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In social dilemmas, most interactions are transient and susceptible to restructuring, leading to continuous changes in social networks over time. Typically, agents assess the rewards of their current interactions and adjust their connections to optimize outcomes. In this paper, we introduce an adaptive network model in the snowdrift game to examine dynamic levels of cooperation and network topology, involving the potential for both the termination of existing connections and the establishment of new ones. In particular, we define the agent's asymmetric disassociation tendency toward their neighbors, which fundamentally determines the probability of edge dismantlement. The mechanism allows agents to selectively sever and rewire their connections to alternative individuals to refine partnerships. Our findings reveal that adaptive networks are particularly effective in promoting a robust evolution toward states of either pure cooperation or complete defection, especially under conditions of extreme cost-benefit ratios, as compared to static network models. Moreover, the dynamic restructuring of connections and the distribution of network degrees among agents are closely linked to the levels of cooperation in stationary states. Specifically, cooperators tend to seek broader neighborhoods when confronted with the invasion of multiple defectors. [ABSTRACT FROM AUTHOR]

Highlights • In this paper, we developed a novel spatial HD model replacing the best takes over update rule with different one. • We investigated the effect of modifying update rules on the problem of cooperators extinction in the space HD games. • We found that our model generated characteristic population patterns and represented the survival of cooperators compared with the classical spatial HD model in which the updated rule was fixed. Abstract Since Maynard Smith and Price proposed the earliest version of Hawk–Dove (HD) game, it attracted researchers' attention as one of models of conflict for two players in game theory. In conflict game, the players' benefit depends on the strategy of opponent for each other. In the classical spatial HD games, if one player adopts defector strategy, it tends to get high payoffs, and therefore increases population of the same strategy, which resulting in an extinction of cooperators. Several studies tried to solve the problem of an extinction of cooperator in spatial HD game. In this paper, we developed a novel spatial HD model replacing the best takes over update rule with different one, and investigated the effect of modifying update rules on the problem of collaborators extinction in space HD games. We found that our model generated characteristic population patterns and represented the survival of cooperators compared with the classical spatial HD model in which the updated rule was fixed. [ABSTRACT FROM AUTHOR]

In this paper, to state the necessary and the critical number of cooperators for completing the snow shoveling, we investigate the evolutionary dynamics of an N -person snowdrift game with two thresholds in well-mixed populations and structured populations. Firstly, we discuss the effects of these thresholds on equilibria in infinite well-mixed populations by applying the replicator equation, and observe that there exist three types of equilibria with the variations of parameters. Secondly, we study the game in finite well-mixed populations by means of the Markov process, and find that the evolutionary results converge to those in infinite population as the finite population size increases. Finally, we explore such a game in structured populations by using the pair approximation approach, and derive the dynamical equation under weak selection, which is ignored in the previous work. Results present that structured populations can create more complicated behaviors of the cooperative dynamics, and to some extent facilitate cooperation compared with well-mixed populations. Our work helpfully provides a theoretical approximation for the N -person snowdrift game in more complicated scenarios. • Some concise critical conditions of equilibria are obtained in infinite and well-mixed populations. • The relationship between equilibria in finite and infinite well-mixed populations is discussed. • The dynamical equation of the double threshold game in structured populations is derived. • Structure populations to some extent facilitate cooperation compared with well-mixed populations. [ABSTRACT FROM AUTHOR]

The emergence and mechanism of cooperation in social dilemmas have always been fundamental issues in evolutionary game theory. In this paper, we study the snowdrift game, in which individuals in a stronger position can gain additional benefits in cooperation with weaker individuals due to differences in status. Meanwhile, innocuous-type strong individuals will not harm their partners' interests, while harmful-type ones will. In a mixed population, the strong individuals in these two asymmetric snowdrift games are more inclined to cooperate, but the weaker ones are more willing to choose defection. The average cooperation frequency is not lower than in symmetric populations. In structured populations, on the other hand, asymmetry promotes the formation of a configuration with a cooperator cluster with a core of strong cooperators, thereby promoting cooperation among individuals. However, only within a small range of parameters the frequency of cooperation will be slightly reduced. Harmful-type strong individuals can be more conducive to promoting cooperation than innocuous-type ones in some cases. The existence of harmful and strong individuals in the snowdrift game further helps to solve the social loafing effect. • Strong individuals are further divided into innocuous and harmful types. • The complex interactions include symmetry and asymmetry. • The asymmetry and harmful strong agents can increase the frequency of cooperation. • Harmful strong individuals can be more conducive to promoting cooperation. [ABSTRACT FROM AUTHOR]

