable products by changing the remanufacturability level in product design. A product with higher remanufacturability will directly decrease the production cost of the remanufacturer, increase fixed costs and variable costs of new products for the OM, and lower the producing tax to the government. Making use of game theory, we derive the equilibrium decisons for the OM and remanufacturer in the two scenarios that the collection is unconstrained or constrained. We characterize the equilibrium decisions to describe how the OM and remanufacturer behave with respect to changes in government producing tax. We analyse the sensitivity of the equilibrium decisions, and consider the trends of the equilibrium production of remanufactured products, the equilibrium profits of remanufacturer and OM with regard to the percent changes in related parameters. [ABSTRACT FROM AUTHOR]

Owing to the ultra-low frequency vibration isolation performance without compromising static stiffness, high-static-low-dynamic-stiffness (HSLDS) vibration isolators (VIs) have advantages over linear vibration isolators. This paper presents a lever-type HSLDS vibration isolator (L-HSLDS-VI) by employing negative resistance electromagnetic shunt damping (EMSD) together with eddy current damping to eliminate the jump phenomenon and thus to improve the stability of L-HSLDS-VIs. The lever inerter system can amplify the mass effect to broaden the isolation band. The theoretical model of L-HSLDS-VIs with EMSD (L-HSLDS-VI-EMSD) was established. The effects of negative resistance and lever ratio on the vibration isolation performance of L-HSLDS-VI-EMSD were investigated analytically and experimentally. The L-HSLDS-VI can provide significant nonlinear stiffness, which can realize the quasi-zero stiffness (QZS), and thus broaden the isolation band. EMSD produces a considerable damping effect to enhance the vibration mitigation performance of L-HSLDS-VI. The combination of the EMSD and nonlinear ECD damping is an efficient approach to improve the vibration isolation performance to overcome the jump phenomenon. This paper utilizes the lever effect to amplify damping effects, which could provide a guideline to modify the performance of HSLDS-VIs. • A lever-type HSLDS vibration isolator (L-HSLDS-VI) is modeled and analyzed. • Electromagnetic shunt damping (EMSD) with negative resistance and eddy current damping are applied to eliminate the jump phenomenon of L-HSLDS-VIs. • The mass effect can be amplified by the lever inerter system to broaden the isolation band. • The lever effect can enlarge the relative motion between the coil and permanent magnet to enhance the damping effect. [ABSTRACT FROM AUTHOR]

• Statistical analysis of hourly wind speed series. • Finding out the optimal distribution to characterize the hourly wind speed series. • Guiding wind farm operation with the hourly expected wind power. Accurate wind speed characterization is important for wind farms to efficiently utilize wind energy which plays a significant role in reducing the dependence on fossil fuels and promoting global carbon peak and carbon neutrality. Since hourly wind speed density exhibit a variety of shapes, their characteristic features change substantially within a day, influenced by meteorological factors, therefore, the hourly wind speed analysis is considered to improve the accuracy of wind speed characterization. In this paper, 4 commonly used wind speed probability distributions (Weibull, Rayleigh, Gamma, Lognormal distribution) are applied for hourly wind speed analysis, and the best fitting distribution of each hourly wind speed series is identified by the goodness-of-fit test. Then the hourly wind power distribution of wind farms is determined by the corresponding optimal hourly wind speed distribution and the relation between wind power and wind speed. Finally, the hourly expected wind power calculated by the hourly wind power distribution is used to guide the hourly operation of the wind farm. The measured wind speed and wind power data of Dashuikeng wind farm in the Ningxia Autonomous Region of China is taken as an example to illustrate the results, 1) the hourly wind speed analysis performs a more accurate characterization of wind speed than annual wind speed series analysis. 2) The range of the average value of hourly wind speed series is 5.7 m/s–6.9 m/s, and the average wind speed, overall, during the daytime is smaller than that during the nighttime. 3) Gamma distribution shows a better performance than the other three distributions in characterizing the hourly wind speed series. 4) Wind energy resources are not fully consumed during the daytime, especially the period of 11:00–18:00. The proposed method improves the characterization of wind speed and guidance of the hourly operation for the wind farm, which has an important significance in raising the efficiency of wind energy utilization. [ABSTRACT FROM AUTHOR]

• A lever-type vibration isolator (LVI) with electromagnetic shunt damping (EMSD) is modelled and analysed. • The lever structure can simultaneously amplify damping force and lower natural frequency to improve the vibration isolation performance of LVI-EMSD. • Both the NR and NR resonant shunts produce the considerable damping to improve the vibration isolation performance of LVIs. • The NR resonant shunt acts like an electrical tuned mass damper to drastically reduce low-frequency vibrations. Considering the damping limitation of traditional lever-type vibration isolators (LVIs) in the low-frequency range, electromagnetic shunt damping (EMSD) utilising a lever to amplify the damping force is introduced in this study to improve the vibration isolation performance of LVIs. Negative resistance (NR) and NR resonant shunts were used to compensate for inherent resistance to improve the effect of LVI with EMSD (LVI-EMSD). A theoretical model of LVI-EMSD was established, and displacement transmissibility was derived. The optimal parameters of the NR resonant shunt were derived according to the fixed-point theorem. The effects of the lever ratio, negative resistance, and resonant frequency of the circuit on the vibration isolation performance of the LVI-EMSD were numerically and experimentally analysed. The lever structure can simultaneously tune the natural frequency and damping to improve the vibration isolation performance of the LVI-EMSD. Both the NR and NR resonant shunts effectively produce a considerable damping effect, and the NR resonant shunt outperforms the NR shunt in the low-frequency region. The NR shunt could produce a mass effect when the negative resistance was carefully designed. This study provides guidelines for the design, modelling, and optimisation of LVI-EMSD. Graphical abstract [Display omitted]. [ABSTRACT FROM AUTHOR]

• We introduce multi-game populations and explore the evolutionary dynamics in this kind of populations. • We consider the diversity of perceptions among all agents. • We consider the perceptions of agents obeys a norm distribution. This paper introduces a multi-game population to describe the fact that people have heterogeneous perceptions on their interactions. Besides, we also consider the diversity of perceptions among all agents in a structured population. Then, we established the theoretical model to investigate the evolutionary dynamics of cooperation in a spatial multi-game population. By means of the Monte Carlo method, we get some insightful observations regarding to the promotion of cooperation. Firstly, simulation results show that agents are more likely to take cooperation action in a multi-game population than in a homogeneous population. Moreover, we also find out that agents playing prisoner's dilemma game are possible to adopt cooperation strategy when they interact with agents playing snowdrift game. [ABSTRACT FROM AUTHOR]

