What do corruption, resource overexploitation, climate inaction, vaccine hesitancy, traffic congestion, and even cancer metastasis have in common? All these socioeconomic and sociobiological phenomena are known as social dilemmas because they embody in one form or another a fundamental conflict between immediate self-interest and long-term collective interest. A shortcut to the resolution of social dilemmas has thus far been reserved solely for highly stylised cases reducible to dyadic games (e.g., the Prisoner’s Dilemma), whose nature and outcome coalesce in the concept of dilemma strength. We show that a social efficiency deficit, measuring an actor’s potential gain in utility or fitness by switching from an evolutionary equilibrium to a social optimum, generalises dilemma strength irrespective of the underlying social dilemma’s complexity. We progressively build from the simplicity of dyadic games for which the social efficiency deficit and dilemma strength are mathematical duals, to the complexity of carcinogenesis and a vaccination dilemma for which only the social efficiency deficit is numerically calculable. The results send a clear message to policymakers to enact measures that increase the social efficiency deficit until the strain between what is and what could be incentivises society to switch to a more desirable state.

Pre-emptive vaccination is regarded as one of the most protective measures to control influenza outbreak. There are mainly two types of influenza viruses—influenza A and B with several subtypes—that are commonly found to circulate among humans. The traditional trivalent (TIV) flu vaccine targets two strains of influenza A and one strain of influenza B. The quadrivalent (QIV) vaccine targets one extra B virus strain that ensures better protection against influenza; however, the use of QIV vaccine can be costly, hence impose an extra financial burden to society. This scenario might create a dilemma in choosing vaccine types at the individual level. This article endeavours to explain such a dilemma through the framework of a vaccination game, where individuals can opt for one of the three options: choose either of QIV or TIV vaccine or none. Our approach presumes a mean-field framework of a vaccination game in an infinite and well-mixed population, entangling the disease spreading process of influenza with the coevolution of two types of vaccination decision-making processes taking place before an epidemic season. We conduct a series of numerical simulations as an attempt to illustrate different scenarios. The framework has been validated by the so-called multi-agent simulation (MAS) approach.

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We propose a mean-field vaccination game framework that combines two distinct processes: the simultaneous spreading of two strains of an influenza-like disease, and the adoption of vaccination based on evolutionary game theory presuming an infinite and well-mixed population. The vaccine is presumed to be imperfect such that it shows better efficacy against the original (resident) strain rather than the new one (mutant). The vaccination-decision takes place at the beginning of an epidemic season and depends upon the vaccine-effectiveness along with the cost. Additionally, we explore a situation if the original strain continuously converts to a new strain through the process of mutation. With the aid of numerical experiments, we explore the impact of vaccinating behavior on a specific strain prevalence. Our results suggest that the emergence of vaccinators can create the possibility of infection-prevalence of the new strain if the vaccine cannot bestow a considerable level of efficiency against that strain. On the other hand, the resident strain can continue to dominate under large-scale vaccine avoidance. Moreover, in the case of continuous mutation, the vaccine efficacy against the new strain plays a pivotal role to control the disease prevalence. We successfully obtain phase diagrams, displaying the infected fraction with each strain, final epidemic size, vaccination coverage, and average social payoff considering two-different strategy-update rules and provide a comprehensive discussion to get an encompassing idea, justifying how the vaccinating behavior can affect the spread of a disease having two strains. Highlights –We build a mean-field vaccination game scheme to analyze the effect of an imperfect vaccine on a two-strain epidemic spreading taking into account individuals’ vaccination behavior. –En masse vaccine avoidance can enhance the possibility of the original strain prevalence. –Propensity for vaccination can create the possibility of infection by the new strain if the vaccine is unable to provide a considerable level of efficiency against that strain.

Vaccinating decisions can be influenced by imitation as well as self-evaluation or aspiration. This work analyses vaccinating behaviours by coupling both imitation and aspiration update rules, adopting an existing set-up of the mean-field vaccination game. We incorporate the imitation mechanism with several variants of the aspiration protocol, encompassing constant and adaptive aspirations. Equations of the combined dynamics have been derived by grouping the population according to (i) vaccinating strategies and (ii) healthy and infected status within each strategy. If aspiration levels are fixed but differentiated by vaccinating strategies, then vaccinators aspiring less than non-vaccinators are found to ameliorate the vaccination coverage, thereby yielding a less infectious state. The adaptive aspirations maintain a positive correlation with the vaccine efficacy while keeping the opposite relation with vaccination cost. When vaccinating strategies, aspirations and update rules are allowed to evolve synchronously, then either the imitation or aspiration process takes over the entire population. If aspiration rules prevail, then vaccinees and non-vaccinees coexist equally (according to (i)) or vaccine uptake follows a non-monotonic trend with the efficacy (according to (ii)). The imitative rule performs better when vaccination is less expensive or cheap, while aspiration updating safeguards the tenacity of vaccinees despite vaccination being expensive.

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