The emergence and mechanism of cooperation in social dilemmas have always been fundamental issues in evolutionary game theory. In this paper, we study the snowdrift game, in which individuals in a stronger position can gain additional benefits in cooperation with weaker individuals due to differences in status. Meanwhile, innocuous-type strong individuals will not harm their partners' interests, while harmful-type ones will. In a mixed population, the strong individuals in these two asymmetric snowdrift games are more inclined to cooperate, but the weaker ones are more willing to choose defection. The average cooperation frequency is not lower than in symmetric populations. In structured populations, on the other hand, asymmetry promotes the formation of a configuration with a cooperator cluster with a core of strong cooperators, thereby promoting cooperation among individuals. However, only within a small range of parameters the frequency of cooperation will be slightly reduced. Harmful-type strong individuals can be more conducive to promoting cooperation than innocuous-type ones in some cases. The existence of harmful and strong individuals in the snowdrift game further helps to solve the social loafing effect. • Strong individuals are further divided into innocuous and harmful types. • The complex interactions include symmetry and asymmetry. • The asymmetry and harmful strong agents can increase the frequency of cooperation. • Harmful strong individuals can be more conducive to promoting cooperation. [ABSTRACT FROM AUTHOR]

Over the past two decades, it has been of great concern to solve the puzzle of social dilemmas in spatial public goods games. It has been demonstrated that the introduction of memory effects can effectively promote cooperative emergence to some extent. In this paper, we focus on the impact of scale-free and high aggregation properties on the public goods game of memory heterogeneous groups. Here, we propose an optimal strategy selection mechanism based on long-term historical payoffs. In our model, a memory loss function ω is introduced to characterize the memory length of players, and accordingly, pairs determine the optimal strategy by comparing historical gains for the next game cycle. Experiments conducted on scale-free networks and small world networks show that the strategy selection mechanism based on long-term payoff can keep the proportion of cooperators at a high level. In addition, this study demonstrates that the heterogeneity of memory length in the network promotes the enhancement of network reciprocity and robustness, which is beneficial to further reveal the mechanism of cooperative behaviour emergence in complex networks. • A strategy updating mechanism based on weighted long-term payoffs is proposed. • The mechanism promotes cooperation in scale-free and small-world networks. • The propensity to cooperate is related to the components of various memory lengths. • Memory heterogeneity benefits the strength and robustness of network reciprocity. [ABSTRACT FROM AUTHOR]

The governance of common-pool resources has vital importance for sustainability. However, in the realistic management systems of common-pool resources, the institutions do not necessarily execute the management policies completely, which will induce that the real implementation intensity is uncertain. In this paper, we consider a feedback-evolving game model with the inspection for investigating the management of renewable resource and assume that there exists the implementation uncertainty of inspection. Furthermore, we use the nonlinear model reference adaptive control approach to handle this uncertainty. We accordingly design a protocol, which is an update law of adjusting the institutional inspection intensity. We obtain a sufficient condition under which the update law can drive the actual system to reach the expected outcome. In addition, we provide several numerical examples, which can confirm our theoretical results. Our work presents a novel approach to address the implementation uncertainty in the feedback-evolving games and thus our results can be helpful for effectively managing the common-pool resources in the human social systems. • A powerful approach is presented to address the implementation uncertainty in the feedback-evolving games. • The protocol can drive the feedback-evolving game system with uncertainty to reach the expected outcome. • Our results can be helpful for effectively managing the common-pool resources in the human social systems. [ABSTRACT FROM AUTHOR]