• A group-level selection dynamic induced by the implementation of an individual-level selection is proposed. • The existence of an independent cooperator group is beneficial to the rise of cooperation in the population with multiple groups. • Mutation and migration will inhibit the prevalence of cooperation by destroying the independence and purity of cooperator groups. • A special kind of multi-person migration, group division, will inhibit the anti-cooperation effect of the mutation. It is a challenge to understand why cooperation is prevalent in human society, especially without a mechanism that benefits cooperators such as direct, indirect and strong reciprocity. We study an evolutionary process of public goods game among individuals in multiple groups in a population. We find that the existence of an independent cooperator group is beneficial to the rise of cooperation in the population, which is applicable to both Moran process and a so-called disaster update process proposed in this paper. However, the introduction of mutation can completely overturn the emerging trend of cooperation, and even let the defectors occupy the whole population for a short period of time, by continuously reducing the number of cooperator groups. In addition, the migration of individuals between groups can also inhibit cooperation. More specifically, a higher frequency of migration can reduce the probability of cooperators occupying the population, and extend the time it takes for the population to reach the stationary state. Furthermore, we find that a special kind of multi-individual migration, namely group division, can resist the anti-cooperation effect of mutation to some extent, mainly by maintaining a certain number of cooperator groups in the population. The aforementioned results suggest that cooperation can rise without strengthening the ability of cooperators to directly confront the defectors in a population composed of multiple groups. [ABSTRACT FROM AUTHOR]

Data communication service has an important influence on e-commerce. The key challenge for the users is, ultimately, to select a suitable provider. However, in this article, we do not focus on this aspect but the viewpoint and decision-making of providers for order allocation and pricing policy when orders exceed service capacity. It is a multiple criteria decision-making problem such as profit and cancellation ratio. Meanwhile, we know realistic situations in which much of the input information is uncertain. Thus, it becomes very complex in a real-life environment. In this situation, fuzzy sets theory is the best tool for solving this problem. Our fuzzy model is formulated in such a way as to simultaneously consider the imprecision of information, price sensitive demand, stochastic variables, cancellation fee and the general membership function. For solving the problem, a new fuzzy programming is developed. Finally, a numerical example is presented to illustrate the proposed method. The results show that it is effective for determining the suitable order set and pricing policy of provider in data communication service with different quality of service (QoS) levels. [ABSTRACT FROM PUBLISHER]

Abstract: This paper proposes a new approach to design optimal double auction mechanism with multi-objectives. In the optimal double auction mechanism, optimality is represented as multi-objectives to maximize the expected total revenue of sellers and buyers respectively at the same time. We give representation of allocation rules and payment rules of the optimal double auction mechanism that satisfies incentive compatibility, individual rationality, market clearing, and budget-balanced restrictions. Finally, we present a numerical example to demonstrate the function of the developed optimal double auction mechanism and its efficiency. [Copyright &y& Elsevier]

This paper studies a class of bilevel multi-followers programming in which there are partial shared variables among followers. A fuzzy interactive decision making approach is proposed to derive a satisfactory solution for decision makers not only considering the dominated action of the leader but also treating the ratios of satisfaction between the leader and the followers. Finally, a numerical example is illustrated to demonstrate the feasibility of the proposed approach. [Copyright &y& Elsevier]

Abstract: Bilevel programming, one of the multilevel programming, is a class of optimization with hierarchical structure. This paper proposes a globally convergent algorithm for a class of bilevel nonlinear programming. In this algorithm, by use of the dual theory, the bilevel nonlinear programming is transformed into a traditional programming problem, which can be turned into a series of programming problem without constraints. So we can solve the infinite nonlinear programming in parallelism to obtain the globally convergent solution of the original bilevel nonlinear programming. And the example illustrates the feasibility and efficiency of the proposed algorithm. [Copyright &y& Elsevier]

• Climate change dilemma is formulated as a public goods game with environmental feedback. • A dynamic model based on Particle Swarm Optimization algorithm is proposed with restricted exchange of information. • Theoretical analysis and simulation results both show that environmental feedback promotes cooperation. • Continuous contribution is more conducive to cooperation. • Population composed of individuals that make decisions replying more on historical information than social information can promote cooperation. This paper formulates the climate change dilemma as an adaption of public goods game. The Nash equilibrium of the climate change dilemma is analyzed in the cases of discrete contribution and continuous contribution. Analytic results show that environmental feedback promotes cooperation to a certain extent, but as the number of players increases, zero contribution becomes the only Nash equilibrium in most cases. A dynamic model based on Particle Swarm Optimization algorithm is then proposed for the climate change dilemma, where the information exchange is restricted by a network. Simulation results show that the proposed dynamic model can effectively promote cooperation, especially in the case of continuous contribution, and making decisions based on historical information can largely boost the average contribution. [ABSTRACT FROM AUTHOR]

• Repeated PDG with crosstalk is studied within memory-one strategies. • Cooperative and evolutionarily stable memory-one strategies are explored. • WSLS and FBF effectively promote cooperation in game dynamics with crosstalk. • The tolerance to CD and DD is mutually restrained in keeping strategy stability. Crosstalk represents a ubiquitous phenomenon in which strategic moves made in one game can influence actions in another. Reiter et al. [1] first integrated crosstalk with the repeated prisoner's dilemma model in structured populations. We extend their strategic space from one-step reactive strategies that consider only the actions of the opponent to memory-one strategies that consider the actions of both parties. We explore the cooperation rate of some representative memory-one strategies in repeated prisoner's dilemma games for multi-player structured populations when crosstalk exists, and focus on finding evolutionarily stable strategies that are cooperative in the memory-one strategy space under the impact of crosstalk. Simulation results in the strategic dynamics show that appropriately forgiving defection is conducive to cooperative stability in the population when crosstalk exists. Specifically, for strategies that can promote cooperation, there is a mutual restriction between tolerating the behavior of both defecting (the focused player and his opponent both defecting, DD) and forgiving unilateral defecting (the focused player cooperating while his opponent defecting, CD). That is, a more forgiving behavior of CD requires a lower tolerance for DD, while a higher tolerance of DD requires a less forgiving behavior of CD. Notably, we find two effective strategies, namely, Win-Stay-Lose-Shift (WSLS) and Firm‑but-Fair (FBF) in the facilitation of cooperation in game dynamics with crosstalk. Moreover, we reveal that the structured population can better suppress the negative impact of crosstalk on cooperation. This investigation provides complementary insights into the interplay between strategic decision-making and the influence of crosstalk within the context of memory-one strategies. [ABSTRACT FROM AUTHOR]

