Effects of the quarantine on the individuals' risk of Covid-19 infection: Game theoretical approach

Abstract

In this study, we analyze the general or self-quarantine effects to the spread of the first wave of Covid-19 pandemic in the view of the game-theoretical approach. As in some other applications of game theory in different aspects of the literature, we focus on only the application of game theory to present the effects of quarantine during the three different stages -the start, the spread, the end- of the pandemic. We first choose three countries such as South Korea for self-quarantine, Italy, and Turkey for general quarantine during the analysis of the different stages of the spread. Then, we present a formula that will be an important tool for the creation of the payoff matrices and give the general procedure for the creation of the payoff matrix for each stage of the pandemic process. After that, we generate the payoff bimatrix for each stage of the pandemic by using the average of the daily diagnosis number/number of tests for each country. Moreover, we try to find the optimal strategy of the game. Additionally, to determine the necessity of the continuity of the quarantine, we use the repeated game approach in our analysis, as well. Therefore, we convert the game only for the spread stage to the repeated game for each country. Finally, we obtain the Nash equilibrium of all games for each level of the pandemic. The results show that the quarantine has important effects to be infected or not, and the spread of the pandemic at each level. In addition to these analysis results, we compare the death rates of the considered countries and show that the results are almost parallel to that are obtained for the quarantine requirement of each country by game-theoretical approaches.