Game-Theoretic Approach to Fair Allocation of Vaccines
In the paper “A game theoretic approach identifies conditions that foster vaccine-rich to vaccine-poor country donation of surplus vaccines” published by Commun Med (Lond), the authors propose a vaccine donation game to combat the issue of unequal allocation of vaccines. Given certain conditions, this model builds upon the coordination efforts that can be made by policymakers to increase the willingness of self-interested vaccine-rich to make vaccine donations – out of their surplus vaccine doses – to vaccine-poor countries.
In game theory, a game can be defined when the following elements are specified: players of the game, a set of actions available to each player, and payoffs of each outcome. Using these elements, a pictorial representation of the game can be constructed in the form of a payoff matrix. For the vaccine donation game:
- Players: vaccine-rich countries
- Assumptions:
- each player has three times the amount of vaccine doses they need to vaccinate their country’s population implying that they have two extra doses per capita
- each player will choose to donate only if their population is fully vaccinated
- each vaccine-rich country has two self-interested motivations to donate that include facilitating international travel and trade, and reducing the risk of new variants of concern (VOCs)
- vaccine-rich countries are rational, self-interested, the same-size, and risk-neutral
- emergence of variants is independent of one another
- the cost of each subsequent outbreak is the same as that of the previous
- Strategies: 0, 1, or 2 doses of vaccine (per capita) to donate to vaccine-poor countries
As suggested by the authors, the payoffs of this game were determined by three factors:
- “the fraction of the global unvaccinated population potentially covered if all vaccine-rich countries fully donate their surplus;
- the baseline expected annual rate of VOCs;
- the fraction of the total cost of a new VOC outbreak that is unavoidable despite having surplus doses”
The model uses the concepts of Nash equilibrium and Self-Enforcing International Agreement to find an optimal allocation of vaccines that maximizes societal welfare and minimizes the cost of a virus outbreak. A Nash equilibrium outcome is one in which each player’s strategy is a best-response to the other player’s strategy, such that none of the players wish to deviate from this outcome. A Self-Enforcing International Agreement is an outcome in which it is in the player’s self-interest to abide by the strategies that lead to this outcome.
The two major findings of this study suggest that vaccine-rich countries would fully donate if the fraction of the global vaccinated population that could be vaccinated by donations is high and storing additional doses of vaccine does not reduce the cost of a potential virus outbreak, and donations do not prove to be a completely stable strategy (even if they are optimal) if the total number of surplus doses are distributed over a large number of vaccine-rich countries.
Hence, I believe that this model would work under the conditions specified by the authors, however, establishing such conditions would be unrealistic. This model can be considered as a simple model which could be manipulated to adapt to real-world conditions.
Citations: Lampert A, Sulitzeanu-Kenan R, Vanhuysse P, Tepe M. A game theoretic approach identifies conditions that foster vaccine-rich to vaccine-poor country donation of surplus vaccines. Commun Med (Lond). 2022 Aug 23;2:107. doi: 10.1038/s43856-022-00173-w. PMID: 36004278; PMCID: PMC9395896.
Source link: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9395896/