To investigate the influence of emotional tendency on the dissemination and evolution of opinions, in this paper, we first propose a novel algorithm to construct a two-layer social networks, who is composed of a strong-tie subnet and a weak-tie subnet. Considering the weights on the strong-tie and weak-tie networks and the subjective emotional tendencies of individuals, the HK model with emotional tendency (i.e. E-HK model), the weight HK model (i.e. WHK model), and the weight HK model with emotional tendency (i.e. E-WHK model) are put forward. Finally, according to the algorithm and the E-WHK model newly presented, we use the seventh census data to construct a social network, and explore individuals' opinion evolution, as well as the influence of three factors, including the level of subjective emotional tendency, the trust radius, and the proportions of individuals with different emotional tendencies. Abundant simulations demonstrate that the E-WHK model can explain the dissemination and evolution of opinions very well. In addition, the greater the level of emotional tendency, the faster the convergence of individuals' opinions. Increasing the trust radius will make completely positive and negative opinions decrease. Enhancing the proportion of optimists/pessimists, most individuals' ultimate opinions tend to be completely positive/negative. The results of this paper provide theoretical methods and analytical tools for managers in guiding public sentiment during public events. [ABSTRACT FROM AUTHOR]

Hypergraph neural networks are widely used in link prediction because of their ability to learn the high-order structure relationship. However, most existing hypergraph modeling relies on the attribute information of nodes. And as for the link prediction, missing links are not utilized when training link predictors, so conventional transductive hypergraph learning are generally not consistent with link prediction tasks. To address these limitations, we propose the N etwork S tructure L inear R epresentation (NSLR) method to model hypergraph for general networks without node attribute information and the inductive hypergraph learning method H ypergraph M ulti-view A ttention N eural N etwork (HMANN) that learns the rich high-order structure information from node-level and hyperedge-level. Also, this paper put forwards a novel NSLR-HMANN link prediction algorithm based on NSLR and HMANN methods. Extensive comparison and ablation experiments show that the NSLR-HMANN link prediction algorithm achieves state-of-the-art performance on link prediction and has better performance on robustness. • The hypergraph modeling method without node information is proposed. • An inductive hypergraph learning method to explore the high-order structure. • We propose a link prediction algorithm using high-order structure information. • Experiments are conducted to verify the advanced performance of the algorithm. [ABSTRACT FROM AUTHOR]

The operation of the Three Gorges Reservoir (TGR) has changed the original flow regimes in the reservoir area, as well as middle and lower reaches of the Yangtze River, which may lead to algal blooms in the tributaries of TGR, changing conditions in the downstream of TGR for fish spawning and breeding, and saltwater intrusion in water sources area of Yangtze estuary. In this study, a multi-objective model is developed to improve the environmental issues both upstream and downstream of TGR by trading off the contradiction between the ecological benefits and the power generation considering these environmental problems mentioned above caused by the operation of TGR. Solving the multi-objective model with the non-dominated sorting genetic algorithm III (NSGA-III), the non-inferior solutions are obtained. And then the concept of subjective trade-off rate (STOR) is introduced to measure the level of preference of the decision-makers for each objective. Combining the STOR method and ecological risk analysis, a decision-making method is proposed to select the most suitable alternative. As a case study, the operation process of TGR in 2015 on a daily scale is simulated with the multi-objective model, and the most suitable operation rule is selected by decision-making method within the interval ranges for decision-makers' preference. Analyzing the effect of different trade-off rates combinations on the level of objectives in the suitable alternative, and the result indicates that when the trade-off rates in the combinations increase, the power generation increases but the ecological benefits reduce. Considering this relationship and the trade-off rate ranges both determined to be [1,1.5] with a step of 0.05, some schemes are established. And then the most suitable solution is selected from these schemes, whose power generation is 1.74% less than the maximum and its ecological risk probability is optimal. The most suitable operation rule derived by the multi-objective model and decision-making method provides an operational reference for decision-makers to coordinate the water conflict between ecological benefits and power generation. • Solve the ecological issues by the operation of TGR with a multi-objective model. • Establish response relationships between ecological issues and water level, discharge. • Improve the STOR method to solve engineering problems with multiple trade-off rates. • Combine the STOR method and risk analysis to determine the most suitable solution. [ABSTRACT FROM AUTHOR]

• In this paper, 2 × 2 symmetric games in which the game payoff matrix is represented by fuzzy numbers were studied. • We introduce the fuzzy dilemma strength to classify fuzzy games. • The fuzzy fixation probability of the strategy is calculated when the game payoff matrix is represented by the normal fuzzy numbers. • The proposed fuzzy Moran model was applied to solve the problem of strategy selection in the interaction between pollution-producing enterprises. Most of the previous studies on the evolutionary dynamics of the Moran process assumed that the payoff obtained by the participant from the games is deterministic and expressed in precise numbers. However, because of the influence of various uncertain factors of the environment, the individual's payoff is not an accurate number but needs to be expressed by a fuzzy number. In this paper, 2 × 2 symmetric games in which the game payoff matrix is represented by fuzzy numbers were studied. Firstly, we introduce the fuzzy dilemma strength to classify fuzzy games. Then, the evolution dynamics of a fuzzy Moran process of a finite population are analyzed by using the operation of a fuzzy number. Under the condition of weak selection, the fuzzy fixation probability of the strategy is calculated when the game payoff matrix is represented by the normal fuzzy numbers. Furthermore, the conditions under which natural selection favors one strategy to be fixed in population and a strategy to become a fuzzy evolutionary stability strategy are analyzed. Lastly, the proposed fuzzy Moran model was applied to solve the problem of strategy selection in the interaction between pollution-producing enterprises. By numerical analysis, the effect of fuzzy dilemma strength on the fuzzy fixation probability was illustrated and then the feasibility and effectiveness of the method were verified. The extension of classical game dynamics to a fuzzy environment enriches the theory of evolutionary games and is more realistic. [ABSTRACT FROM AUTHOR]

