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.

Figure 1

Vaccine company $k$ ’s and drug company $j$ ’s timeline of research and development, production, bringing its product to the market, and sale, $j,k=1,2$ . Decision nodes by each company are squares.

Figure 2

Two-period game between person i, i = 1, . . ., N, in period 1 and nature in period 2 on safe versus risky behavior and whether or not to contract the disease. The filled square decision node is for person i. The filled circle chance node is for nature.

Figure 3

Two-period game between vaccine companies 1 and 2, the donor, and the part of N persons who have not contracted the disease. The framed square decision node (unfilled square with 2 demarcating lines along each side) is for the vaccine companies and the donor. The filled square decision nodes are for person i.

Figure 4

Three-period game between drug companies 1 and 2, the donor, the part of the persons N who have contracted the disease, and nature. The unfilled square decision node is for the drug companies and the donor. The filled square decision nodes are for person i. The filled circle chance i nodes are for nature.

Figure 5

N persons dispersed across 7 groups.