A Game Theoretic Analysis of Competition Between Vaccine and Drug Companies during Disease Contraction and Recovery (original) (raw)
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Humanities and Social Sciences Communications
Disease contraction and recovery depend on complex interaction between persons potentially contracting and recovering from the disease, the pharmaceutical industry potentially developing drugs, and donors potentially subsidizing drug development and drug purchases. Instead of analyzing each of these three kinds of players separately, assuming the behavior of the other two kinds of players to be given, this article analyzes the three kinds of players holistically and how they mutually interact and react to each other. A five-period game between N persons and a pharmaceutical company is developed. Each person chooses safe or risky behavior, and whether or not to buy a drug. The objectives are to determine which strategies the N persons and the pharmaceutical company choose depending on the model parameters. The pharmaceutical company develops the drug if sufficiently many persons contract the disease and buy the drug. A donor chooses parametrically whether to subsidize drug developmen...
Game theoretic modelling of infectious disease dynamics and intervention methods: a review
Journal of Biological Dynamics, 2020
We review research papers which use game theory to model the decision making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. We show that the literature can be classified based on (i) type of population modelling (compartmental or network-based), (ii) frequency of the game (non-iterative or iterative), and (iii) type of strategy adoption (self-evaluation or imitation). We highlight that the choice of model depends on many factors such as the type of immunity the disease confers, the type of immunity the vaccine confers, and size of population and level of mixing therein. We show that while early studies used compartmental modelling with self-evaluation based strategy adoption, the recent trend is to use network-based modelling with imitation-based strategy adoption. Our review indicates that game theory continues to be an effective tool to model intervention (vaccination or social distancing) decision-making by individuals.
Game Theory : A Case of Infectious Diseases
International Journal of Scientific Research in Computer Science, Engineering and Information Technology, 2020
Game theory is a mathematical model which deals with interactions between various entities by analyzing the strategies and choices. In today’s world, Game Theory is being extensively used in fields like computer science, economics, sociology, political science, and so on, due to its versatile nature and applications in numerous conflicts and problems. The application of game theory has been extended to real life problems also due to its versatility and robustness. In this research, various game theory methodologies applied during pandemic was reviewed. Various aspects of these methodologies were highlighted such as methods applied, description, expected result and limitation. This research will act as a reliable and efficient way of understanding the concept of game theory and its application in combating infectious diseases, analyze and eventually understand different strategic scenarios. The main importance of game theory is to formulate the alternative strategy to compete with one another and in the same sense it is an essential tool for decision making process according to fluctuations in relevant contents. These reviewed methodologies would be further categorized into prevent, control or both based on the application they favour most.
Journal of Biological Dynamics, 2020
We review research studies which use game theory to model the decision-making of individuals during an epidemic, attempting to classify the literature and identify the emerging trends in this field. The literature is classified based on (i) type of population modelling (classical or network-based), (ii) frequency of the game (non-repeated or repeated), and (iii) type of strategy adoption (self-learning or imitation). The choice of model is shown to depend on many factors such as the immunity to the disease, the strength of immunity conferred by the vaccine, the size of population and the level of mixing therein. We highlight that while early studies used classical compartmental modelling with self-learning games, in recent years, there is a substantial growth of network-based modelling with imitation games. The review indicates that game theory continues to be an effective tool to model decision-making by individuals with respect to intervention (vaccination or social distancing).
Interplay between cost and effectiveness in influenza vaccine uptake: a vaccination game approach
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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 proc...
Health Economics Review, 2021
Background The article develops an eight-period game between N persons and a pharmaceutical company. The choices of a donor and Nature are parametric. Methods Persons choose between safe and risky behavior, and whether or not to buy drugs. The pharmaceutical company chooses whether or not to develop drugs. The donor chooses parametrically whether to subsidize drug purchases and drug developments. Nature chooses disease contraction, recovery, death, and virus mutation. The game is solved with backward induction. Results The conditions are specified for each of seven outcomes ranging from safe behavior to risky behavior and buying no or one or both drugs. The seven outcomes distribute themselves across three outcomes for the pharmaceutical company, which are to develop no drugs, develop one drug, and develop two drugs if the virus mutates. For these three outcomes the donor’s expected utility is specified. Conclusion HIV/AIDS data is used to present a procedure for parameter estimatio...