Public goods game as a multi-player social dilemma game plays an important role in studying the emergence of cooperation, which remains an open question. This paper studies the impact of heterogeneous investments on cooperative behavior in public goods game, where players adopting exclusion strategy can exclude defectors from the group. Our research shows that the heterogeneous investment mechanism can significantly promote cooperation. When the cost of exclusion is low, the excluders can obtain higher payoff than other players, which leads that cooperators and excluders coexist and dominate the population. As the cost of exclusion increases, the advantage of excluders weakens and population keeps high cooperation level in some regions of contribution rate ω. For low or middle values of r , the too small or relatively large values of ω will be not beneficial to the evolution of cooperation. For high values of r , a small increase in ω will be beneficial to the evolution of cooperation. This paper provides a new understanding of cooperation under heterogeneous investment mechanism. [ABSTRACT FROM AUTHOR]

• We introduce the multigame environment and prove that the evolutionary dynamics is different from that in previous work. • We combine the evolutionary dynamics with the Particle Swarm Optimization. • We consider a continuous strategy version. This paper studies the evolution of cooperation in a so-called multigame environment based on the Particle Swarm Optimization (PSO) algorithm. In a multigame environment, players use different game payoff matrices and acquire their utilities from their interactions with their neighbors. According to the PSO algorithm, each player updates its strategy according to both the strategy adopted by the player with the highest utility in its neighborhood and the most profitable strategy in their own past actions. Simulation results show that the multigame environment is conducive to the promotion of cooperation. Besides, within the multigame environment, for any player, imitating the most profitable strategy in its past actions promotes cooperation more effectively than imitating the strategy adopted by the player with the highest utility in its neighborhood. [ABSTRACT FROM AUTHOR]

Social exclusion can prevent free riders from participating in social activities and deprive them of sharing cooperative benefits, which is an effective mechanism for the evolution of cooperation. However, traditional peer-exclusion strategies are unconditional, and as long as there are defectors in the group, they will pay a cost to exclude the defectors. In reality, one of the reasons for the complexity of these strategies is that individuals may react differently depending on the environment in which they are located. Based on this consideration, we introduce a kind of conditional peer-exclusion strategy in the spatial public goods game model. Specifically, the behavior of conditional exclusion depends on the number of defectors in the group and can be adjusted by a tolerance parameter. Only if the number of defectors in the group exceeds the tolerance threshold, conditional exclusion can be triggered to exclude defectors. We explore the effects of parameters such as tolerance, exclusion cost, and probability of exclusion success on the evolution of cooperation. Simulation results confirmed that conditional exclusion can greatly reduce the threshold values of the synergy factor above which cooperation can emerge. Especially, when the tolerance is low, very small synergy factors can promote the population to achieve a high level of cooperation. Moreover, even if the probability of exclusion success is low, or the unit exclusion cost is relatively high, conditional exclusion is effective in promoting cooperation. These results allow us to better understand the role of exclusion strategies in the emergence of cooperation. [ABSTRACT FROM AUTHOR]

• A feedback-evolving repeated PGG model with nonlinear effects is explored. • Synergy and discount effects are adopted to realize the heterogeneous feedback. • Cooperation can be promoted since groups interact in heterogeneous environments. • The result is verified when the environment changes between two or three states. • The results are emphasized under the probabilistic transition of the states. The mutual feedback between the environment and the strategy is a significant mechanism in the evolution of cooperation. A feedback-evolving repeated public goods game model with nonlinear effects is explored. The players' behaviors in the current round may influence the environment, leading the environment feedback on the behavior by the modulation of payoffs in the form of positive or negative. Under the former case, the groups realize the synergy effect of payoffs in the next round. Vice versa, the discount effect will be instead. The introduction of nonlinear effects enables heterogeneous feedback of the environment on different groups without introducing too many environmental states. The results show the enhancing role of the nonlinear effects on the evolution of cooperation compared to linear switching of enforcement factors. Compared to static game environments, the dynamic feedback scenario can realize better performance in the evolution of cooperation. The effect is more pronounced as the synergy factor increases or the discount factor decreases. The results are verified when the game environment changes between two or three states and under different environment transition structures. In addition, under the scenarios of probabilistic transition, the results are explored by taking into account the cases of state-independent and state-dependent, where both the homogeneity and heterogeneity transition probability are considered in the state-independent case, respectively. The probabilistic transition results further emphasized the transition probability's significant role in the evolution of cooperation when cooperation behaviors are more likely incentivized to interact in the valuable environment. [ABSTRACT FROM AUTHOR]

How to explain the evolution of cooperation in social dilemmas has plagued the theorists of various disciplines. In this paper, we study the public goods game on two structured populations, assuming that each individual can make a continuous contribution in its strategy space. In our model, individuals have memory and imitation ability. They can remember their best history strategy and learn their best neighbors by obtaining the local information. We use the particle swarm optimization (PSO) algorithm to simulate the learning process of individuals. Two network structures of the square lattice and the nearest-neighbor coupled network are considered respectively. We investigate the combined effects of memory, the invest enhancement and the network structure on the average cooperation level of the population. By simulation experiments, we find that the PSO learning mechanism can promote the evolution of cooperation in a large range of parameters under both of the two kinds of networks. Compared with the square lattice network, the nearest-neighbor coupled network can promote the evolution of cooperation in a larger parameter scope. Compared with the Fermi rule and the Genetic Algorithm learning, the PSO learning can induce the population achieve a wider range of cooperation level, which makes it possible to achieve a higher level of cooperation. These results are conducive to a better understanding of the emergence of cooperation in the real world. [ABSTRACT FROM AUTHOR]

