Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative-unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure.

In this paper, we study the problem of cost optimisation of individual-based institutional incentives (reward, punishment, and hybrid) for guaranteeing a certain minimal level of cooperative behaviour in a well-mixed, finite population. In this scheme, the individuals in the population interact via cooperation dilemmas (Donation Game or Public Goods Game) in which institutional reward is carried out only if cooperation is not abundant enough (i.e., the number of cooperators is below a threshold 1 ≤ t ≤ N - 1 , where N is the population size); and similarly, institutional punishment is carried out only when defection is too abundant. We study analytically the cases t = 1 for the reward incentive under the small mutation limit assumption and two different initial states, showing that the cost function is always non-decreasing. We derive the neutral drift and strong selection limits when the intensity of selection tends to zero and infinity, respectively. We numerically investigate the problem for other values of t and for population dynamics with arbitrary mutation rates.

A novel approach rooted in co-evolutionary game theory has been introduced to investigate how the interaction between human decision-making and the dynamics of the epidemic environment can shape vaccine acceptance during disease outbreaks. This innovative framework combines two key game concepts: the cooperation-defection game and the cost-benefit vaccination game. By doing so, it enables us to delve into the various factors that influence the success of a vaccination campaign amid an outbreak. Within this framework, individuals engage in a thorough evaluation of the risks, benefits and incentives associated with either cooperating by getting vaccinated or defecting by refusing the vaccine. Additionally, it involves a careful analysis of the costs and benefits linked to vaccine acceptance. The outcomes of this study stress the importance of two main factors: the effectiveness of the vaccine and the prevalence of a cooperative culture within society. This insight into the strategic interactions between individuals and their decisions about vaccination holds significant implications for public health policymakers. It equips to boost vaccination coverage and address vaccine hesitancy within society ultimately contributing to better public health outcomes during epidemic outbreaks.

This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game\'s playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes.

This work explored the changes in production decision-making trends of Chinese steel enterprises under the influence of the carbon border adjustment mechanism. First, using evolutionary game theory, the interactive mechanism of complex production strategies among steel enterprises considering the carbon border adjustment mechanism was studied, including the impact of government subsidy coefficients, additional profits and carbon tax prices on enterprise decision-making. Second, the influence of key parameters on the dynamic evolutionary process was analysed. On this basis, the empirical simulation method was used to verify the game model and the main conclusions. Finally, the sensitivity analysis of the selected parameters was determined using Matlab software. The results showed that additional profits from green investment, government subsidy coefficients, input-output values and carbon tax prices had a higher impact on the evolution of enterprise production strategies. The results of this study provide a decision-making basis for the selection of future production methods for steel enterprises.

Humans update their social behavior in response to past experiences and changing environments. Behavioral decisions are further complicated by uncertainty in the outcome of social interactions. Faced with uncertainty, some individuals exhibit risk aversion while others seek risk. Attitudes toward risk may depend on socioeconomic status; and individuals may update their risk preferences over time, which will feedback on their social behavior. Here, we study how uncertainty and risk preferences shape the evolution of social behaviors. We extend the game-theoretic framework for behavioral evolution to incorporate uncertainty about payoffs and variation in how individuals respond to this uncertainty. We find that different attitudes toward risk can substantially alter behavior and long-term outcomes, as individuals seek to optimize their rewards from social interactions. In a standard setting without risk, for example, defection always overtakes a well-mixed population engaged in the classic Prisoner\'s Dilemma, whereas risk aversion can reverse the direction of evolution, promoting cooperation over defection. When individuals update their risk preferences along with their strategic behaviors, a population can oscillate between periods dominated by risk-averse cooperators and periods of risk-seeking defectors. Our analysis provides a systematic account of how risk preferences modulate, and even coevolve with, behavior in an uncertain social world.

