A Game Theoretic Analysis of Competition Between Vaccine and Drug Companies during Disease Contraction and Recovery

Abstract

Background: Infectious diseases such as COVID-19 and HIV/AIDS are behaviorally challenging for persons, vaccine and drug companies, and donors.

Methods: In 3 linked games in which a disease may or may not be contracted, $N$ persons choose risky or safe behavior (game 1). Two vaccine companies (game 2) and 2 drug companies (game 3) choose whether to develop vaccines and drugs. Each person chooses whether to buy 1 vaccine (if no disease contraction) or 1 drug (if disease contraction). A donor subsidizes vaccine and drug developments and purchases. Nature probabilistically chooses disease contraction, recovery versus death with and without each drug, and whether vaccines and drugs are developed successfully. COVID-19 data are used for parameter estimation.

Results: Each person chooses risky behavior if its utility outweighs safe behavior, accounting for nature's probability of disease contraction which depends on how many are vaccinated. Each person buys a vaccine or drug if the companies produce them and if their utilities (accounting for side effects and virus mutation) outweigh the costs, which may be subsidized by a sponsor.

Discussion: Drug purchases depend on nature's recovery probability exceeding the probability in the absence of a drug. Each company develops and produces a vaccine or drug if nature's probability of successful development is high, if sufficiently many persons buy the vaccine or drug at a sales price that sufficiently exceeds the production price, and if the donor sponsors.

Conclusion: Accounting for all players' interlinked decisions allowing 14 outcomes, which is challenging without a game theoretic analysis, the donor maximizes all persons' expected utilities at the societal level to adjust how persons' purchases and the companies' development and production are subsidized.

Highlights: A game theoretic approach can help explain the production decisions of vaccine and drug companies, and the decisions of persons and a donor, impacted by Nature.In 3 linked games, N persons choose risky behavior if its utility outweighs safe behavior.Vaccine and drug companies develop vaccines and drugs sponsored by a donor if profitable, allowing 14 outcomes.

Keywords: COVID-19; death; disease contraction; donors; drug companies; drug development; game theory; patients; recovery; safe versus risky behavior; subsidies; vaccine companies; vaccine development.