• A type of fairness-based sympathy and retaliation preference is introduced in SPGG. • Payoff-dependent heterogeneously sympathy threshold and reputation-based intensity of sympathy are adopted. • Cooperation can be effectively promoted so long as a few players have this preference. • The results are robust in square lattice networks and WS small-world networks. Fairness preference is common in real society and natural communities. We consider this preference and explore the effect of individual sympathy and retaliation caused by payoff inequality on the evolution of cooperation in multi-player dilemma games with a structured population. Specifically, by setting payoff-dependent heterogeneously sympathy threshold and reputation-based intensity of sympathy, we make high-payoff players more likely to perceive payoff lead, and the payoff redistribution proportion is determined by the reputation of low-payoff players. While all players have the same perception of payoff lag and retaliate against high-payoff players by damaging their payoff with a cost. We find that even if only a few players have this preference, cooperation can be effectively promoted regardless of whether sympathy and retaliation are considered separately or together. Although retaliation is indeed a Pareto loss behavior that damages social welfare, the reduction of the payoff gap can increase the frequency of cooperators. Moreover, a relatively small upper limit of reputation enables high-payoff players to more accurately identify defectors in the process of payoff redistribution. Moreover, high positive correlations between strategy, payoff, and reputation convince us that sympathy groups and retaliation groups are mainly composed of cooperators and defectors, respectively. By analyzing the underlying micro process of the redistribution of players' payoffs, we observe that the reduction of payoff gaps increases the probability that defectors imitate the cooperative strategy, which further expands the areas of cooperative groups. These findings enrich our knowledge of the positive effect of sympathizing with the poor and retaliating with the rich caused by payoff inequality on cooperation. [ABSTRACT FROM AUTHOR]

The dilemma of global public issues is a grave challenge, characterized by conflicts between rich and poor nations, and a lack of national consensus on future benefits. The impact of initial wealth heterogeneity on the emergence of cooperation in collective risk dilemmas has been a topic of intense debate. In this study, we examine the impact of endogenous endowment heterogeneity on cooperation in collective risk dilemmas. Using a two-stage game model with endogenous endowments, we investigate the dynamics of cooperation and the potential stable-state composition of the population under various parameters. Simulation results show that a higher risk probability leads to greater investment. Besides, cooperative behavior thrives when individuals are encouraged to achieve higher targets by setting small contribution ratios in multiple stages. Moreover, the promotion of cooperation by the benefit coefficient of the first-stage public goods game is influenced by the second-stage contribution ratio. Generally, a higher enhancement factor increases the likelihood of averting risk. However, when the contribution ratio is in the middle range, a moderate level of the enhancement factor yields the best performance in terms of risk aversion. Our findings have offered some information for real-life collective risk games that involve economic game relations between countries. [ABSTRACT FROM AUTHOR]

How cooperative behavior emerges and evolves in human society remains a puzzle. It has been observed that the sense of guilt rooted from free-riding and the sense of justice for punishing the free-riders are prevalent in the real world. Inspired by this observation, two punishment mechanisms have been introduced in the spatial public goods game which are called self-punishment and peer punishment respectively in this paper. In each situation, we have introduced a corresponding parameter to describe the level of individual tolerance or social tolerance. For each individual, whether to punish others or whether it will be punished by others depends on the corresponding tolerance parameter. We focus on the effects of the two kinds of tolerance parameters on the cooperation of the population. The particle swarm optimization (PSO)-based learning rule is used to describe the strategy updating process of individuals. We consider both of the memory and the imitation in our model. Via simulation experiments, we find that both of the two punishment mechanisms could facilitate the promotion of cooperation to a large extent. For the self-punishment and for most parameters in the peer punishment, the smaller the tolerance parameter, the more conducive it is to promote cooperation. These results can help us to better understand the prevailing phenomenon of cooperation in the real world. [ABSTRACT FROM AUTHOR]

Staff planning in Home Health Care (HHC) context is challenging due to the complexity, such as, unavailability of resources, variation in patient health conditions, and diversity of continuity of care (COC) and patient's priority (PP). This necessitates the implementation of adequately effective models and intelligent systems to improve the robustness of care plans that run with limited input from the support staff. The work proposed an effective, simple, compatible and extensible model for the therapist assignment problem (TAP). The model aims at maximizing the assignment rate of demand, subject to the constraints of workload capacity limitation and available time selection clash. It helps the HHC structure managers to make proper decisions through preferred time periods (PTPs) selections and weight allocations. The analysis of the PTPs claims that the HHC structures applying the TAP model should offer a selection of at most five PTPs to each patient for the sake of effectiveness and efficiency. Following this suggestion, optimal solutions for all instances can be provided within 0.4 s. The weight allocations depend on the various requirements for COC and PP. The analysis of results suggests that the HHC structures can adopt PP in the TAP model without hesitation. However, it also advises that they should pay attention on the adoption of COC, because it has a visible effect on the assignment rate of demand with the lower COC levels and the utilization rate of therapists, while slightly affecting the computational time of the TAP model and the total number of assigned demands. The work offers the HHC structures a demonstration of the core part of an effective planning system to help them make better decisions that satisfy patient demand, achieve high quality of service, and enhance efficiency. [ABSTRACT FROM AUTHOR]

The existing link predictability indexes for networks often depend on specific structural characteristics and don't make full use of all the structural information of networks. This paper finds that network energy can efficiently characterize the information of the network structure. Firstly, a novel and simple network predictability index is proposed via normalized network energy. To enhance the global topology information of the predictability index, we then extend this index and define a new effective predictability index by integrating the network structural consistency index. Secondly, based on modified maximum likelihood probability method, we develop the approximate relationship between the probability of the original network (subject to the condition of the observation network) and the maximum likelihood probability of the perturbed network. Furthermore, a novel link prediction algorithm (LCPA) is presented. Numerical experiments on both generative and real networks confirm that the LCPA algorithm outperforms the existing state-of-the-art methods in most cases. Finally, this paper takes the precision obtained by the LCPA algorithm as the network predictability value and also verifies the effectiveness of the two proposed predictability indexes. It is also shown that the above-defined indexes can efficiently characterize the network predictability. The latter defined index also shows a linear relationship with the network predictability. The data and code are publicly available at https://github.com/pinglanchu/LCPA. [ABSTRACT FROM AUTHOR]

In order to investigate the evolution of stock market in any period of time, in this paper, combined with sliding window method, Granger causality test and cointegration test, a novel algorithm of constructing directed-weighted financial stock networks via meso-scale. We use the proposed algorithm on the financial stock data of the Shanghai Stock Exchange from January 1st, 2016 to December 31st, 2020 divided at the meso-scale level to construct some directed-weighted financial stock networks with fixed meso-scale and different meso-scale. Analyzing the topology and robustness of these constructed networks indicates that the robustness of financial stock networks with fixed meso-scale (assuming one year) is generally poor. By comparison, in 2018, the financial stocks were closely in contact with each other while the stock market was relatively stable. We also noted that the financial stock networks with different meso-scale show a high level of robustness when being attacked according to descending arrangement of in-degree or out-degree. They are however less robust against attacks according to descending arrangement of degree. Besides, the networks perform best for a meso-scale of 190. Hence, long-term investors are advised to consider a 190-day holding. • A novel algorithm of constructing directed-weighted financial networks is proposed. • The financial stock networks with fixed and different meso-scale are constructed. • The topology characteristics and robustness of the proposed networks are discussed. • The optimal holding time is achieved for long-term investors. [ABSTRACT FROM AUTHOR]