• A nonlinear duopoly Stackelberg model of competition on output between bounded rational players is investigated. • For the duopoly Stackelberg model, the time evolution with marginal costs is analyzed. • Complex dynamic behaviors would occur by varying the values of some main parameters. • Appropriate controlling parameter can be chosen to force the chaotic system back to stability. In this paper, the complex dynamics of a duopoly game with bounded rational players are investigated. The model of a dynamic production game is formulated in yield decision making process. A nonlinear Stackelberg system which describes the time evolution with marginal costs is analyzed and the stability situations of Nash equilibrium points are studied. Numerical simulations show a series of chaotic behaviors. The results demonstrate that complex dynamics of the game can be showed by simulating. As for the chaos emerged, effective method has been applied to force it back to stability. [ABSTRACT FROM AUTHOR]

An interest coalition of sharing benefits and risks, such as cross shareholding between companies, allows them to transfer risks in a competitive business world. In a public goods game, cooperators are at the risk of being exploited by defectors. This paper studies whether such risk-transfer mechanism can induce cooperative behaviors in social dilemmas. We model a public goods game with coalition mechanism in a structured population. The players are categorized by whether they cooperate as well as whether they are willing to form coalitions. Those who are willing (unwilling) to form coalitions with others are called coalitional (traditional) individuals. By exploring the phase transitions of systems, the spatial dynamics of some phases and the evolution of characteristic spatial distributions of strategies, we study the effect of this mechanism on cooperation. The results show that the positive (negative) impact of such interest coalitions on the competitiveness of cooperators (defectors) can be improved as the closeness of interest relationship within coalitions increases. However, this does not mean that a closer coalition can absolutely increase the overall level of cooperation in a more complex four-strategy system. This is related to the transformation from CCs (coalitional cooperators) to TDs (traditional defectors) due to CCs' breaking of the encirclement formed by CDs (coalitional defectors) at a low synergy coefficient, as well as the invasion of TCs (traditional cooperators) to CCs at the boundary separating CCs, TCs and TDs at a high synergy coefficient. [ABSTRACT FROM AUTHOR]

Humans try to escape from their mundane lives and look for different experiences. Based on this assumption and story, this paper considers asynchronous public goods games on coevolving networks driven by payoff difference. Starting from a regular square lattice, agents disconnect from neighbors who have similar payoff, and they connect to new agents with different payoff. We measure network cohesion by the clustering coefficient. The results demonstrate multiple stages of the system. There are two stages where cooperation sustains. One is convex, and another is concave. When there is a shift from the defective stage to a cooperative one, the system generates a strong network cohesion facilitating cooperation to begin emerging. Near the tipping point of the two cooperative stages, the system strengthens the network cohesion to promote the stage transition. The time-dependent networks weaken the possibility of counteracting defection by forming cooperative alliances, which happens in the classic public goods game. However, the disconnection from similar payoff and the connection to different payoff can be matched appropriately to sustain cooperation best. [ABSTRACT FROM AUTHOR]

In recent years, the division of labor game has received widespread attention, however, the time delay in payoffs has been ignored. Hence, in this paper, we consider that there is a time delay for the player to gain the payoffs in the game, and the delay in payoffs leads to a Hopf bifurcation. When the time delay is greater than the critical time delay, the replicator dynamics oscillates near the equilibrium point, the critical time delay is determined by the cost difference between the two tasks and the cooperation benefits between the two players. We obtain the expression of the critical time delay by applying the characteristic equation analysis method, and clearly analyze various cases through observation and numerical simulation. With the increase of time delays, the dynamic system shows a transition from asymptotic stability to oscillation near equilibrium. [ABSTRACT FROM AUTHOR]

• We introduce a model to study the evolution of inequality in the framework of snowdrift game. • Inequality is generally stronger in social communities with fewer average interactions among the individuals, and weaker in the case of dense interactions. • Introducing incentives and punishments makes it harder for cooperators to get a fair share of the profits. • The simulation results confirm such theoretical analysis, in both the infinite unstructured populations and the finite structured populations. Social inequality takes many forms, but its most basic form is that individuals give the least and get the most in return. In this paper, we introduce an extended model based on the snowdrift game model, involving the concept of inequality (unequal distribution of benefit). We calculated the critical threshold for the benefits distribution under the dominant cooperative strategy through numerical simulation and theoretical analysis. We illustrate the similarities and differences in the evolution of cooperation with and without incentives and punishments. Both theoretical and simulation results show that within the limited resource range, the larger the resource is, the larger the critical proportion of benefits that defectors can exploit, whether in unstructured or structured population. We also show that the inequality is stronger in social structures with sparse connections and weaker in those with dense connections. Moreover, we revealed that introducing incentives and punishments makes it harder for cooperators to get a fair share of the profits. [ABSTRACT FROM AUTHOR]

