Game theory of pandemic control: Can collaborative vaccine allocation strategies lead to better outcomes?

Abstract

Introduction

Increasing vaccine uptake is an effective way to prevent COVID-19 infection in individual countries after the relaxation of social distancing. However, under the limited vaccine resources, vaccine inequality between high- and low-income countries can also produce more infection and cost. Reducing such inequality relies on a more cooperative (unselfish) strategy, such as vaccine donation from high-income countries, which may initially increase their cost. The study aims to analyze the impact of vaccine inequality on cooperative decision-making between two populations. The results provide important insights on achieving global control of infectious disease outbreaks.

Material and Methods

We developed a transmission model incorporating virus evolution under different vaccine-induced natural selection and the migration to allow a long-term repeated outbreak. Vaccine allocation strategies were implemented between two populations the high vaccine coverage population (HC) and the low coverage population (LC). A game theory approach was employed to explore whether pursuing minimum cost for both sides (cooperative strategy) or itself (non-cooperative strategy) for each population. We estimated the effect of each strategy on the total cost (i.e. the sum of vaccine, hospitalization and labor costs). The Nash equilibrium was obtained by minimizing their own cost for individual countries under different vaccine inequality scenarios (from low to high inequality).

Results

Under low inequality, both populations achieved the same optimal cost with both cooperative and non-cooperative strategies. Under medium or high inequality, both populations reached a Nash equilibrium with non-cooperative strategies and could not reach global optimum. When inequality was high, HC tended towards vaccine donation even though non-cooperative strategies were adopted.

Discussion

When inequality is high, although cooperative decisions can obtain global optimal outcomes, populations tend to choose non-cooperative decisions, increasing extra global costs. The results suggested that effective global control of outbreaks is difficult but vaccine donation can be a win-win strategy.