• Two types of agents and two learning rules are introduced in SPGG. • Rational conformity behavior in social learning is conducive to cooperation. • Large proportions of link-type agents are more conducive to cooperation. • There is an optimal payoff threshold to make a peak of cooperation. Conformity behavior is crucial in human social learning and we consider this effect on spatial public goods game (SPGG). Two types of agents and two corresponding social learning rules are introduced in SPGG. One is link-type agents based on the rational conformity learning rule, whose strategies are independent in different groups. The other is node-type agents based on the Fermi learning rule, whose strategies are the same in different groups. Rational conformity behavior signifies that conformity only occurs when individuals are unsatisfied with their payoffs. Through simulation experiments, we find that cooperation can be induced constantly with a large proportion of link-type agents, in which situation rational conformity behavior in social learning is conducive to the emergence of cooperation. We further find that the independent strategies of link-type agents favor reciprocity to be enhanced among cooperative groups and the extended imitation range is beneficial to distinguish cooperative groups which also improves cooperation. Moreover, an appropriate payoff threshold is favorable to induce a positive correlation between payoffs and contributions, and thus a more reasonable distribution of payoffs and strategies. Meanwhile, the payoff threshold in the rational conformity learning rule is also contributed to diminishing the spread of defective behavior for those defectors with outstandingly high payoffs. These results expand our comprehension of individuals' conformity behavior in social learning and its effect on cooperation in social dilemmas. [ABSTRACT FROM AUTHOR]

• A new second-order reputation evaluation rule is proposed in the SPGG. • Reputation-dependent social learning on the evolution of cooperation is explored. • Incomplete accessibility of reputation information is described by a reputation reasoning parameter. • Three cases where the reputation reasoning parameter is homogeneous, endogenous, and exogenous are compared. In this study, we propose a new second-order reputation evaluation rule in the spatial public goods games, in which both actions of the individual and his neighbors with the worst reputation are taken into account. Considering the incomplete accessibility of individual reputation information, we introduce a reputation reasoning ability parameter and study the effect of reputation on individual strategy updating from the perspective of social learning, in which individuals with large reputation reasoning abilities are more likely to choose neighbors with a high reputation for strategy imitation. Three cases where the reputation reasoning ability parameter is homogeneous, endogenous, and exogenous are considered and compared. From simulation results, we find that high reputation reasoning ability can promote cooperation in all cases. Specifically, in the homogeneous reputation reasoning ability situation, compared with the first-order rules, the second-order information on reputation inhibits cooperation rather than promotes it and a significant magnitude of reputation change can also inhibit cooperation. In endogenous situations where reasoning ability is negatively correlated with individual reputation, large correlation coefficients can inhibit cooperation. In exogenous situations of the normal distribution, a high mean of reputation reasoning ability boosts cooperation, but when the variance is sufficiently large, the level of cooperation will no longer be affected. In scenarios of the power law distribution, the cooperation level improves with an increase in the power index. These findings further expand our understanding of high-order reputation evaluation rules in multiplayer games and incomplete reputation information environment on the evolution of cooperation from the perspective of reputation-dependent social learning. [ABSTRACT FROM AUTHOR]

Abstract: The bilevel programming problems are useful tools for solving the hierarchy decision problems. In this paper, a genetic algorithm based on the simplex method is constructed to solve the linear-quadratic bilevel programming problem (LQBP). By use of Kuhn–Tucker conditions of the lower level programming, the LQBP is transformed into a single level programming which can be simplified to a linear programming by the chromosome according to the rule. Thus, in our proposed genetic algorithm, only the linear programming is solved by the simplex method to obtain the feasibility and fitness value of the chromosome. Finally, the feasibility of the proposed approach is demonstrated by the example. [Copyright &y& Elsevier]

Abstract: A combined homotopy interior point method for the linear complementarity problem (LCP) is proposed in this paper. We construct a homotopy path for the linear complementarity problem and prove that the homotopy path determines a smooth interior path from an arbitrary given interior point to the solution of LCP. Furthermore, we modify a predictor corrector algorithm with the technique of the cone neighborhood to trace the homotopy path. Finally, a numerical example is provided to show the effectiveness and feasibility of this method. [Copyright &y& Elsevier]

• Nonlinear payoff based on synergy and discounting is considered in SPGG model. • Two parameters to describe the synergy and discounting effect are introduced. • Phase transition process and stable state of the evolutionary system are explored. • Effects of synergy and discounting on cooperation are investigated. Hauert et al. [1] first observed the effects of discounting and synergy in social dilemma games and systematically studied these effects on cooperation in an unstructured population. This paper extends the effects of discounting and synergy into spatial public goods games (PGG) with a population structure. Specifically, an economy-scale threshold and an amplitude parameter to describe conditions and degrees of discounting and synergy are introduced, respectively. Simulation results show that nonlinear payoff based on synergy and discounting effects can promote cooperation more significantly than linear payoff structure. Moreover, the smaller the threshold value, the easier to trigger the synergy effect and remove the discounting effect; the larger the amplitude parameter, the stronger the effect of synergy and discounting to play a role. In both situations, it is more favorable for the emergence and prosperity of cooperation. These results are helpful to understand the evolution of cooperation in nonlinear PGG. [ABSTRACT FROM AUTHOR]