“Wait and see” vaccinating behaviour during a pandemic: A game theoretic analysis
Vaccine, 2011
During the 2009 H1N1 pandemic, many individuals did not seek vaccination immediately but rather decided to "wait and see" until further information was available on vaccination costs. This behaviour implies two sources of strategic interaction: as more individuals become vaccinated, both the perceived vaccination cost and the probability that susceptible individuals become infected decline. Here we analyze the outcome of these two strategic interactions by combining game theory with a disease transmission model during an outbreak of a novel influenza strain. The model exhibits a "wait and see" Nash equilibrium strategy, with vaccine delayers relying on herd immunity and vaccine safety information generated by early vaccinators. This strategic behaviour causes the timing of the epidemic peak to be strongly conserved across a broad range of plausible transmission rates, in contrast to models without such adaptive behaviour. The model exhibits not only feedback mechanisms but also a feed-forward mechanism: a high initial perceived vaccination cost perpetuates high perceived vaccine costs (and lower vaccine coverage) throughout the remainder of the outbreak. This suggests that any effect of risk communication at the start of a pandemic outbreak will be amplified compared to the same amount of risk communication effort distributed throughout the outbreak.
Optimal Control of a Vaccinating Game toward Increasing Overall Coverage
Journal of Applied Mathematics and Physics
In this paper, we study an asymmetric game that characterizes the intentions of players to adopt a vaccine. The game describes a decision-making process of two players differentiated by income level and perceived treatment cost, who consider a vaccination against an infectious disease. The process is a noncooperative game since their vaccination decision has a direct impact on vaccine coverage in the population. We introduce a replicator dynamics (RD) to investigate the players' optimal strategy selections over time. The dynamics reveal the long-term stability of the unique Nash-Pareto equilibrium strategy of this game, which is an extension of the notion of an evolutionarily stable strategy pair for asymmetric games. This Nash-Pareto pair is dependent on perceived costs to each player type, on perceived loss upon getting infected, and on the probability of getting infected from an infected person. Last but not least, we introduce a payoff parameter that plays the role of cost-incentive towards vaccination. We use an optimal control problem associated with the RD system to show that the Nash-Pareto pair can be controlled to evolve towards vaccination strategies that lead to a higher overall expected vaccine coverage.
Using Game Theory to Examine Incentives in Influenza Vaccination Behavior
Psychological Science, 2012
The social good often depends on the altruistic behavior of specific individuals. For example, epidemiological studies of influenza indicate that elderly individuals, who face the highest mortality risk, are best protected by vaccination of young individuals, who contribute most to disease transmission. To examine the conditions under which young people would get vaccinated to protect elderly people, we conducted a game-theory experiment that mirrored real-world influenza transmission, with "young" players contributing more than "elderly" players to herd immunity. Participants could spend points to get vaccinated and reduce the risk of influenza. When players were paid according to individual point totals, more elderly than young players got vaccinated, a finding consistent with the Nash equilibrium predicting self-interested behavior. When players were paid according to group point totals, however, more young than elderly players got vaccinated-a finding consistent with the utilitarian equilibrium predicting group-optimal behavior-which resulted in higher point totals than when players were paid for their individual totals. Thus, payout structure affected whether individuals got vaccinated for self-interest or group benefit.
Price and Treatment Decisions in Epidemics: A Differential Game Approach
Mathematics
We consider a pharmaceutical company that sells a drug that is useful in the treatment of an infectious disease. A public authority buys the drug to heal at least a portion of the infected population. The authority has an overall budget for all health care costs in the country and can only allocate a (small) part of the budget to the purchase of the drug. The government chooses the amount of drug to be purchased in order to minimize both the number of infectious people and the perceived cost of the operation along a given time horizon. This cost can be modeled through a linear or quadratic function of the monetary cost (as generally happens in the literature) or through a specific function (blow-up) that makes the budget constraint endogenous. The pharmaceutical company chooses the price of the drug in order to maximize its profit and knowing the budget constraints of the buyer. The resulting differential game is studied by supposing the simplest possible dynamics for the population...