Plants emit biogenic volatile organic compounds (BVOCs) as signaling molecules, playing a crucial role in inducing resistance against herbivores. Neighboring plants that eavesdrop on BVOC signals can also increase defenses against herbivores or alter growth patterns to respond to potential risks of herbivore damage. Despite the significance of BVOC emissions, the evolutionary rationales behind their release and the factors contributing to the diversity in such emissions remain poorly understood. To unravel the conditions for the evolution of BVOC emission, we developed a spatially explicit model that formalizes the evolutionary dynamics of BVOC emission and non-emission strategies. Our model considered two effects of BVOC signaling that impact the fitness of plants: intra-individual communication, which mitigates herbivore damage through the plant\'s own BVOC signaling incurring emission costs, and inter-individual communication, which alters the influence of herbivory based on BVOC signals from other individuals without incurring emission costs. Employing two mathematical models-the lattice model and the random distribution model-we investigated how intra-individual communication, inter-individual communication, and spatial structure influenced the evolution of BVOC emission strategies. Our analysis revealed that the increase in intra-individual communication promotes the evolution of the BVOC emission strategy. In contrast, the increase in inter-individual communication effect favors cheaters who benefit from the BVOCs released from neighboring plants without bearing the costs associated with BVOC emission. Our analysis also demonstrated that the narrower the spatial scale of BVOC signaling, the higher the likelihood of BVOC evolution. This research sheds light on the intricate dynamics governing the evolution of BVOC emissions and their implications for plant-plant communication.

Non-pharmaceutical personal protective (NPP) measures such as face masks use, and hand and respiratory hygiene can be effective measures for mitigating the spread of aerosol/airborne diseases, such as COVID-19, in the absence of vaccination or treatment. However, the usage of such measures is constrained by their inherent perceived cost and effectiveness for reducing transmission risk. To understand the complex interaction of disease dynamics and individuals decision whether to adopt NPP or not, we incorporate evolutionary game theory into an epidemic model such as COVID-19. To compare how self-interested NPP use differs from social optimum, we also investigated optional control from a central planner\'s perspective. We use Pontryagin\'s maximum principle to identify the population-level NPP uptake that minimizes disease incidence by incurring the minimum costs. The evolutionary behavior model shows that NPP uptake increases at lower perceived costs of NPP, higher transmission risk, shorter duration of NPP use, higher effectiveness of NPP, and shorter duration of disease-induced immunity. Though social optimum NPP usage is generally more effective in reducing disease incidence than self-interested usage, our analysis identifies conditions under which both strategies get closer. Our model provides new insights for public health in mitigating a disease outbreak through NPP.

Evolutionary epidemiology models have substantially impacted the study of various infections and prevention methods in the biology field. These models are called Susceptible, Lockdown, Vaccinated, Infected, and Recovered (SLVIR) epidemic dynamics. We explore how human behavior, particularly in the context of disease transmission, is influenced by two intervention strategies: vaccination and lockdown, both of which are grounded in the principles of evolutionary game theory (EGT). This comprehensive study using evolutionary game theory delves into the dynamics of epidemics, explicitly focusing on the transition rate from susceptibility to immunity and susceptibility to lockdown measures. Our research involves a thorough analysis of the structural aspects of the SLVIR epidemic model, which delineates disease-free equilibria to ensure stability in the system. Our investigation supports the notion that implementing lockdown measures effectively reduces the required level of vaccinations to curtail the prevalence of new infections. Furthermore, it highlights that combining both strategies is particularly potent when an epidemic spreads rapidly. In regions where the disease spreads comparatively more, our research demonstrates that lockdown measures are more effective in reducing the spread of the disease than relying solely on vaccines. Through significant numerical simulations, our research illustrates that integrating lockdown measures and efficient vaccination strategies can indirectly lower the risk of infection within the population, provided they are both dependable and affordable. The outcomes reveal a nuanced and beneficial scenario where we examine the interplay between the evolution of vaccination strategies and lockdown measures, assessing their coexistence through indicators of average social payoff.

In contemporary society, the effective utilization of public resources remains a subject of significant concern. A common issue arises from defectors seeking to obtain an excessive share of these resources for personal gain, potentially leading to resource depletion. To mitigate this tragedy and ensure sustainable development of resources, implementing mechanisms to either reward those who adhere to distribution rules or penalize those who do not, appears advantageous. We introduce two models: a tax-reward model and a tax-punishment model, to address this issue. Our analysis reveals that in the tax-reward model, the evolutionary trajectory of the system is influenced not only by the tax revenue collected but also by the natural growth rate of the resources. Conversely, the tax-punishment model exhibits distinct characteristics when compared with the tax-reward model, notably the potential for bistability. In such scenarios, the selection of initial conditions is critical, as it can determine the system\'s path. Furthermore, our study identifies instances where the system lacks stable points, exemplified by a limit cycle phenomenon, underscoring the complexity and dynamism inherent in managing public resources using these models.