Reputation provides important information to society by recording the historical behavior of individuals. The introduction of reputation helps explain the cooperation phenomenon in human society to some extent. However, in previous explanation models, the benefits of a good reputation bring to individuals are generally described from the perspective of future payoffs they can obtain. In reality, the reputation system also affects the process of mutual imitation among individuals. For instance, the willingness of an individual with a high reputation learning from an individual with a low reputation can be greatly discounted. As such, this paper considers the reputation-based discount effect in imitation and extends the research on reputation from the perspective of imitation learning. Specifically, two situations of discount effect are considered. One is based on relative reputation difference, that is, if the reputation of an individual being imitated is too low compared to the strategy updater and the difference between which exceeds a threshold, the probability of imitation will be discounted. The other is based on absolute reputation difference, that is, if the absolute reputation of an individual being imitated falls below a threshold, the probability of imitation will be discounted. The effect of different thresholds and discount parameters on the evolution of cooperation in spatial public goods games is investigated, respectively, in both situations. Simulation results show that the reputation-based discount effect in mutual imitation plays an important role in the emergence and maintenance of cooperative behavior. Especially, low threshold differences for reputation and high discounts can greatly expand the range of parameters in which cooperation emerges. Moreover, compared with the relative reputation situation, the discount effect based on the absolute reputation is more conducive to the evolution of cooperation. • Reputation-based discount effect in imitation is considered in the SPGG model. • Effect of reputation threshold and discount parameter on cooperation is investigated. • Two situations of discount effect on the evolution of cooperation are compared. • The absolute reputation situation is more conducive to the evolution of cooperation. [ABSTRACT FROM AUTHOR]

To alleviate the challenges posed by privacy protection, sparse data, cold-start problem and weak interpretation, in this paper, we investigate how to uncover the implicit "social relationships" for user/item pairs and create recommendation relationships between users and items in the recommendation systems with no explicit trust relationships. Firstly, according to complex network theory, a recommendation system is presented by a heterogeneous network with five various types of subnets. Secondly, a novel algorithm ISimRank-ISR is designed based on the improved SimRank similarity index, which mainly integrates common and non-common behavior information, as well as attribute information for exploring the implicit social relations, and generates two types of social subnets. Further, introducing these implicit social relations into the nonnegative matrix factorization (NMF) model, another novel algorithm INMF-RRM is proposed to reconstruct the user-item rating subnet. Then, the integration of the above two algorithms derives an algorithm ISR-RRM to create recommendation relationships for the recommendation task. Finally, numerical experiments on two Movielens datasets are conducted to verify the feasibility and effectiveness of the three new algorithms mentioned above, and we come to the following conclusions. (1) The ISimRank-ISR algorithm provides an in-depth exploration of the implicit social relationships for user/item pairs. (2) The INMF-RRM algorithm has convergence properties. (3) To perform better and obtain more accurate recommendations, with the ISR-RRM algorithm, there are optimal parameters achieved. (4) Compared with the other seven benchmark algorithms, the ISR-RRM algorithm shows excellent performance, and its RMSE and MAE are reduced by a maximum of 14.75% and 8.05%, respectively. Additionally, it is more effective in alleviating the cold-start problem. [ABSTRACT FROM AUTHOR]

Reputation information plays an important role in human behavioral interactions. There have been many studies that have considered reputation in spatial public goods game models, but they essentially assumed that reputation will only change the payoff structure of the game (individuals with a good reputation will get more benefits in the future). In fact, individuals with good reputation will have greater influences which can also affect the decision of neighbors around them in the strategy updating process. Grounded on this observation, we proposed an improved strategy learning rule considering both reputation and payoff information. We employ evidence theory to fuse these two aspects of information, based on which individual strategies can be updated. In addition, we construct a weight coefficient to quantify the importance and reliability of reputation. Through numerical simulations, it is unraveled that the reputation effect can greatly attract nearest neighbors to form greater clusters, thus promoting the emergence of cooperation. With the reputation weight increasing gradually, the critical enhancement factor for cooperation to arise is by degrees reduced to the lower boundary, demonstrating that an increasing tendency of strategy adoption relying on reputation is more likely to allow cooperation to thrive. In the region of low reputation weights, reputation only plays a subtle role in inducing cooperation. Within the region of high reputation weights, cooperation is dramatically boosted by reputation and cooperators can swiftly occupy the whole population. Our work may be helpful to further understand the effect of reputation on the emergence of cooperation. [ABSTRACT FROM AUTHOR]

This paper establishes a stochastic evolutionary public goods game (PGG) model with exclusion-type strategies in a well-mixed and finite size population. The effect of increasing-returns-to-scale in public goods investment is considered. We focus on the stochastic stable equilibrium (SSE) of the evolutionary system. By numerical experiments, we observe that there are two types of SSE in the system, namely, "All individuals choosing defection" ("All D" state) and "the coexistence of cooperation and exclusion" ("C+E" states); and three types of phases, namely, choosing the "All D" state with probability one ("D" phase), choosing the "C+E" states with probability one ("C+E" phase) and choosing the "All D" and "C+E" states with non-zero probabilities ("C+E+D" phase). We study the combined effects of four parameters (probability of exclusion success, unit exclusion cost, increasing-returns-to-scale coefficient, investment amplification factor) on the phase selection of the system. We get the boundary curves or surfaces for each pair or set of combined parameters, thus conditions for the evolution of cooperative strategies depending on these parameters can be given. Notably, we observe that in a well-mixed population with exclusion-type strategies, the increasing-returns-to-scale coefficient cannot change the parameter boundary between the "C+E" phase and the "C+E+D" phase within our parameters. Corresponding simulation experiments are also carried out in a structured population, and it is found that the increasing-returns-to-scale effect can greatly reduce critical values of the amplification factor under which cooperation can emerge, and the increase in the increasing-returns-to-scale coefficient can induce the system to transfer directly from the "D" phase to the "C+E" phase, which is different from the well-mixed situation. This research can help us better understand the emergence of cooperation in the PGG with increasing-returns-to-scale effect under social exclusion mechanism. • Increasing returns to scale in PGG under social exclusion mechanism is studied. • Possible stochastic stable equilibriums (SSEs) of the model are investigated. • The range of parameters for the system to choose different SSEs is studied. • The cooperation behavior of the population is revealed in the stochastic system. [ABSTRACT FROM AUTHOR]

Mechanisms and conditions for the spontaneous emergence of cooperation in multi-player social dilemma games remain an open question. This paper focuses on stochastic evolutionary optional public goods games with different exclusion strategies. We introduce four strategy types in the population, namely, cooperation, defection, loner and exclusion. Synchronous and asynchronous exclusion forms have been compared in finite-sized, well-mixed and structured populations. In addition, we verify that the asynchronous exclusion mechanism is indeed better than the synchronous exclusion mechanism in all cases. The benefits of the asynchronous exclusion are measured by comparing the probability that the system chooses the cooperative states in the two situations. In the well-mixed population cases, only when the investment amplification factor is small and the probability of exclusion success is high will the asynchronous exclusion mechanism have a relatively large advantage in promoting cooperation. However, in the structured population cases, the range of the investment amplification factor, in which the asynchronous exclusion mechanism has relatively large advantages in promoting cooperation, is somewhat different and is mainly in the middle of the interval under our parameters. Our study further corroborated that when non-participation and exclusion strategies exist, a structured population does not necessarily promote cooperation compared with a well-mixed population for some parameter combinations. Thus, we acquire a good understanding of the emergence of cooperation under different exclusion mechanisms. [ABSTRACT FROM AUTHOR]