• A public goods game of two cooperative strategies with different quantities of input cost is proposed. • Two scenarios where different strategies are independent and interdependent are discussed. • If the two strategies are independent, the quasi-defective cost should be reduced to promote the quasi-cooperation. • When the two strategies are interdependent, the indispensability of the quasi-defection sometimes brings to the system more quasi-cooperative agents than when the two strategies are independent. This paper proposes a public goods game (PGG) of two cooperative strategies with different quantities of input cost: the strategy with a higher quantity of input cost is labeled as quasi-cooperation, while that with lower input cost is labeled as quasi-defection. In an ideal classless society, the two strategies are independent, as in the classical PGG; however, in a more realistic class society, they are interdependent. On this basis, two models (An-PGG and In-PGG) are built to respectively describe the two class scenarios. The results for the An-PGG demonstrate that, to promote the quasi-cooperation, the quasi-defective cost should be reduced. The results for the In-PGG indicate that, the closer the two types of input are, the smaller is the difference between the proportions of the two strategies in the system, hence the more effective are the inputs and the greater is the economic benefit. The indispensability of the quasi-defection in an interdependence mechanism sometimes brings to the system more quasi-cooperative agents. The class system is more advantageous than the classless system when the synergy factor and the quasi-defective degree are too small. [ABSTRACT FROM AUTHOR]

• Smaller formats likely lead to increases in the tactical behaviors associated with penetration and defensive delays. • Larger formats lead to an increase in the frequency of collective behaviors associated with attacking and defensive unity. • Larger pitches are associated with a greater variability of movements during SSGs. • Older players tend to explore the width of the pitch more and disperse themselves more than younger players during SSGs. The present systematic review aims to describe evidence about the effects of different small-sided soccer games (SSGs) on tactical behaviors and collective dynamics. This study presents a systematic review, organizes the acute effects of the most common task conditions, and describes the common methodologies used in previous studies. Following the preferred reporting items for systematic reviews and meta-analyses (PRISMA) guidelines, this systematic review searched for studies on Web of Science, PubMed, and SPORTDiscus. The search returned 95 papers. After screening the records against set criteria, 34 articles were fully reviewed. The main topics related to tactical behaviors and collective dynamics were (1) the effects of different formats; (2) the effects of different pitch sizes and configurations; (3) the effects of tasks adjustments; (4) the effects of age and competitive and expertise levels; and (5) multidimensional effects. In summary, and among other evidence, this systematic review revealed that smaller formats likely lead to increases in the tactical behaviors associated with penetration and defensive delays, while larger formats may lead to an increase in the frequency of collective behaviors associated with attacking and defensive unity. Moreover, using floaters may increases the effective playing space, and considerable numerical imbalances contribute to a possible more stable defensive dynamic. Finally, the few studies that tested such a hypothesis revealed greater variability of movements in larger pitches comparing to smaller ones. [ABSTRACT FROM AUTHOR]

• An ultimatum game model with similarity between players is proposed. • The evolution of fairness under such model and the underlying reason are studied. • A toy model for quantitatively analysis is given. • Effect of different distribution of similarity on our result is also studied. The ultimatum game (UG) is a useful game model for investigating the evolution of fairness. In this paper, considering the similarity between individuals, we introduce a similarity parameter into the spatial UG and focus on the evolution of the average offer and acceptance threshold. Under this mechanism, individuals can be either more generous or stingier to those who they are similar to. The simulation result shows that the fairness of the system decreases when the strategy is affected by the similarity between players. The greater the influence of similarity, the more fairness is decreased. Equal treatment, hence, is the best way to obtain fairness. Our results may provide some critical insights into the effect of similarity and favoritism on fairness among people. [ABSTRACT FROM AUTHOR]