Currently, among the link prediction researches based on low-rank representation, almost none of literature has considered how to select an appropriate base-matrix and the impact of the structural characteristics of the reconstructed network on the link prediction. Therefore, in this paper, we use the adjacency matrix of the fully connected network (FCN) as the base-matrix for low-rank representation, and any local structure of the observed networks can be represented by the interactions of FCN structures. To explore the properties of link predictions, the nuclear norm of the adjacency matrix for the reconstructed network is taken as a penalty term in the newly proposed low-rank representation objective function. According to the optimal interactive coefficients achieved by solving the novel objective function, in this paper, we design a novel link prediction algorithm (LRNP algorithm) and its optimized algorithm (OLRNP algorithm). Experimental results based on real networks and synthetic networks lead to several conclusions. (1) The LRNP algorithm has good convergence properties. When changing the parameters of the LRNP algorithm, the changes along prediction performance do not exceed 9.48%. LRNP also performs well for sparse networks. (2) Compared with baseline link prediction algorithms, LRNP also shows excellent performance, and its AUC and Precision can increase by 14.35% and 14.89%. (3) The OLRNP algorithm exhibits better performance than the LRNP algorithm, and its AUC and Precision can rise by up to 7.50% and 6.79%, respectively. The data and codes are publicly available at https://github.com/pinglanchu/LRNP-OLRNP. [ABSTRACT FROM AUTHOR]

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation. [ABSTRACT FROM AUTHOR]

• A new mechanism, the reputation-based probabilistic punishment, are introduced into the spatial public goods game model. • Players with time-dependent reputations are divided into two types, good players and bad players. • A higher value of the reputation threshold is more conducive to promoting and maintaining cooperation. Low-reputation defectors are more likely to be punished than defectors with high reputations. Motivated by this reality, this paper proposes a new mechanism, the reputation-based probabilistic punishment, into the spatial public goods game model. In this mechanism, players with time-dependent reputations are divided into two types, good players with reputations higher than the reputation threshold and bad players with reputations lower than the threshold. A defector considered a good player is less likely to be punished than a defector considered a bad player. Based on these assumptions, we systematically explore how this mechanism influences the evolution of cooperation. Through extensive simulations, we verify that a higher value of the reputation threshold is more conducive to promoting and maintaining cooperation. Moreover, increasing the cost of being punished could effectively encourage players to take cooperative behaviors. Simulation results show that both increasing the punishment intensity and increasing the punishment fine could increase the cost of being punished and are beneficial to the promotion of cooperation. Additionally, in the structured population, the distributions of strategies, reputation, and payoff in the evolutionary stable state are mainly present in the form of clusters. [ABSTRACT FROM AUTHOR]

Extortion strategy can play the role of a Trojan horse for cooperators and act as a catalyst for the evolution of cooperation in social dilemma games. Based on the prisoner's dilemma game model with extortion, an emotion-imitating rule for strategy updating is proposed in this study, which takes into account the diverse attitudes of a player towards a strong or weak opponent. Furthermore, by employing evidential reasoning, we establish an improved rule for strategy updating, which integrates the emotion-imitating rule into strategy learning as well as the original myopic best response rule, and via a fusion weight, the role of emotion-imitating can be subtly adjusted in the process of strategy learning. The effect of emotion-imitating on cooperation is investigated in the presence of extortioners. Through Monte Carlo simulations, it is shown that the new rule can significantly boost cooperation when the fusion weight is close to 0.5. In strategy learning, the emotion-imitating rule relieves the direct exploitation from defectors for cooperators and also facilitates cooperators to cluster and spread in the population. The extortion strategy provides shelter for cooperators to survive even at the extremely high temptation to defect. In addition, the myopic best response rule can also improve the performance of the emotion-imitating rule, especially in the region of high temptation to defect. Based on evidential reasoning, the new rule integrates sophisticatedly the advantage of the two single rules, enhancing the emergence of cooperation as well as the average payoffs of the whole system. The robustness of the shelter effects of extortioners under the new learning rule model is also studied by considering action errors and the cognition cost of extortioners respectively. The results further support the catalyst roles of extortioners, provided that the dilemma strength is not too strong. We also demonstrate the enhancement of cooperation when the model is extended to four competing strategies where the tit for tat (TFT) strategy is also included. The coexistence of extortioners and TFT players restricts the expansion of defectors, and the extortioners' catalyst role still works prominently in the interval of low tempt values. [ABSTRACT FROM AUTHOR]

Social exclusion, as a special form of punishment, can effectively promote cooperation in spatial public goods game (SPGG). Previous research usually assumes that the unit cost of exclusion and the probability of exclusion success are statically fixed. As such, the total cost of an excluder can only be described as a linear function of the number of defectors. However, the scale return effect generally results in nonlinear characteristics of costs. In this study, we have thus relaxed the linear assumption and introduced a state-dependent kind of social exclusion with dynamic costs. Specifically, we describe the unit cost of exclusion as a function of the state of the group in which individuals are located. Due to the scale effect of punishment, an increase in the number of defectors in the group will result in a decrease in the unit cost of exclusion. We explore the impacts of this exclusion-type strategy in the SPGG with nonlinear exclusion cost on the evolution of cooperation. We further investigate parameters such as the cost parameter, the probability of exclusion success and the dilemma strength of the PGG on the evolution of cooperation. Simulations are performed on a square lattice with the traditional neighborhood structure and the Moore neighborhood structure, respectively. The results show that social exclusion with state-dependent costs can promote cooperation within a wide range of parameters in both cases. Especially, when the probability of exclusion success is high, a very strong dilemma strength can lead the system to form huge cooperative clusters to beat defectors. We further confirm that the Moore neighborhood case is more conducive to the evolution of cooperation in our social exclusion mechanism with dynamic cost compared with the traditional neighborhood case. These results allow us to better understand the role of the dynamic cost of punishment in the emergence of prosocial behavior. [ABSTRACT FROM AUTHOR]